Identifier
Mp00298:
Parking functions
—repeats to leading⟶
Parking functions
Mp00056: Parking functions —to Dyck path⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00056: Parking functions —to Dyck path⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Images
=>
Cc0005;cc-rep-2Cc0005;cc-rep-3
[1]=>[1]=>[1,0]=>[1,0]
[1,1]=>[1,1]=>[1,1,0,0]=>[1,1,0,0]
[1,2]=>[1,2]=>[1,0,1,0]=>[1,0,1,0]
[2,1]=>[2,1]=>[1,0,1,0]=>[1,0,1,0]
[1,1,1]=>[1,1,1]=>[1,1,1,0,0,0]=>[1,1,1,0,0,0]
[1,1,2]=>[1,1,2]=>[1,1,0,1,0,0]=>[1,0,1,1,0,0]
[1,2,1]=>[2,3,1]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]
[2,1,1]=>[2,1,2]=>[1,0,1,1,0,0]=>[1,1,0,1,0,0]
[1,1,3]=>[1,1,3]=>[1,1,0,0,1,0]=>[1,1,0,0,1,0]
[1,3,1]=>[3,1,1]=>[1,1,0,0,1,0]=>[1,1,0,0,1,0]
[3,1,1]=>[1,3,1]=>[1,1,0,0,1,0]=>[1,1,0,0,1,0]
[1,2,2]=>[1,2,1]=>[1,1,0,1,0,0]=>[1,0,1,1,0,0]
[2,1,2]=>[2,1,3]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]
[2,2,1]=>[2,2,1]=>[1,0,1,1,0,0]=>[1,1,0,1,0,0]
[1,2,3]=>[1,2,2]=>[1,0,1,1,0,0]=>[1,1,0,1,0,0]
[1,3,2]=>[3,1,2]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]
[2,1,3]=>[3,2,1]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]
[2,3,1]=>[1,2,3]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]
[3,1,2]=>[1,3,2]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]
[3,2,1]=>[2,1,1]=>[1,1,0,1,0,0]=>[1,0,1,1,0,0]
[1,1,1,1]=>[1,1,1,1]=>[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]
[1,1,1,2]=>[1,1,1,2]=>[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]
[1,1,2,1]=>[2,2,3,1]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[1,2,1,1]=>[2,3,1,2]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,1,1,1]=>[2,1,2,2]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0]
[1,1,1,3]=>[1,1,1,3]=>[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]
[1,1,3,1]=>[1,1,3,4]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[1,3,1,1]=>[1,3,4,1]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[3,1,1,1]=>[1,4,1,1]=>[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[1,1,1,4]=>[1,1,1,4]=>[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[1,1,4,1]=>[1,1,4,3]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[1,4,1,1]=>[1,4,3,1]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[4,1,1,1]=>[1,3,1,1]=>[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]
[1,1,2,2]=>[1,1,2,1]=>[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]
[1,2,1,2]=>[2,3,1,3]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,2,2,1]=>[2,3,2,1]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,1,1,2]=>[2,1,2,3]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,1,2,1]=>[2,1,3,1]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[2,2,1,1]=>[2,2,1,2]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0]
[1,1,2,3]=>[1,1,2,2]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,1,3,2]=>[2,2,4,1]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[1,2,1,3]=>[2,3,1,4]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,2,3,1]=>[1,2,2,4]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[1,3,1,2]=>[1,3,4,2]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,3,2,1]=>[2,4,1,1]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[2,1,1,3]=>[2,1,2,4]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[2,1,3,1]=>[4,3,1,2]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[2,3,1,1]=>[1,2,4,1]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[3,1,1,2]=>[1,4,1,2]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[3,1,2,1]=>[3,1,4,2]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[3,2,1,1]=>[2,1,1,2]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,1,2,4]=>[1,1,2,3]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[1,1,4,2]=>[3,3,1,1]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]
[1,2,1,4]=>[3,4,2,1]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,2,4,1]=>[1,2,3,3]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,4,1,2]=>[1,4,3,2]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,4,2,1]=>[3,1,1,2]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[2,1,1,4]=>[3,2,3,1]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[2,1,4,1]=>[4,3,2,1]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[2,4,1,1]=>[1,3,3,1]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]
[4,1,1,2]=>[1,3,1,2]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[4,1,2,1]=>[2,4,3,1]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[4,2,1,1]=>[3,1,2,3]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,1,3,3]=>[1,1,3,1]=>[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]
[1,3,1,3]=>[4,1,2,1]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[1,3,3,1]=>[1,3,1,4]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[3,1,1,3]=>[1,4,1,3]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[3,1,3,1]=>[4,2,1,2]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[3,3,1,1]=>[1,1,4,1]=>[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[1,1,3,4]=>[1,1,3,2]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[1,1,4,3]=>[3,3,1,2]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,3,1,4]=>[4,1,2,2]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[1,3,4,1]=>[1,3,2,3]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,4,1,3]=>[4,2,1,1]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[1,4,3,1]=>[3,1,2,1]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[3,1,1,4]=>[3,1,3,1]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]
[3,1,4,1]=>[4,2,2,1]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[3,4,1,1]=>[1,2,3,1]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[4,1,1,3]=>[1,3,1,3]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]
[4,1,3,1]=>[4,1,1,2]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[4,3,1,1]=>[3,2,1,3]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,2,2,2]=>[1,2,1,1]=>[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]
[2,1,2,2]=>[2,1,3,2]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,2,1,2]=>[2,2,1,3]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,2,2,1]=>[2,2,2,1]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0]
[1,2,2,3]=>[1,2,1,2]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,2,3,2]=>[2,3,3,1]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,3,2,2]=>[2,4,1,2]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[2,1,2,3]=>[2,1,3,3]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[2,1,3,2]=>[2,1,4,1]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[2,2,1,3]=>[2,2,1,4]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[2,2,3,1]=>[1,1,2,4]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[2,3,1,2]=>[1,2,4,2]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[2,3,2,1]=>[2,3,1,1]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[3,1,2,2]=>[1,4,2,1]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[3,2,1,2]=>[2,1,1,3]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[3,2,2,1]=>[2,1,2,1]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,2,2,4]=>[1,2,1,3]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[1,2,4,2]=>[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,4,2,2]=>[3,1,1,3]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]
[2,1,2,4]=>[2,1,3,4]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[2,1,4,2]=>[3,2,1,1]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[2,2,1,4]=>[3,3,2,1]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[2,2,4,1]=>[1,1,3,3]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]
[2,4,1,2]=>[1,3,3,2]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[2,4,2,1]=>[4,1,2,3]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[4,1,2,2]=>[1,3,2,1]=>[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]
[4,2,1,2]=>[3,1,2,4]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[4,2,2,1]=>[3,1,3,2]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]
[1,2,3,3]=>[1,2,2,1]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,3,2,3]=>[2,4,1,3]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,3,3,2]=>[2,4,2,1]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[2,1,3,3]=>[2,1,4,2]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[2,3,1,3]=>[1,2,4,3]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[2,3,3,1]=>[1,2,1,4]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[3,1,2,3]=>[1,4,2,2]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]
[3,1,3,2]=>[4,2,1,3]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[3,2,1,3]=>[2,1,1,4]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[3,2,3,1]=>[3,2,4,1]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[3,3,1,2]=>[1,1,4,2]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]
[3,3,2,1]=>[2,2,1,1]=>[1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0]
[1,2,3,4]=>[1,2,2,2]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0]
[1,2,4,3]=>[2,3,4,1]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,3,2,4]=>[4,1,3,1]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[1,3,4,2]=>[1,3,2,4]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[1,4,2,3]=>[3,1,1,4]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[1,4,3,2]=>[3,1,2,2]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,1,3,4]=>[2,1,4,3]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[2,1,4,3]=>[3,2,1,2]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,3,1,4]=>[3,4,1,1]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[2,3,4,1]=>[1,2,2,3]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[2,4,1,3]=>[4,1,1,1]=>[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[2,4,3,1]=>[4,1,3,2]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[3,1,2,4]=>[1,4,2,3]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[3,1,4,2]=>[3,1,1,1]=>[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]
[3,2,1,4]=>[3,2,2,1]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[3,2,4,1]=>[4,3,1,1]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[3,4,1,2]=>[1,2,3,2]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[3,4,2,1]=>[3,4,1,2]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[4,1,2,3]=>[1,3,2,2]=>[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]
[4,1,3,2]=>[4,1,1,3]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[4,2,1,3]=>[4,2,3,1]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[4,2,3,1]=>[3,1,4,1]=>[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]
[4,3,1,2]=>[3,2,1,4]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]
[4,3,2,1]=>[2,1,1,1]=>[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]
[1,1,1,1,1]=>[1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2]=>[1,1,1,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,1]=>[2,2,2,3,1]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,1,2,1,1]=>[2,2,3,1,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,2,1,1,1]=>[2,3,1,2,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,1,1,1,1]=>[2,1,2,2,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,3]=>[1,1,1,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,1,3,1]=>[1,1,1,3,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,1,3,1,1]=>[1,1,3,5,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,3,1,1,1]=>[1,3,5,1,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,1,1,1]=>[1,5,1,1,1]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,4]=>[1,1,1,1,4]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,1,4,1]=>[1,1,1,4,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,4,1,1]=>[1,1,4,4,1]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,4,1,1,1]=>[1,4,4,1,1]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[4,1,1,1,1]=>[1,4,1,1,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,5]=>[1,1,1,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,1,5,1]=>[1,1,1,5,3]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,1,5,1,1]=>[1,1,5,3,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,5,1,1,1]=>[1,5,3,1,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[5,1,1,1,1]=>[1,3,1,1,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,1,2,2]=>[1,1,1,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,2,1,2]=>[2,2,3,1,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,2,2,1]=>[2,2,3,2,1]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[1,2,1,1,2]=>[2,3,1,2,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,1,2,1]=>[2,3,1,3,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,2,2,1,1]=>[2,3,2,1,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,1,1,1,2]=>[2,1,2,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,1,1,2,1]=>[2,1,2,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,1,2,1,1]=>[2,1,3,1,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,2,1,1,1]=>[2,2,1,2,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,1,2,3]=>[1,1,1,2,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,1,1,3,2]=>[2,2,2,4,1]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,2,1,3]=>[2,2,3,1,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,2,3,1]=>[1,1,2,2,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,1,3,1,2]=>[1,1,3,5,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,3,2,1]=>[2,2,4,1,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[1,2,1,1,3]=>[2,3,1,2,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,1,3,1]=>[3,4,2,5,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,2,3,1,1]=>[1,2,2,5,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,3,1,1,2]=>[1,3,5,1,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,3,1,2,1]=>[3,5,1,4,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,2,1,1]=>[2,4,1,1,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,1,1,1,3]=>[2,1,2,2,4]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,1,1,3,1]=>[3,2,3,5,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,1,3,1,1]=>[3,2,5,1,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,3,1,1,1]=>[1,2,5,1,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,1,1,1,2]=>[1,5,1,1,2]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,1,1,2,1]=>[3,1,3,4,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,1,2,1,1]=>[3,1,4,2,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,2,1,1,1]=>[2,1,1,2,2]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,1,1,2,4]=>[1,1,1,2,3]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,4,2]=>[1,1,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,1,2,1,4]=>[2,2,3,1,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,2,4,1]=>[1,1,2,3,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,4,1,2]=>[1,1,4,4,2]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,4,2,1]=>[4,4,1,2,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,2,1,1,4]=>[2,3,1,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,1,4,1]=>[4,5,3,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,2,4,1,1]=>[1,2,3,4,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,2]=>[1,4,4,1,2]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,4,1,2,1]=>[4,1,1,5,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,4,2,1,1]=>[4,1,2,3,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,1,1,4]=>[2,1,2,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,1,1,4,1]=>[4,3,4,1,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,1,4,1,1]=>[4,3,1,1,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,4,1,1,1]=>[1,3,4,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[4,1,1,1,2]=>[1,4,1,1,2]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,1,1,2,1]=>[2,5,2,3,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,1,2,1,1]=>[2,5,3,1,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,2,1,1,1]=>[3,1,2,3,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,1,2,5]=>[1,1,1,2,4]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,1,1,5,2]=>[1,1,1,5,4]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,1,2,1,5]=>[3,3,4,2,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,1,2,5,1]=>[1,1,2,4,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,5,1,2]=>[1,1,5,3,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,5,2,1]=>[4,4,2,1,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,2,1,1,5]=>[3,4,2,3,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,1,5,1]=>[3,4,2,1,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,2,5,1,1]=>[1,2,4,3,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,5,1,1,2]=>[1,5,3,1,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,5,1,2,1]=>[3,1,5,4,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,2,1,1]=>[4,2,1,3,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,1,1,5]=>[3,2,3,3,1]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[2,1,1,5,1]=>[3,2,3,1,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,1,5,1,1]=>[3,2,1,5,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,5,1,1,1]=>[1,4,3,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[5,1,1,1,2]=>[1,3,1,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[5,1,1,2,1]=>[2,4,2,3,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[5,1,2,1,1]=>[2,4,3,1,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[5,2,1,1,1]=>[2,5,1,2,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,1,3,3]=>[1,1,1,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,3,1,3]=>[1,1,3,5,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,1,3,3,1]=>[1,1,3,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,3,1,1,3]=>[1,3,5,1,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,3,1,3,1]=>[5,1,3,1,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,3,3,1,1]=>[1,3,1,5,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,1,1,3]=>[1,5,1,1,3]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,1,3,1]=>[3,1,3,5,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,1,3,1,1]=>[3,1,5,1,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,3,1,1,1]=>[1,1,5,1,1]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,1,3,4]=>[1,1,1,3,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,1,4,3]=>[2,2,2,5,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,3,1,4]=>[1,1,3,5,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,3,4,1]=>[1,1,3,2,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,4,1,3]=>[1,1,4,4,3]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,1,4,3,1]=>[4,4,1,3,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,3,1,1,4]=>[1,3,5,1,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,3,1,4,1]=>[5,1,3,2,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,3,4,1,1]=>[1,3,2,4,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,3]=>[1,4,4,1,3]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,4,1,3,1]=>[5,2,2,1,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,4,3,1,1]=>[4,1,3,2,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,1,1,1,4]=>[1,5,1,1,4]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[3,1,1,4,1]=>[4,2,4,1,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[3,1,4,1,1]=>[4,2,1,1,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[3,4,1,1,1]=>[1,2,4,1,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,1,1,1,3]=>[1,4,1,1,3]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[4,1,1,3,1]=>[1,4,1,3,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,1,3,1,1]=>[1,4,3,5,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,3,1,1,1]=>[3,2,1,3,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,1,3,5]=>[1,1,1,3,3]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,1,5,3]=>[3,3,3,1,1]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,1,3,1,5]=>[3,3,5,1,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,1,3,5,1]=>[1,1,3,3,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,1,5,1,3]=>[1,1,5,3,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,1,5,3,1]=>[3,3,1,1,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[1,3,1,1,5]=>[3,5,1,3,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,3,1,5,1]=>[5,1,3,3,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,3,5,1,1]=>[1,3,3,3,1]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,5,1,1,3]=>[1,5,3,1,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,5,1,3,1]=>[5,3,1,1,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,5,3,1,1]=>[3,1,1,1,3]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[3,1,1,1,5]=>[3,1,3,3,1]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[3,1,1,5,1]=>[3,1,3,1,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,1,5,1,1]=>[3,1,1,5,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,5,1,1,1]=>[1,3,3,1,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[5,1,1,1,3]=>[1,3,1,1,3]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[5,1,1,3,1]=>[1,3,1,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[5,1,3,1,1]=>[1,3,3,5,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[5,3,1,1,1]=>[3,1,1,3,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,1,1,4,4]=>[1,1,1,4,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,4,1,4]=>[4,4,1,1,1]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,4,4,1]=>[1,1,4,1,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,4,1,1,4]=>[4,1,1,4,1]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[1,4,1,4,1]=>[4,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,4,4,1,1]=>[1,4,1,4,1]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[4,1,1,1,4]=>[1,4,1,1,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[4,1,1,4,1]=>[4,1,4,1,1]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[4,1,4,1,1]=>[4,1,1,1,4]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]
[4,4,1,1,1]=>[1,1,4,1,1]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,1,4,5]=>[1,1,1,4,2]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,1,1,5,4]=>[3,3,3,1,2]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,4,1,5]=>[4,4,1,1,2]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,4,5,1]=>[1,1,4,2,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,1,5,1,4]=>[1,1,5,3,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,5,4,1]=>[4,4,2,3,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,4,1,1,5]=>[4,1,1,4,2]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,4,1,5,1]=>[5,2,2,3,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,4,5,1,1]=>[1,4,2,3,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,5,1,1,4]=>[1,5,3,1,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,5,1,4,1]=>[5,3,1,2,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,5,4,1,1]=>[4,2,3,1,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,1,1,1,5]=>[1,4,1,1,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[4,1,1,5,1]=>[1,4,1,5,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,1,5,1,1]=>[1,4,5,3,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,5,1,1,1]=>[1,2,3,1,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[5,1,1,1,4]=>[1,3,1,1,4]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[5,1,1,4,1]=>[1,3,1,4,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,1,4,1,1]=>[1,3,4,4,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,4,1,1,1]=>[2,1,5,2,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,2,2,2]=>[1,1,2,1,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,2,1,2,2]=>[2,3,1,3,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,2,1,2]=>[2,3,2,1,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,2,2,1]=>[2,3,2,2,1]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,1,1,2,2]=>[2,1,2,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,1,2,1,2]=>[2,1,3,1,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,1,2,2,1]=>[2,1,3,2,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,2,1,1,2]=>[2,2,1,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,2,1,2,1]=>[2,2,1,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,2,2,1,1]=>[2,2,2,1,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,2,2,3]=>[1,1,2,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,1,2,3,2]=>[2,2,3,3,1]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,3,2,2]=>[2,2,4,1,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,2,1,2,3]=>[2,3,1,3,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,2,1,3,2]=>[2,3,1,4,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,2,2,1,3]=>[2,3,2,1,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,2,3,1]=>[1,2,1,2,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,2,3,1,2]=>[1,2,2,5,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,2,3,2,1]=>[2,3,3,1,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,3,1,2,2]=>[1,3,5,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,3,2,1,2]=>[2,4,1,1,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,3,2,2,1]=>[2,4,1,2,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,1,1,2,3]=>[2,1,2,3,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,1,1,3,2]=>[2,1,2,4,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,1,2,1,3]=>[2,1,3,1,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,1,2,3,1]=>[3,2,4,4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,3,1,2]=>[3,2,5,1,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,3,2,1]=>[2,1,4,1,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[2,2,1,1,3]=>[2,2,1,2,4]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,2,1,3,1]=>[3,3,2,5,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,2,3,1,1]=>[1,1,2,5,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[2,3,1,1,2]=>[1,2,5,1,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,3,1,2,1]=>[3,4,1,4,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,3,2,1,1]=>[2,3,1,1,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,1,1,2,2]=>[1,5,1,2,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,1,2,1,2]=>[3,1,4,2,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,1,2,2,1]=>[3,1,4,3,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,2,1,1,2]=>[2,1,1,2,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,2,1,2,1]=>[2,1,1,3,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[3,2,2,1,1]=>[2,1,2,1,2]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,1,2,2,4]=>[1,1,2,1,3]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,2,4,2]=>[1,1,2,3,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,4,2,2]=>[1,1,4,5,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,2,1,2,4]=>[2,3,1,3,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,1,4,2]=>[4,5,3,1,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,2,2,1,4]=>[2,3,2,1,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,2,4,1]=>[1,2,1,3,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,2,4,1,2]=>[1,2,3,4,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,4,2,1]=>[3,4,5,1,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,1,2,2]=>[1,4,4,2,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,4,2,1,2]=>[4,1,2,3,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,2,2,1]=>[4,1,2,4,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,1,2,4]=>[2,1,2,3,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,1,1,4,2]=>[4,3,4,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,2,1,4]=>[2,1,3,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,1,2,4,1]=>[2,1,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,4,1,2]=>[4,3,1,1,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,4,2,1]=>[4,3,1,2,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,2,1,1,4]=>[2,2,1,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,2,1,4,1]=>[4,4,3,1,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,2,4,1,1]=>[1,1,3,4,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,4,1,1,2]=>[1,3,4,1,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,4,1,2,1]=>[2,4,5,3,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,4,2,1,1]=>[3,5,1,2,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,1,1,2,2]=>[1,4,1,2,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,1,2,1,2]=>[2,5,3,1,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,1,2,2,1]=>[2,5,3,2,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,2,1,1,2]=>[3,1,2,3,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,2,1,2,1]=>[3,1,2,4,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,2,2,1,1]=>[3,1,3,2,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,2,2,5]=>[1,1,2,1,4]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,1,2,5,2]=>[1,1,2,4,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,5,2,2]=>[1,1,5,4,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,2,1,2,5]=>[2,3,1,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,2,1,5,2]=>[4,5,3,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,2,2,1,5]=>[3,4,3,2,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,2,5,1]=>[1,2,1,4,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,2,5,1,2]=>[1,2,4,3,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,5,2,1]=>[4,5,1,1,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,5,1,2,2]=>[1,5,3,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,5,2,1,2]=>[4,2,1,3,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,2,2,1]=>[4,2,1,4,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,1,2,5]=>[2,1,2,3,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,1,1,5,2]=>[4,3,4,2,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,2,1,5]=>[3,2,4,2,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,1,2,5,1]=>[2,1,3,5,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,5,1,2]=>[3,2,1,5,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,5,2,1]=>[4,3,2,1,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,2,1,1,5]=>[3,3,2,3,1]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[2,2,1,5,1]=>[3,3,2,1,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,2,5,1,1]=>[1,1,4,3,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,5,1,1,2]=>[1,4,3,1,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,5,1,2,1]=>[2,5,4,3,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,5,2,1,1]=>[4,1,1,3,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,1,1,2,2]=>[1,3,1,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[5,1,2,1,2]=>[2,4,3,1,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[5,1,2,2,1]=>[2,4,3,2,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[5,2,1,1,2]=>[2,5,1,2,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,2,1,2,1]=>[2,5,1,3,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[5,2,2,1,1]=>[2,5,2,1,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,2,3,3]=>[1,1,2,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,1,3,2,3]=>[2,2,4,1,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,3,3,2]=>[2,2,4,2,1]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,2,1,3,3]=>[2,3,1,4,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,3,1,3]=>[1,2,2,5,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,3,3,1]=>[1,2,2,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,3,1,2,3]=>[1,3,5,2,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,3,1,3,2]=>[5,1,3,1,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,3,2,1,3]=>[2,4,1,1,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,3,2,3,1]=>[3,5,2,4,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,3,1,2]=>[1,3,1,5,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,3,3,2,1]=>[2,4,2,1,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,1,1,3,3]=>[2,1,2,4,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,1,3,1,3]=>[5,4,1,3,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,3,3,1]=>[3,2,5,3,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,3,1,1,3]=>[1,2,5,1,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,3,1,3,1]=>[3,4,1,5,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,3,3,1,1]=>[1,2,1,5,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,1,1,2,3]=>[1,5,1,2,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,1,1,3,2]=>[3,1,3,5,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,2,1,3]=>[3,1,4,2,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,2,3,1]=>[3,1,4,4,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[3,1,3,1,2]=>[3,1,5,1,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[3,1,3,2,1]=>[3,1,5,2,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,2,1,1,3]=>[2,1,1,2,4]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,2,1,3,1]=>[3,2,2,5,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,2,3,1,1]=>[3,2,4,1,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,3,1,1,2]=>[1,1,5,1,2]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,3,1,2,1]=>[3,3,1,4,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,3,2,1,1]=>[2,2,1,1,2]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,1,2,3,4]=>[1,1,2,2,2]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,1,2,4,3]=>[2,2,3,4,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,3,2,4]=>[2,2,4,1,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,1,3,4,2]=>[1,1,3,2,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,1,4,2,3]=>[1,1,4,5,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,4,3,2]=>[2,2,5,1,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,2,1,3,4]=>[2,3,1,4,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,1,4,3]=>[2,3,1,5,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,2,3,1,4]=>[1,2,2,5,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,2,3,4,1]=>[1,2,2,2,4]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,2,4,1,3]=>[1,2,3,4,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,4,3,1]=>[3,4,5,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,1,2,4]=>[1,3,5,2,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,3,1,4,2]=>[5,1,3,2,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,3,2,1,4]=>[2,4,1,1,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,3,2,4,1]=>[5,1,4,1,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,3,4,1,2]=>[1,3,2,4,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,3,4,2,1]=>[3,5,4,1,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,1,2,3]=>[1,4,4,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,4,1,3,2]=>[5,2,2,1,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,4,2,1,3]=>[5,2,3,4,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,2,3,1]=>[4,1,2,5,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,4,3,1,2]=>[4,1,3,2,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,3,2,1]=>[2,5,1,1,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[2,1,1,3,4]=>[2,1,2,4,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,1,1,4,3]=>[2,1,2,5,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,1,3,1,4]=>[5,4,1,3,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,1]=>[2,1,4,3,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,4,1,3]=>[5,4,2,2,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,1,4,3,1]=>[4,3,1,3,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,3,1,1,4]=>[1,2,5,1,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,3,1,4,1]=>[4,5,2,1,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,3,4,1,1]=>[1,2,2,4,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,4,1,1,3]=>[1,3,4,1,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,4,1,3,1]=>[5,1,2,1,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,4,3,1,1]=>[3,5,2,1,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,1,2,4]=>[1,5,1,2,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,1,1,4,2]=>[4,2,4,1,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,1,2,1,4]=>[4,2,5,3,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,2,4,1]=>[1,5,2,3,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,4,1,2]=>[4,2,1,1,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,1,4,2,1]=>[4,2,1,2,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[3,2,1,1,4]=>[2,1,1,2,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,2,1,4,1]=>[4,3,3,1,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[3,2,4,1,1]=>[2,1,4,5,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,4,1,1,2]=>[1,2,4,1,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,4,1,2,1]=>[2,3,5,3,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,4,2,1,1]=>[3,4,1,2,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,1,1,2,3]=>[1,4,1,2,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[4,1,1,3,2]=>[2,5,2,4,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,1,2,1,3]=>[2,5,3,1,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,2,3,1]=>[1,4,2,2,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,1,3,1,2]=>[1,4,3,5,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,3,2,1]=>[2,5,4,1,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,2,1,1,3]=>[3,1,2,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,2,1,3,1]=>[3,1,2,5,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,2,3,1,1]=>[3,1,4,1,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[4,3,1,1,2]=>[3,2,1,3,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,3,1,2,1]=>[3,2,1,4,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,3,2,1,1]=>[2,1,1,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,1,2,3,5]=>[1,1,2,2,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,1,2,5,3]=>[1,1,2,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,3,2,5]=>[2,2,4,1,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,3,5,2]=>[1,1,3,3,4]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,5,2,3]=>[1,1,5,4,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,5,3,2]=>[3,3,1,1,2]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,2,1,3,5]=>[2,3,1,4,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,2,1,5,3]=>[3,4,2,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,2,3,1,5]=>[3,4,4,1,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,2,3,5,1]=>[1,2,2,3,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,5,1,3]=>[1,2,4,3,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,5,3,1]=>[4,5,1,2,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,3,1,2,5]=>[1,3,5,2,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,2]=>[5,1,3,3,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,3,2,1,5]=>[3,5,2,2,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,3,2,5,1]=>[5,1,4,2,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,3,5,1,2]=>[1,3,3,3,2]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,3,5,2,1]=>[5,1,1,2,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,5,1,2,3]=>[1,5,3,2,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,5,1,3,2]=>[5,3,1,1,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,5,2,1,3]=>[5,3,2,4,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,2,3,1]=>[4,2,1,5,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,5,3,1,2]=>[3,1,1,1,4]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[1,5,3,2,1]=>[3,1,1,2,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,1,1,3,5]=>[2,1,2,4,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[2,1,1,5,3]=>[3,2,3,1,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,1,3,1,5]=>[3,2,5,1,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,1,3,5,1]=>[5,4,1,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[2,1,5,1,3]=>[5,4,3,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,5,3,1]=>[3,2,1,1,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[2,3,1,1,5]=>[3,4,1,3,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,3,1,5,1]=>[3,4,1,1,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,3,5,1,1]=>[1,2,3,3,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,5,1,1,3]=>[1,4,3,1,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,5,1,3,1]=>[5,2,1,1,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,5,3,1,1]=>[4,1,2,2,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,1,1,2,5]=>[1,5,1,2,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,1,1,5,2]=>[4,2,4,2,1]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,1,2,1,5]=>[3,1,4,2,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[3,1,2,5,1]=>[1,5,2,4,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,2]=>[3,1,1,5,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,1]=>[4,2,2,1,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[3,2,1,1,5]=>[3,2,2,3,1]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[3,2,1,5,1]=>[3,2,2,1,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,2,5,1,1]=>[2,1,5,4,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,5,1,1,2]=>[1,3,3,1,2]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[3,5,1,2,1]=>[2,4,4,3,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,5,2,1,1]=>[2,4,5,1,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,1,1,2,3]=>[1,3,1,2,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[5,1,1,3,2]=>[2,4,2,4,1]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[5,1,2,1,3]=>[2,4,3,1,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[5,1,2,3,1]=>[1,3,2,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,1,3,1,2]=>[1,3,3,5,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[5,1,3,2,1]=>[2,4,4,1,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[5,2,1,1,3]=>[2,5,1,2,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,2,1,3,1]=>[5,2,4,1,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,2,3,1,1]=>[1,4,2,5,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,3,1,1,2]=>[3,1,1,3,4]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[5,3,1,2,1]=>[3,1,1,4,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[5,3,2,1,1]=>[3,1,2,2,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,2,4,4]=>[1,1,2,3,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,4,2,4]=>[1,1,4,5,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,4,4,2]=>[1,1,4,1,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,2,1,4,4]=>[2,3,1,5,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,4,1,4]=>[1,2,3,4,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,2,4,4,1]=>[1,2,3,1,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,4,1,2,4]=>[1,4,4,2,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,4,1,4,2]=>[4,1,1,1,2]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,4,2,1,4]=>[4,1,2,3,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,4,2,4,1]=>[5,2,3,1,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,4,4,1,2]=>[1,4,1,4,2]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,4,4,2,1]=>[4,1,4,2,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,1,1,4,4]=>[2,1,2,5,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,1,4,1,4]=>[4,3,1,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,1,4,4,1]=>[4,3,1,4,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,4,1,1,4]=>[1,3,4,1,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,4,1,4,1]=>[5,1,2,2,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,4,4,1,1]=>[1,3,1,4,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[4,1,1,2,4]=>[1,4,1,2,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,1,1,4,2]=>[4,1,4,1,2]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[4,1,2,1,4]=>[4,1,5,3,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,1,2,4,1]=>[1,4,2,3,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,1,4,1,2]=>[4,1,1,1,5]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[4,1,4,2,1]=>[4,1,1,2,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,2,1,1,4]=>[4,2,3,4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,2,1,4,1]=>[4,2,3,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,2,4,1,1]=>[1,5,3,4,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,4,1,1,2]=>[1,1,4,1,2]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,4,1,2,1]=>[2,2,5,3,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,4,2,1,1]=>[3,3,1,2,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,2,4,5]=>[1,1,2,3,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,1,2,5,4]=>[2,2,3,5,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,4,2,5]=>[4,4,1,2,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,4,5,2]=>[1,1,4,2,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,5,2,4]=>[1,1,5,4,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,5,4,2]=>[3,3,1,2,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[1,2,1,4,5]=>[2,3,1,5,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,2,1,5,4]=>[3,4,2,1,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,4,1,5]=>[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,2,4,5,1]=>[1,2,3,2,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,5,1,4]=>[1,2,4,3,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,2,5,4,1]=>[4,5,1,3,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,4,1,2,5]=>[4,1,1,5,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[1,4,1,5,2]=>[4,1,1,2,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,4,2,1,5]=>[4,1,2,3,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,4,2,5,1]=>[5,2,3,2,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,4,5,1,2]=>[1,4,2,3,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,4,5,2,1]=>[4,1,5,1,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,5,1,2,4]=>[1,5,3,2,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,5,1,4,2]=>[5,3,1,2,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,5,2,1,4]=>[4,2,1,3,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,5,2,4,1]=>[5,3,2,1,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,5,4,1,2]=>[4,2,3,1,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,4,2,1]=>[3,1,2,1,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,1,1,4,5]=>[2,1,2,5,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,1,1,5,4]=>[3,2,3,1,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,1,4,1,5]=>[4,3,1,1,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,1,4,5,1]=>[2,1,5,3,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,5,1,4]=>[5,4,3,1,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,5,4,1]=>[4,3,2,3,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,4,1,1,5]=>[1,3,4,1,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,4,1,5,1]=>[5,1,2,3,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,4,5,1,1]=>[1,3,2,3,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,5,1,1,4]=>[1,4,3,1,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,5,1,4,1]=>[5,2,1,2,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,5,4,1,1]=>[4,1,3,1,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[4,1,1,2,5]=>[1,4,1,2,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[4,1,1,5,2]=>[4,1,4,2,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[4,1,2,1,5]=>[4,1,5,3,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,2,5,1]=>[1,4,2,4,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,1,5,1,2]=>[1,4,5,3,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,5,2,1]=>[4,1,2,1,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,2,1,1,5]=>[3,1,2,3,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[4,2,1,5,1]=>[3,1,2,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,2,5,1,1]=>[1,5,4,3,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,5,1,1,2]=>[1,2,3,1,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[4,5,1,2,1]=>[2,3,4,3,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,5,2,1,1]=>[2,3,5,1,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,1,1,2,4]=>[1,3,1,2,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[5,1,1,4,2]=>[1,3,1,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[5,1,2,1,4]=>[2,4,3,1,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,1,2,4,1]=>[1,3,2,3,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[5,1,4,1,2]=>[1,3,4,4,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[5,1,4,2,1]=>[5,1,2,3,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,2,1,1,4]=>[4,1,3,4,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,2,1,4,1]=>[4,1,3,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[5,2,4,1,1]=>[1,4,3,4,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,4,1,1,2]=>[2,1,5,2,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,4,1,2,1]=>[2,1,5,3,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[5,4,2,1,1]=>[3,2,1,2,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,3,3,3]=>[1,1,3,1,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[1,3,1,3,3]=>[1,3,5,3,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,3,3,1,3]=>[1,3,1,5,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,3,3,3,1]=>[1,3,1,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,1,3,3]=>[1,5,1,3,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,3,1,3]=>[5,3,1,3,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,1,3,3,1]=>[3,1,5,3,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,3,1,1,3]=>[1,1,5,1,3]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,3,1,3,1]=>[3,3,1,5,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,3,3,1,1]=>[1,1,1,5,1]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,3,3,4]=>[1,1,3,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,3,4,3]=>[2,2,4,3,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,1,4,3,3]=>[2,2,5,1,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,3,1,3,4]=>[1,3,5,3,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,3,1,4,3]=>[5,1,3,2,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,3,1,4]=>[1,3,1,5,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,3,3,4,1]=>[1,3,1,2,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,3,4,1,3]=>[1,3,2,4,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,3,4,3,1]=>[3,5,4,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,1,3,3]=>[1,4,4,3,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,4,3,1,3]=>[5,2,4,3,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,3,3,1]=>[4,1,3,4,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,1,1,3,4]=>[1,5,1,3,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,1,1,4,3]=>[4,2,4,1,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,1,3,1,4]=>[5,3,1,3,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,3,4,1]=>[1,5,3,2,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,4,1,3]=>[5,3,2,2,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,1,4,3,1]=>[4,2,1,3,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[3,3,1,1,4]=>[1,1,5,1,4]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[3,3,1,4,1]=>[4,4,2,1,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[3,3,4,1,1]=>[1,1,2,4,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[3,4,1,1,3]=>[1,2,4,1,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[3,4,1,3,1]=>[1,2,4,3,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,4,3,1,1]=>[3,4,2,1,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,1,1,3,3]=>[1,4,1,3,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[4,1,3,1,3]=>[5,2,1,3,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,1,3,3,1]=>[1,4,3,1,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,3,1,1,3]=>[3,2,1,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,3,1,3,1]=>[3,2,1,5,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,3,3,1,1]=>[3,2,3,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,3,3,5]=>[1,1,3,1,3]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,3,5,3]=>[1,1,3,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,1,5,3,3]=>[3,3,1,1,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,3,1,3,5]=>[5,1,3,1,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,3,1,5,3]=>[3,5,1,1,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,3,3,1,5]=>[3,5,3,1,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,3,3,5,1]=>[1,3,1,3,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,3,5,1,3]=>[5,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]
[1,3,5,3,1]=>[5,1,1,3,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,5,1,3,3]=>[1,5,3,3,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[1,5,3,1,3]=>[3,1,1,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[1,5,3,3,1]=>[3,1,1,3,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[3,1,1,3,5]=>[1,5,1,3,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,1,1,5,3]=>[3,1,3,1,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[3,1,3,1,5]=>[3,1,5,1,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,3,5,1]=>[5,3,1,1,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,1,5,1,3]=>[5,3,3,1,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,1,5,3,1]=>[3,1,1,1,1]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]
[3,3,1,1,5]=>[3,3,1,3,1]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[3,3,1,5,1]=>[3,3,1,1,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[3,3,5,1,1]=>[1,1,3,3,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[3,5,1,1,3]=>[1,3,3,1,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[3,5,1,3,1]=>[5,1,1,1,3]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[3,5,3,1,1]=>[3,5,1,1,3]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[5,1,1,3,3]=>[1,3,1,3,1]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]
[5,1,3,1,3]=>[5,1,1,3,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[5,1,3,3,1]=>[1,3,3,1,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[5,3,1,1,3]=>[3,1,1,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[5,3,1,3,1]=>[3,1,1,5,1]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[5,3,3,1,1]=>[3,1,3,1,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]
[1,1,3,4,4]=>[1,1,3,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,1,4,3,4]=>[2,2,5,1,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,1,4,4,3]=>[2,2,5,2,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,3,1,4,4]=>[1,3,5,4,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,3,4,1,4]=>[1,3,2,4,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,3,4,4,1]=>[1,3,2,1,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,4,1,3,4]=>[1,4,4,3,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,4,1,4,3]=>[4,1,1,1,3]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[1,4,3,1,4]=>[4,1,3,2,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,4,3,4,1]=>[4,1,3,5,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,4,4,1,3]=>[1,4,1,4,3]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[1,4,4,3,1]=>[4,1,4,3,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,1,1,4,4]=>[1,5,1,4,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[3,1,4,1,4]=>[4,2,1,1,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[3,1,4,4,1]=>[4,2,1,4,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[3,4,1,1,4]=>[1,2,4,1,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[3,4,1,4,1]=>[4,5,1,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[3,4,4,1,1]=>[1,2,1,4,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,1,1,3,4]=>[1,4,1,3,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,1,1,4,3]=>[4,1,4,1,3]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[4,1,3,1,4]=>[5,2,1,3,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,1,3,4,1]=>[1,4,3,2,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,1,4,1,3]=>[5,2,2,2,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[4,1,4,3,1]=>[4,1,1,3,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,3,1,1,4]=>[4,3,2,4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,3,1,4,1]=>[4,3,2,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,3,4,1,1]=>[2,1,3,5,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,4,1,1,3]=>[1,1,4,1,3]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[4,4,1,3,1]=>[1,1,4,3,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,4,3,1,1]=>[3,3,2,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,3,4,5]=>[1,1,3,2,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,1,3,5,4]=>[2,2,4,4,1]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,1,4,3,5]=>[2,2,5,1,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,4,5,3]=>[1,1,4,2,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,1,5,3,4]=>[3,3,1,1,4]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,1,5,4,3]=>[3,3,1,2,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,3,1,4,5]=>[1,3,5,4,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,4]=>[3,5,1,1,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,3,4,1,5]=>[1,3,2,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,4,5,1]=>[1,3,2,2,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,3,5,1,4]=>[5,1,1,1,2]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,3,5,4,1]=>[5,1,1,4,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,4,1,3,5]=>[5,2,2,1,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[1,4,1,5,3]=>[4,1,1,2,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[1,4,3,1,5]=>[4,1,3,2,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,4,3,5,1]=>[5,2,4,1,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,4,5,1,3]=>[1,4,2,3,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,4,5,3,1]=>[4,1,5,2,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,5,1,3,4]=>[1,5,3,3,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,5,1,4,3]=>[5,3,1,2,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,3,1,4]=>[4,2,2,2,1]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[1,5,3,4,1]=>[4,2,2,5,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,5,4,1,3]=>[5,3,4,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,4,3,1]=>[3,1,2,2,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,1,1,4,5]=>[1,5,1,4,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,1,1,5,4]=>[3,1,3,1,2]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[3,1,4,1,5]=>[4,2,1,1,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,1,4,5,1]=>[1,5,4,2,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,4]=>[5,3,3,1,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,5,4,1]=>[4,2,2,3,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[3,4,1,1,5]=>[1,2,4,1,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,4,1,5,1]=>[1,2,4,5,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,4,5,1,1]=>[1,2,2,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,5,1,1,4]=>[1,3,3,1,4]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[3,5,1,4,1]=>[5,1,1,2,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,5,4,1,1]=>[2,4,1,5,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,1,1,3,5]=>[1,4,1,3,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[4,1,1,5,3]=>[4,1,4,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[4,1,3,1,5]=>[5,2,1,3,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,1,3,5,1]=>[5,2,1,1,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[4,1,5,1,3]=>[5,2,3,1,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,1,5,3,1]=>[4,1,2,2,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[4,3,1,1,5]=>[3,2,1,3,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[4,3,1,5,1]=>[3,2,1,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,3,5,1,1]=>[2,1,4,4,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[4,5,1,1,3]=>[1,2,3,1,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[4,5,1,3,1]=>[1,2,3,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,5,3,1,1]=>[3,4,1,1,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[5,1,1,3,4]=>[1,3,1,3,2]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[5,1,1,4,3]=>[2,4,2,5,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,1,3,1,4]=>[5,1,1,3,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[5,1,3,4,1]=>[1,3,3,2,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[5,1,4,1,3]=>[5,1,2,2,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[5,1,4,3,1]=>[5,1,2,4,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,3,1,1,4]=>[4,2,2,4,1]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[5,3,1,4,1]=>[4,2,2,1,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[5,3,4,1,1]=>[1,5,2,4,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,4,1,1,3]=>[2,1,5,2,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,4,1,3,1]=>[5,4,2,1,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,4,3,1,1]=>[3,2,2,1,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,2,2,2]=>[1,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[2,1,2,2,2]=>[2,1,3,2,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,2,1,2,2]=>[2,2,1,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,2,2,1,2]=>[2,2,2,1,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,2,2,2,1]=>[2,2,2,2,1]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,2,2,2,3]=>[1,2,1,1,2]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,2,2,3,2]=>[2,3,2,3,1]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,3,2,2]=>[2,3,3,1,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,3,2,2,2]=>[2,4,1,2,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,1,2,2,3]=>[2,1,3,2,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,1,2,3,2]=>[2,1,3,3,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,1,3,2,2]=>[2,1,4,1,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,2,1,2,3]=>[2,2,1,3,3]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,2,1,3,2]=>[2,2,1,4,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,2,2,1,3]=>[2,2,2,1,4]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,2,2,3,1]=>[1,1,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[2,2,3,1,2]=>[1,1,2,5,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,2,3,2,1]=>[2,2,3,1,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,3,1,2,2]=>[1,2,5,2,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,3,2,1,2]=>[2,3,1,1,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,3,2,2,1]=>[2,3,1,2,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,1,2,2,2]=>[1,5,2,1,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,2,1,2,2]=>[2,1,1,3,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,2,2,1,2]=>[2,1,2,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,2,2,2,1]=>[2,1,2,2,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,2,2,2,4]=>[1,2,1,1,3]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,2,2,4,2]=>[1,2,1,3,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,2,4,2,2]=>[1,2,3,5,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,4,2,2,2]=>[1,4,5,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[2,1,2,2,4]=>[2,1,3,2,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,1,2,4,2]=>[3,2,4,5,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,4,2,2]=>[4,3,1,2,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,2,1,2,4]=>[2,2,1,3,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,2,1,4,2]=>[4,4,3,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,2,2,1,4]=>[2,2,2,1,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,2,2,4,1]=>[1,1,1,3,4]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,2,4,1,2]=>[1,1,3,4,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,2,4,2,1]=>[3,3,5,1,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,4,1,2,2]=>[1,3,4,2,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,4,2,1,2]=>[3,5,1,2,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,4,2,2,1]=>[3,5,1,3,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,1,2,2,2]=>[1,4,2,1,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,2,1,2,2]=>[3,1,2,4,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,2,2,1,2]=>[3,1,3,2,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,2,2,2,1]=>[3,1,3,3,2]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,2,2,2,5]=>[1,2,1,1,4]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,2,2,5,2]=>[1,2,1,4,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,2,5,2,2]=>[1,2,4,4,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,5,2,2,2]=>[1,5,4,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[2,1,2,2,5]=>[2,1,3,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,1,2,5,2]=>[4,3,5,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,5,2,2]=>[4,3,2,1,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,2,1,2,5]=>[2,2,1,3,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,2,1,5,2]=>[4,4,3,2,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,2,2,1,5]=>[3,3,3,2,1]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[2,2,2,5,1]=>[1,1,1,4,3]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,2,5,1,2]=>[1,1,4,3,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,2,5,2,1]=>[4,4,1,1,3]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,5,1,2,2]=>[1,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,5,2,1,2]=>[4,1,1,3,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,5,2,2,1]=>[4,1,1,4,3]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,1,2,2,2]=>[1,3,2,1,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[5,2,1,2,2]=>[2,5,1,3,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,2,2,1,2]=>[2,5,2,1,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,2,2,2,1]=>[2,5,2,2,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,2,2,3,3]=>[1,2,1,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,2,3,2,3]=>[2,3,3,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,2,3,3,2]=>[2,3,3,2,1]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,3,2,2,3]=>[2,4,1,2,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,3,2,3,2]=>[2,4,1,3,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,3,3,2,2]=>[2,4,2,1,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,1,2,3,3]=>[2,1,3,3,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,1,3,2,3]=>[2,1,4,1,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,1,3,3,2]=>[2,1,4,2,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,2,1,3,3]=>[2,2,1,4,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,2,3,1,3]=>[1,1,2,5,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,2,3,3,1]=>[1,1,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[2,3,1,2,3]=>[1,2,5,2,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,3,1,3,2]=>[3,4,1,5,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,3,2,1,3]=>[2,3,1,1,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,3,2,3,1]=>[3,4,2,4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,3,3,1,2]=>[1,2,1,5,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,3,3,2,1]=>[2,3,2,1,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,1,2,2,3]=>[1,5,2,1,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,1,2,3,2]=>[3,1,4,4,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,1,3,2,2]=>[3,1,5,2,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,2,1,2,3]=>[2,1,1,3,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[3,2,1,3,2]=>[2,1,1,4,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[3,2,2,1,3]=>[2,1,2,1,4]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,2,2,3,1]=>[3,2,3,4,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,2,3,1,2]=>[3,2,4,1,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,2,3,2,1]=>[2,1,3,1,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[3,3,1,2,2]=>[1,1,5,2,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,3,2,1,2]=>[2,2,1,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,3,2,2,1]=>[2,2,1,2,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,2,2,3,4]=>[1,2,1,2,2]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,2,2,4,3]=>[2,3,2,4,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,3,2,4]=>[2,3,3,1,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,3,4,2]=>[1,2,2,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[1,2,4,2,3]=>[1,2,3,5,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,4,3,2]=>[2,3,4,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,3,2,2,4]=>[2,4,1,2,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,3,2,4,2]=>[5,1,4,1,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,3,4,2,2]=>[1,3,2,5,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,4,2,2,3]=>[1,4,5,1,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,4,2,3,2]=>[4,1,2,5,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,3,2,2]=>[2,5,1,1,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,1,2,3,4]=>[2,1,3,3,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[2,1,2,4,3]=>[2,1,3,4,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,1,3,2,4]=>[2,1,4,1,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[2,1,3,4,2]=>[3,2,5,4,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,4,2,3]=>[4,3,1,2,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,4,3,2]=>[2,1,5,1,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[2,2,1,3,4]=>[2,2,1,4,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,2,1,4,3]=>[2,2,1,5,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,2,3,1,4]=>[1,1,2,5,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,2,3,4,1]=>[1,1,2,2,4]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,2,4,1,3]=>[1,1,3,4,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,2,4,3,1]=>[3,3,5,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,3,1,2,4]=>[1,2,5,2,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,3,1,4,2]=>[4,5,2,1,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,3,2,1,4]=>[2,3,1,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,3,2,4,1]=>[2,3,1,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,3,4,1,2]=>[1,2,2,4,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,3,4,2,1]=>[3,4,4,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,4,1,2,3]=>[1,3,4,2,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,4,1,3,2]=>[5,1,2,1,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,4,2,1,3]=>[5,1,3,4,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,4,2,3,1]=>[3,5,1,4,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,4,3,1,2]=>[3,5,2,1,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,4,3,2,1]=>[2,4,1,1,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[3,1,2,2,4]=>[1,5,2,1,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,1,2,4,2]=>[3,1,4,5,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[3,1,4,2,2]=>[4,2,1,2,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,2,1,2,4]=>[2,1,1,3,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[3,2,1,4,2]=>[4,3,3,1,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,2,2,1,4]=>[2,1,2,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,2,2,4,1]=>[2,1,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,2,4,1,2]=>[2,1,4,5,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,2,4,2,1]=>[3,2,5,1,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,4,1,2,2]=>[1,2,4,2,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,4,2,1,2]=>[3,4,1,2,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,4,2,2,1]=>[3,4,1,3,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,1,2,2,3]=>[1,4,2,1,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[4,1,2,3,2]=>[2,5,3,3,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,1,3,2,2]=>[2,5,4,1,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,2,1,2,3]=>[3,1,2,4,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,2,1,3,2]=>[3,1,2,5,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,2,2,1,3]=>[3,1,3,2,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,2,2,3,1]=>[3,1,3,4,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[4,2,3,1,2]=>[3,1,4,1,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[4,2,3,2,1]=>[3,1,4,2,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,3,1,2,2]=>[3,2,1,4,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,3,2,1,2]=>[2,1,1,1,3]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[4,3,2,2,1]=>[2,1,1,2,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,2,2,3,5]=>[1,2,1,2,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,2,2,5,3]=>[1,2,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,2,3,2,5]=>[2,3,3,1,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,2,3,5,2]=>[1,2,2,3,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,5,2,3]=>[1,2,4,4,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,2,5,3,2]=>[4,5,1,2,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,2,2,5]=>[2,4,1,2,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,3,2,5,2]=>[5,1,4,2,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,3,5,2,2]=>[1,3,3,4,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,5,2,2,3]=>[1,5,4,1,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,5,2,3,2]=>[4,2,1,5,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,3,2,2]=>[3,1,1,2,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,1,2,3,5]=>[2,1,3,3,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,1,2,5,3]=>[4,3,5,1,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,3,2,5]=>[2,1,4,1,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,1,3,5,2]=>[5,4,1,1,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,1,5,2,3]=>[4,3,2,1,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,5,3,2]=>[3,2,1,1,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,2,1,3,5]=>[2,2,1,4,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[2,2,1,5,3]=>[3,3,2,1,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,2,3,1,5]=>[3,3,4,1,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,2,3,5,1]=>[1,1,2,3,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,2,5,1,3]=>[1,1,4,3,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,2,5,3,1]=>[4,4,1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[2,3,1,2,5]=>[1,2,5,2,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,3,1,5,2]=>[4,5,2,2,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,3,2,1,5]=>[3,4,2,2,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,3,2,5,1]=>[2,3,1,5,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,3,5,1,2]=>[1,2,3,3,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,3,5,2,1]=>[2,3,4,5,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,5,1,2,3]=>[1,4,3,2,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,5,1,3,2]=>[5,2,1,1,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,5,2,1,3]=>[5,2,2,4,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,5,2,3,1]=>[4,1,1,5,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,5,3,1,2]=>[4,1,2,2,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,5,3,2,1]=>[4,1,2,3,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,1,2,2,5]=>[1,5,2,1,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,1,2,5,2]=>[4,2,5,1,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,1,5,2,2]=>[4,2,2,1,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,2,1,2,5]=>[2,1,1,3,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,2,1,5,2]=>[4,3,3,2,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,2,2,1,5]=>[3,2,3,2,1]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[3,2,2,5,1]=>[2,1,2,5,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,2,5,1,2]=>[2,1,5,4,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,2,5,2,1]=>[4,3,1,1,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[3,5,1,2,2]=>[1,3,3,2,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[3,5,2,1,2]=>[2,4,5,1,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,5,2,2,1]=>[2,4,5,2,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,1,2,2,3]=>[1,3,2,1,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[5,1,2,3,2]=>[2,4,3,3,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[5,1,3,2,2]=>[2,4,4,1,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[5,2,1,2,3]=>[2,5,1,3,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[5,2,1,3,2]=>[2,5,1,4,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,2,2,1,3]=>[2,5,2,1,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,2,2,3,1]=>[1,4,1,2,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,2,3,1,2]=>[1,4,2,5,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,2,3,2,1]=>[2,5,3,1,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[5,3,1,2,2]=>[3,1,1,4,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[5,3,2,1,2]=>[3,1,2,2,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[5,3,2,2,1]=>[3,1,2,3,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,2,4,4]=>[1,2,1,3,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[1,2,4,2,4]=>[1,2,3,5,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,2,4,4,2]=>[1,2,3,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,4,2,2,4]=>[1,4,5,1,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,4,2,4,2]=>[5,2,3,1,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,4,4,2,2]=>[1,4,1,5,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[2,1,2,4,4]=>[2,1,3,4,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,1,4,2,4]=>[5,4,2,3,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,4,4,2]=>[4,3,1,4,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,2,1,4,4]=>[2,2,1,5,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,2,4,1,4]=>[1,1,3,4,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,2,4,4,1]=>[1,1,3,1,4]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,4,1,2,4]=>[1,3,4,2,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,4,1,4,2]=>[5,1,2,2,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,4,2,1,4]=>[5,1,3,4,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,4,2,4,1]=>[5,1,3,1,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,4,4,1,2]=>[1,3,1,4,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,4,4,2,1]=>[3,5,3,1,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,1,2,2,4]=>[1,4,2,1,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,1,2,4,2]=>[1,4,2,3,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,4,2,2]=>[4,1,1,2,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[4,2,1,2,4]=>[3,1,2,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,2,1,4,2]=>[4,2,3,1,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,2,2,1,4]=>[4,2,4,3,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,2,2,4,1]=>[1,5,1,3,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,2,4,1,2]=>[1,5,3,4,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,2,4,2,1]=>[3,1,5,1,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,4,1,2,2]=>[1,1,4,2,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,4,2,1,2]=>[3,3,1,2,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,4,2,2,1]=>[3,3,1,3,2]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,2,2,4,5]=>[1,2,1,3,2]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,2,2,5,4]=>[2,3,2,5,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,4,2,5]=>[1,2,3,5,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,2,4,5,2]=>[1,2,3,2,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,2,5,2,4]=>[1,2,4,4,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,2,5,4,2]=>[4,5,1,3,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,2,2,5]=>[4,1,2,4,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,4,2,5,2]=>[4,1,2,1,1]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[1,4,5,2,2]=>[1,4,2,4,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,5,2,2,4]=>[1,5,4,1,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,5,2,4,2]=>[5,3,2,1,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,5,4,2,2]=>[3,1,2,1,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,1,2,4,5]=>[2,1,3,4,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,1,2,5,4]=>[2,1,3,5,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,1,4,2,5]=>[4,3,1,2,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,1,4,5,2]=>[4,3,1,5,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,5,2,4]=>[5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,5,4,2]=>[3,2,1,2,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[2,2,1,4,5]=>[2,2,1,5,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,2,1,5,4]=>[3,3,2,1,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,2,4,1,5]=>[1,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,2,4,5,1]=>[1,1,3,2,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,2,5,1,4]=>[1,1,4,3,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,2,5,4,1]=>[4,4,1,3,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[2,4,1,2,5]=>[1,3,4,2,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,4,1,5,2]=>[5,1,2,3,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,4,2,1,5]=>[3,5,1,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,4,2,5,1]=>[5,1,3,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,4,5,1,2]=>[1,3,2,3,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[2,4,5,2,1]=>[2,4,3,5,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,5,1,2,4]=>[1,4,3,2,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,5,1,4,2]=>[5,2,1,2,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,5,2,1,4]=>[4,1,1,3,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,5,2,4,1]=>[5,2,2,1,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[2,5,4,1,2]=>[4,1,3,1,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,5,4,2,1]=>[4,1,3,2,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,1,2,2,5]=>[1,4,2,1,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[4,1,2,5,2]=>[4,1,5,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[4,1,5,2,2]=>[4,1,2,1,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[4,2,1,2,5]=>[4,2,3,5,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,2,1,5,2]=>[4,2,3,2,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,2,2,1,5]=>[3,1,3,2,1]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[4,2,2,5,1]=>[1,5,1,4,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,2,5,1,2]=>[1,5,4,3,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,2,5,2,1]=>[4,2,1,1,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[4,5,1,2,2]=>[1,2,3,2,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[4,5,2,1,2]=>[2,3,5,1,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,5,2,2,1]=>[2,3,5,2,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,1,2,2,4]=>[1,3,2,1,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[5,1,2,4,2]=>[1,3,2,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[5,1,4,2,2]=>[1,3,4,5,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[5,2,1,2,4]=>[2,5,1,3,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,2,1,4,2]=>[4,1,3,1,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[5,2,2,1,4]=>[4,1,4,3,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,2,2,4,1]=>[1,4,1,3,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,2,4,1,2]=>[1,4,3,4,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[5,2,4,2,1]=>[5,2,1,3,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,4,1,2,2]=>[2,1,5,3,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,4,2,1,2]=>[3,2,1,2,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[5,4,2,2,1]=>[3,2,1,3,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,3,3,3]=>[1,2,2,1,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,3,2,3,3]=>[2,4,1,3,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,3,3,2,3]=>[2,4,2,1,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,3,3,3,2]=>[2,4,2,2,1]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,1,3,3,3]=>[2,1,4,2,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[2,3,1,3,3]=>[1,2,5,3,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,3,3,1,3]=>[1,2,1,5,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,3,3,3,1]=>[1,2,1,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,1,2,3,3]=>[1,5,2,2,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,1,3,2,3]=>[3,1,5,2,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,3,3,2]=>[3,1,5,3,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,2,1,3,3]=>[2,1,1,4,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,2,3,1,3]=>[3,2,4,1,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,2,3,3,1]=>[3,2,4,3,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,3,1,2,3]=>[1,1,5,2,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,3,1,3,2]=>[3,3,1,5,2]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,3,2,1,3]=>[2,2,1,1,4]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,3,2,3,1]=>[3,3,2,4,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,3,3,1,2]=>[1,1,1,5,2]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,3,3,2,1]=>[2,2,2,1,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,2,3,3,4]=>[1,2,2,1,2]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,2,3,4,3]=>[2,3,3,3,1]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[1,2,4,3,3]=>[2,3,4,1,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,3,2,3,4]=>[2,4,1,3,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,3,2,4,3]=>[2,4,1,4,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[1,3,3,2,4]=>[2,4,2,1,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,3,3,4,2]=>[1,3,1,2,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,3,4,2,3]=>[1,3,2,5,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,3,4,3,2]=>[2,4,3,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,4,2,3,3]=>[1,4,5,2,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,4,3,2,3]=>[2,5,1,1,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,4,3,3,2]=>[2,5,1,2,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,1,3,3,4]=>[2,1,4,2,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,1,3,4,3]=>[2,1,4,3,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,1,4,3,3]=>[2,1,5,1,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,3,1,3,4]=>[1,2,5,3,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[2,3,1,4,3]=>[4,5,2,1,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,3,3,1,4]=>[1,2,1,5,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,3,3,4,1]=>[1,2,1,2,4]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,3,4,1,3]=>[1,2,2,4,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,3,4,3,1]=>[3,4,4,2,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[2,4,1,3,3]=>[1,3,4,3,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,4,3,1,3]=>[5,1,4,3,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,4,3,3,1]=>[3,5,2,3,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,2,3,4]=>[1,5,2,2,2]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]
[3,1,2,4,3]=>[3,1,4,5,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,3,2,4]=>[5,3,1,4,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[3,1,3,4,2]=>[3,1,5,4,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[3,1,4,2,3]=>[4,2,1,2,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,1,4,3,2]=>[4,2,1,3,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,2,1,3,4]=>[2,1,1,4,3]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[3,2,1,4,3]=>[2,1,1,5,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[3,2,3,1,4]=>[4,3,5,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,2,3,4,1]=>[2,1,3,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,2,4,1,3]=>[5,4,1,2,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,2,4,3,1]=>[3,2,5,2,1]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,3,1,2,4]=>[1,1,5,2,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,3,1,4,2]=>[4,4,2,1,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,3,2,1,4]=>[2,2,1,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,3,2,4,1]=>[2,2,1,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,3,4,1,2]=>[1,1,2,4,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,3,4,2,1]=>[3,3,4,1,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,4,1,2,3]=>[1,2,4,2,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[3,4,1,3,2]=>[2,3,5,4,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,4,2,1,3]=>[3,4,1,2,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,4,2,3,1]=>[3,4,1,4,1]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[3,4,3,1,2]=>[3,4,2,1,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,4,3,2,1]=>[2,3,1,1,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[4,1,2,3,3]=>[1,4,2,2,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[4,1,3,2,3]=>[2,5,4,1,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,3,3,2]=>[2,5,4,2,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,2,1,3,3]=>[3,1,2,5,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,2,3,1,3]=>[3,1,4,1,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,2,3,3,1]=>[3,1,4,3,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[4,3,1,2,3]=>[3,2,1,4,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,3,1,3,2]=>[3,2,1,5,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,3,2,1,3]=>[2,1,1,1,4]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[4,3,2,3,1]=>[3,2,2,4,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,3,3,1,2]=>[3,2,3,1,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,3,3,2,1]=>[2,1,2,1,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,2,3,3,5]=>[1,2,2,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[1,2,3,5,3]=>[1,2,2,3,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,5,3,3]=>[1,2,4,5,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,3,2,3,5]=>[2,4,1,3,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,3,2,5,3]=>[5,1,4,2,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,3,2,5]=>[2,4,2,1,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,3,3,5,2]=>[1,3,1,3,4]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,3,5,2,3]=>[1,3,3,4,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,3,5,3,2]=>[5,1,1,3,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,5,2,3,3]=>[1,5,4,2,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,5,3,2,3]=>[3,1,1,2,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,5,3,3,2]=>[3,1,1,3,2]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,1,3,3,5]=>[2,1,4,2,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[2,1,3,5,3]=>[5,4,1,1,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,1,5,3,3]=>[3,2,1,1,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,3,1,3,5]=>[1,2,5,3,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,3,1,5,3]=>[3,4,1,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[2,3,3,1,5]=>[3,4,3,1,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,3,3,5,1]=>[1,2,1,3,3]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[2,3,5,1,3]=>[1,2,3,3,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[2,3,5,3,1]=>[3,4,5,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,5,1,3,3]=>[1,4,3,3,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,5,3,1,3]=>[5,2,3,3,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,5,3,3,1]=>[4,1,2,4,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,1,2,3,5]=>[1,5,2,2,3]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,1,2,5,3]=>[4,2,5,1,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,1,3,2,5]=>[5,3,1,4,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,3,5,2]=>[5,3,1,1,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,1,5,2,3]=>[4,2,2,1,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,1,5,3,2]=>[3,1,1,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[3,2,1,3,5]=>[2,1,1,4,4]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[3,2,1,5,3]=>[3,2,2,1,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[3,2,3,1,5]=>[3,2,4,1,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[3,2,3,5,1]=>[2,1,3,4,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,2,5,1,3]=>[5,4,2,1,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,2,5,3,1]=>[4,3,1,2,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[3,3,1,2,5]=>[1,1,5,2,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,3,1,5,2]=>[4,4,2,2,1]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,3,2,1,5]=>[3,3,2,2,1]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[3,3,2,5,1]=>[2,2,1,5,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,3,5,1,2]=>[1,1,3,3,2]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[3,3,5,2,1]=>[2,2,4,5,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,5,1,2,3]=>[1,3,3,2,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[3,5,1,3,2]=>[5,1,1,1,4]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[3,5,2,1,3]=>[5,1,2,4,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,5,2,3,1]=>[1,3,4,2,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,5,3,1,2]=>[3,5,1,1,4]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[3,5,3,2,1]=>[3,5,1,2,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,1,2,3,3]=>[1,3,2,2,1]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[5,1,3,2,3]=>[2,4,4,1,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[5,1,3,3,2]=>[2,4,4,2,1]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[5,2,1,3,3]=>[2,5,1,4,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,2,3,1,3]=>[1,4,2,5,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,2,3,3,1]=>[1,4,2,1,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,3,1,2,3]=>[3,1,1,4,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[5,3,1,3,2]=>[3,1,1,5,2]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[5,3,2,1,3]=>[3,1,2,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,3,2,3,1]=>[3,1,2,4,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[5,3,3,1,2]=>[3,1,3,1,4]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[5,3,3,2,1]=>[3,1,3,2,2]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[1,2,3,4,4]=>[1,2,2,2,1]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[1,2,4,3,4]=>[2,3,4,1,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,4,4,3]=>[2,3,4,2,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,3,2,4,4]=>[2,4,1,4,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,3,4,2,4]=>[1,3,2,5,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[1,3,4,4,2]=>[1,3,2,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,4,2,3,4]=>[1,4,5,2,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,4,2,4,3]=>[5,2,3,1,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,3,2,4]=>[2,5,1,1,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,4,3,4,2]=>[4,1,3,5,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,4,2,3]=>[1,4,1,5,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,4,4,3,2]=>[2,5,2,1,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,1,3,4,4]=>[2,1,4,3,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[2,1,4,3,4]=>[2,1,5,1,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,1,4,4,3]=>[2,1,5,2,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[2,3,1,4,4]=>[1,2,5,4,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,3,4,1,4]=>[1,2,2,4,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[2,3,4,4,1]=>[1,2,2,1,4]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,4,1,3,4]=>[1,3,4,3,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,4,1,4,3]=>[5,1,2,2,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,4,3,1,4]=>[5,1,4,3,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,4,3,4,1]=>[2,4,1,3,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,4,4,1,3]=>[1,3,1,4,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[2,4,4,3,1]=>[3,5,3,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,2,4,4]=>[1,5,2,3,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,1,4,2,4]=>[5,3,2,3,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,4,4,2]=>[4,2,1,4,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,2,1,4,4]=>[2,1,1,5,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,2,4,1,4]=>[5,4,1,2,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,2,4,4,1]=>[2,1,4,2,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,4,1,2,4]=>[1,2,4,2,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[3,4,1,4,2]=>[4,5,1,1,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,4,2,1,4]=>[4,5,2,3,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,4,2,4,1]=>[1,2,5,3,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,4,4,1,2]=>[1,2,1,4,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,4,4,2,1]=>[3,4,3,1,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,1,2,3,4]=>[1,4,2,2,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[4,1,2,4,3]=>[2,5,3,4,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,3,2,4]=>[5,2,1,4,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,1,3,4,2]=>[1,4,3,2,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,1,4,2,3]=>[4,1,1,2,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,1,4,3,2]=>[4,1,1,3,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[4,2,1,3,4]=>[3,1,2,5,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,2,1,4,3]=>[4,2,3,1,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,2,3,1,4]=>[4,2,5,2,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,2,3,4,1]=>[1,5,2,2,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,2,4,1,3]=>[5,3,1,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,2,4,3,1]=>[3,1,5,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,3,1,2,4]=>[3,2,1,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,3,1,4,2]=>[4,3,2,1,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,3,2,1,4]=>[2,1,1,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[4,3,2,4,1]=>[2,1,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,3,4,1,2]=>[2,1,3,5,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,3,4,2,1]=>[3,2,4,1,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,4,1,2,3]=>[1,1,4,2,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[4,4,1,3,2]=>[2,2,5,4,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,4,2,1,3]=>[3,3,1,2,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,4,2,3,1]=>[3,3,1,4,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[4,4,3,1,2]=>[3,3,2,1,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[4,4,3,2,1]=>[2,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[1,2,3,4,5]=>[1,2,2,2,2]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[1,2,3,5,4]=>[2,3,3,4,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[1,2,4,3,5]=>[2,3,4,1,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,2,4,5,3]=>[1,2,3,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[1,2,5,3,4]=>[1,2,4,5,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,2,5,4,3]=>[2,3,5,1,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,3,2,4,5]=>[2,4,1,4,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[1,3,2,5,4]=>[2,4,1,5,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[1,3,4,2,5]=>[1,3,2,5,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,3,4,5,2]=>[1,3,2,2,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[1,3,5,2,4]=>[5,1,1,2,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[1,3,5,4,2]=>[5,1,1,4,3]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[1,4,2,3,5]=>[1,4,5,2,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,4,2,5,3]=>[4,1,2,1,2]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[1,4,3,2,5]=>[4,1,3,3,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[1,4,3,5,2]=>[5,2,4,1,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,4,5,2,3]=>[1,4,2,4,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[1,4,5,3,2]=>[4,1,5,2,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,2,3,4]=>[1,5,4,2,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[1,5,2,4,3]=>[5,3,2,1,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[1,5,3,2,4]=>[3,1,1,2,5]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[1,5,3,4,2]=>[3,1,1,4,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[1,5,4,2,3]=>[3,1,2,1,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[1,5,4,3,2]=>[3,1,2,2,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,1,3,4,5]=>[2,1,4,3,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,1,3,5,4]=>[2,1,4,4,1]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]
[2,1,4,3,5]=>[2,1,5,1,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,1,4,5,3]=>[4,3,1,5,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,1,5,3,4]=>[3,2,1,1,4]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,1,5,4,3]=>[3,2,1,2,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,3,1,4,5]=>[1,2,5,4,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,3,1,5,4]=>[3,4,1,1,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[2,3,4,1,5]=>[1,2,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,3,4,5,1]=>[1,2,2,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[2,3,5,1,4]=>[1,2,3,3,4]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,3,5,4,1]=>[2,3,4,1,5]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[2,4,1,3,5]=>[5,1,2,1,1]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]
[2,4,1,5,3]=>[5,1,2,3,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[2,4,3,1,5]=>[3,5,2,1,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[2,4,3,5,1]=>[5,1,4,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[2,4,5,1,3]=>[1,3,2,3,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[2,4,5,3,1]=>[3,5,4,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[2,5,1,3,4]=>[1,4,3,3,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[2,5,1,4,3]=>[5,2,1,2,4]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,5,3,1,4]=>[4,1,2,2,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[2,5,3,4,1]=>[4,1,2,5,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[2,5,4,1,3]=>[5,2,4,2,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[2,5,4,3,1]=>[4,1,3,3,2]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[3,1,2,4,5]=>[1,5,2,3,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[3,1,2,5,4]=>[4,2,5,1,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,1,4,2,5]=>[4,2,1,2,1]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[3,1,4,5,2]=>[4,2,1,5,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,1,5,2,4]=>[5,3,3,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,1,5,4,2]=>[3,1,1,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[3,2,1,4,5]=>[2,1,1,5,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,2,1,5,4]=>[3,2,2,1,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[3,2,4,1,5]=>[5,4,1,2,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,2,4,5,1]=>[2,1,4,3,4]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[3,2,5,1,4]=>[5,4,2,1,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,2,5,4,1]=>[4,3,1,3,1]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[3,4,1,2,5]=>[1,2,4,2,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[3,4,1,5,2]=>[4,5,1,2,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[3,4,2,1,5]=>[3,4,1,2,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[3,4,2,5,1]=>[1,2,5,4,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,4,5,1,2]=>[1,2,2,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[3,4,5,2,1]=>[2,3,3,5,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[3,5,1,2,4]=>[1,3,3,2,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[3,5,1,4,2]=>[5,1,1,2,3]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[3,5,2,1,4]=>[5,1,2,4,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[3,5,2,4,1]=>[5,1,2,1,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[3,5,4,1,2]=>[2,4,1,5,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[3,5,4,2,1]=>[3,5,2,1,2]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[4,1,2,3,5]=>[1,4,2,2,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,1,2,5,3]=>[4,1,5,1,2]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,1,3,2,5]=>[5,2,1,4,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,1,3,5,2]=>[5,2,1,1,2]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[4,1,5,2,3]=>[4,1,2,1,5]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,1,5,3,2]=>[4,1,2,2,3]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,2,1,3,5]=>[5,3,4,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[4,2,1,5,3]=>[3,1,2,1,1]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[4,2,3,1,5]=>[3,1,4,1,1]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]
[4,2,3,5,1]=>[1,5,2,3,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[4,2,5,1,3]=>[5,3,2,1,1]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]
[4,2,5,3,1]=>[4,2,1,2,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[4,3,1,2,5]=>[4,3,2,5,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,3,1,5,2]=>[4,3,2,2,1]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[4,3,2,1,5]=>[3,2,2,2,1]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[4,3,2,5,1]=>[2,1,1,5,4]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,3,5,1,2]=>[2,1,4,4,3]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,3,5,2,1]=>[2,1,4,5,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[4,5,1,2,3]=>[1,2,3,2,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[4,5,1,3,2]=>[2,3,4,4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[4,5,2,1,3]=>[2,3,5,1,4]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[4,5,2,3,1]=>[1,2,4,2,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[4,5,3,1,2]=>[3,4,1,1,4]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[4,5,3,2,1]=>[3,4,1,2,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[5,1,2,3,4]=>[1,3,2,2,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[5,1,2,4,3]=>[2,4,3,4,1]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[5,1,3,2,4]=>[5,1,1,4,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[5,1,3,4,2]=>[1,3,3,2,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[5,1,4,2,3]=>[1,3,4,5,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,1,4,3,2]=>[2,4,5,1,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,2,1,3,4]=>[2,5,1,4,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,2,1,4,3]=>[4,1,3,1,3]=>[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[5,2,3,1,4]=>[4,1,5,2,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,2,3,4,1]=>[1,4,2,2,4]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]
[5,2,4,1,3]=>[5,2,1,2,1]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]
[5,2,4,3,1]=>[5,2,1,4,3]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,3,1,2,4]=>[3,1,1,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[5,3,1,4,2]=>[4,2,2,1,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[5,3,2,1,4]=>[4,2,3,3,1]=>[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[5,3,2,4,1]=>[5,3,4,1,2]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]
[5,3,4,1,2]=>[1,5,2,4,2]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]
[5,3,4,2,1]=>[3,1,4,1,2]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[5,4,1,2,3]=>[2,1,5,3,3]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]
[5,4,1,3,2]=>[2,1,5,4,1]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]
[5,4,2,1,3]=>[3,2,1,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]
[5,4,2,3,1]=>[3,2,1,4,1]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[5,4,3,1,2]=>[3,2,2,1,4]=>[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[5,4,3,2,1]=>[2,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,1,1]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,2]=>[1,1,1,1,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,1,2,1]=>[2,2,2,2,3,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,2,1,1]=>[2,2,2,3,1,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,2,1,1,1]=>[2,2,3,1,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,1,1,1,1]=>[2,3,1,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,1,1,1,1]=>[2,1,2,2,2,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,3]=>[1,1,1,1,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,3,1]=>[1,1,1,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,3,1,1]=>[1,1,1,3,6,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,3,1,1,1]=>[1,1,3,6,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,3,1,1,1,1]=>[1,3,6,1,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,1,1,1,1]=>[1,6,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,4]=>[1,1,1,1,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,4,1]=>[1,1,1,1,4,5]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,4,1,1]=>[1,1,1,4,5,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,4,1,1,1]=>[1,1,4,5,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,4,1,1,1,1]=>[1,4,5,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,1,1,1,1,1]=>[1,5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,5]=>[1,1,1,1,1,5]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,5,1]=>[1,1,1,1,5,4]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,5,1,1]=>[1,1,1,5,4,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,5,1,1,1]=>[1,1,5,4,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,1,1,1,1]=>[1,5,4,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[5,1,1,1,1,1]=>[1,4,1,1,1,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,6]=>[1,1,1,1,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,6,1]=>[1,1,1,1,6,3]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,6,1,1]=>[1,1,1,6,3,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,6,1,1,1]=>[1,1,6,3,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,6,1,1,1,1]=>[1,6,3,1,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[6,1,1,1,1,1]=>[1,3,1,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,2,2]=>[1,1,1,1,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,2,1,2]=>[2,2,2,3,1,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,2,2,1]=>[2,2,2,3,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,2,1,1,2]=>[2,2,3,1,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,1,2,1]=>[2,2,3,1,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,2,2,1,1]=>[2,2,3,2,1,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,1,1,1,2]=>[2,3,1,2,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,1,1,2,1]=>[2,3,1,2,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,1,2,1,1]=>[2,3,1,3,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,2,1,1,1]=>[2,3,2,1,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,1,1,1,2]=>[2,1,2,2,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,1,1,2,1]=>[2,1,2,2,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,2,1,1]=>[2,1,2,3,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,2,1,1,1]=>[2,1,3,1,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,1,1,1]=>[2,2,1,2,2,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,2,3]=>[1,1,1,1,2,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,3,2]=>[2,2,2,2,4,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,2,1,3]=>[2,2,2,3,1,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,2,3,1]=>[1,1,1,2,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,3,1,2]=>[1,1,1,3,6,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,3,2,1]=>[2,2,2,4,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,2,1,1,3]=>[2,2,3,1,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,2,1,3,1]=>[3,3,4,2,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,2,3,1,1]=>[1,1,2,2,6,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,3,1,1,2]=>[1,1,3,6,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,3,1,2,1]=>[3,3,5,1,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,3,2,1,1]=>[2,2,4,1,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,2,1,1,1,3]=>[2,3,1,2,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,1,1,3,1]=>[3,4,2,3,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,1,3,1,1]=>[3,4,2,5,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,1,1,1]=>[1,2,2,6,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,1,1,1,2]=>[1,3,6,1,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,1,1,2,1]=>[3,5,1,3,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,1,2,1,1]=>[3,5,1,4,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,1,1,1]=>[2,4,1,1,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,1,1,1,3]=>[2,1,2,2,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,1,1,3,1]=>[3,2,3,3,5,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,1,1,3,1,1]=>[3,2,3,5,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,1,3,1,1,1]=>[3,2,5,1,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,3,1,1,1,1]=>[1,2,6,1,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,1,1,1,2]=>[1,6,1,1,1,2]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,1,1,2,1]=>[3,1,3,3,4,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,1,2,1,1]=>[3,1,3,4,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,2,1,1,1]=>[3,1,4,2,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,1,1,1,1]=>[2,1,1,2,2,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,2,4]=>[1,1,1,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,4,2]=>[1,1,1,1,4,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,2,1,4]=>[2,2,2,3,1,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,2,4,1]=>[1,1,1,2,3,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,4,1,2]=>[1,1,1,4,5,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,4,2,1]=>[3,3,3,6,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,2,1,1,4]=>[2,2,3,1,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,2,1,4,1]=>[2,2,3,1,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,2,4,1,1]=>[1,1,2,3,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,4,1,1,2]=>[1,1,4,5,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,4,1,2,1]=>[2,2,5,6,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,4,2,1,1]=>[3,3,6,1,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,1,1,1,4]=>[2,3,1,2,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,1,1,4,1]=>[2,3,1,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,1,4,1,1]=>[2,3,1,5,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,4,1,1,1]=>[1,2,3,5,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,1,1,2]=>[1,4,5,1,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,1,1,2,1]=>[2,5,6,2,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,2,1,1]=>[2,5,6,3,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,2,1,1,1]=>[3,6,1,2,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,1,1,4]=>[2,1,2,2,2,5]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,1,1,1,4,1]=>[2,1,2,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,1,4,1,1]=>[2,1,2,5,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,4,1,1,1]=>[2,1,5,6,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,4,1,1,1,1]=>[1,3,5,1,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,1,1,1,2]=>[1,5,1,1,1,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,1,1,1,2,1]=>[2,6,2,2,3,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,1,2,1,1]=>[2,6,2,3,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,2,1,1,1]=>[2,6,3,1,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,2,1,1,1,1]=>[3,1,2,3,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,2,5]=>[1,1,1,1,2,4]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,5,2]=>[1,1,1,1,5,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,2,1,5]=>[2,2,2,3,1,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,2,5,1]=>[1,1,1,2,4,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,5,1,2]=>[1,1,1,5,4,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,5,2,1]=>[4,4,4,1,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,2,1,1,5]=>[2,2,3,1,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,2,1,5,1]=>[2,2,3,1,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,2,5,1,1]=>[1,1,2,4,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,5,1,1,2]=>[1,1,5,4,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,5,1,2,1]=>[2,2,6,5,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,5,2,1,1]=>[4,4,1,1,3,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,2,1,1,1,5]=>[2,3,1,2,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,1,1,5,1]=>[2,3,1,2,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,1,5,1,1]=>[2,3,1,6,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,5,1,1,1]=>[1,2,4,4,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,5,1,1,1,2]=>[1,5,4,1,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,1,1,2,1]=>[2,6,5,2,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,2,1,1]=>[2,6,5,3,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,2,1,1,1]=>[4,1,1,3,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,1,1,1,5]=>[2,1,2,2,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,1,1,5,1]=>[2,1,2,2,6,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,1,5,1,1]=>[2,1,2,6,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,5,1,1,1]=>[2,1,6,5,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,1,1,1]=>[1,4,4,1,1,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[5,1,1,1,1,2]=>[1,4,1,1,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,1,1,1,2,1]=>[2,5,2,2,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,1,2,1,1]=>[2,5,2,3,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,2,1,1,1]=>[2,5,3,1,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,2,1,1,1,1]=>[2,6,1,2,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,2,6]=>[1,1,1,1,2,5]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,6,2]=>[1,1,1,1,6,4]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,2,1,6]=>[3,3,3,4,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,2,6,1]=>[1,1,1,2,5,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,6,1,2]=>[1,1,1,6,3,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,6,2,1]=>[3,3,3,1,6,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,2,1,1,6]=>[3,3,4,2,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,2,1,6,1]=>[3,3,4,2,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,2,6,1,1]=>[1,1,2,5,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,6,1,1,2]=>[1,1,6,3,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,6,1,2,1]=>[3,3,1,5,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,6,2,1,1]=>[3,3,1,6,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,1,1,1,6]=>[3,4,2,3,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,1,1,6,1]=>[3,4,2,3,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,1,6,1,1]=>[3,4,2,1,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,6,1,1,1]=>[1,2,5,3,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,6,1,1,1,2]=>[1,6,3,1,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,6,1,1,2,1]=>[3,1,5,3,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,1,2,1,1]=>[3,1,5,4,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,2,1,1,1]=>[3,1,6,2,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,1,1,6]=>[3,2,3,3,3,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,1,1,6,1]=>[3,2,3,3,1,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,1,1,6,1,1]=>[3,2,3,1,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,1,6,1,1,1]=>[3,2,1,5,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,6,1,1,1,1]=>[1,5,3,1,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[6,1,1,1,1,2]=>[1,3,1,1,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[6,1,1,1,2,1]=>[2,4,2,2,3,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,1,1,2,1,1]=>[2,4,2,3,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,1,2,1,1,1]=>[2,4,3,1,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,2,1,1,1,1]=>[2,5,1,2,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,3,3]=>[1,1,1,1,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,3,1,3]=>[1,1,1,3,6,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,3,3,1]=>[1,1,1,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,3,1,1,3]=>[1,1,3,6,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,3,1,3,1]=>[3,3,5,1,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,3,3,1,1]=>[1,1,3,1,6,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,3,1,1,1,3]=>[1,3,6,1,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,1,1,3,1]=>[3,5,1,3,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,1,3,1,1]=>[3,5,1,5,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,3,1,1,1]=>[1,3,1,6,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,1,1,1,3]=>[1,6,1,1,1,3]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,1,1,3,1]=>[3,1,3,3,5,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,1,3,1,1]=>[3,1,3,5,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,3,1,1,1]=>[3,1,5,1,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,1,1,1,1]=>[1,1,6,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,3,4]=>[1,1,1,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,1,4,3]=>[2,2,2,2,5,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,3,1,4]=>[1,1,1,3,6,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,3,4,1]=>[1,1,1,3,2,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,4,1,3]=>[1,1,1,4,5,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,4,3,1]=>[3,3,3,6,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,3,1,1,4]=>[1,1,3,6,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,3,1,4,1]=>[1,1,3,6,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,3,4,1,1]=>[1,1,3,2,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,4,1,1,3]=>[1,1,4,5,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,4,1,3,1]=>[1,1,4,5,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,4,3,1,1]=>[3,3,6,2,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,3,1,1,1,4]=>[1,3,6,1,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,1,1,4,1]=>[1,3,6,1,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,4,1,1]=>[1,3,6,4,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,4,1,1,1]=>[1,3,2,5,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,1,1,3]=>[1,4,5,1,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,1,1,3,1]=>[1,4,5,1,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,1,3,1,1]=>[1,4,5,3,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,3,1,1,1]=>[3,6,2,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,1,1,1,4]=>[1,6,1,1,1,4]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,1,1,4,1]=>[1,6,1,1,4,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,1,4,1,1]=>[1,6,1,4,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,4,1,1,1]=>[1,6,4,5,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,4,1,1,1,1]=>[1,2,5,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,1,1,1,1,3]=>[1,5,1,1,1,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,1,1,3,1]=>[1,5,1,1,3,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,1,1,3,1,1]=>[1,5,1,3,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,1,3,1,1,1]=>[1,5,3,6,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,3,1,1,1,1]=>[3,2,1,3,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,3,5]=>[1,1,1,1,3,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,5,3]=>[1,1,1,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,3,1,5]=>[1,1,1,3,6,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,3,5,1]=>[1,1,1,3,3,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,5,1,3]=>[1,1,1,5,4,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,5,3,1]=>[4,4,4,1,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,3,1,1,5]=>[1,1,3,6,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,3,1,5,1]=>[1,1,3,6,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,3,5,1,1]=>[1,1,3,3,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,5,1,1,3]=>[1,1,5,4,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,5,1,3,1]=>[1,1,5,4,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,5,3,1,1]=>[4,4,1,2,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,1,1,1,5]=>[1,3,6,1,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,1,1,5,1]=>[1,3,6,1,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,5,1,1]=>[1,3,6,5,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,5,1,1,1]=>[1,3,3,4,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,5,1,1,1,3]=>[1,5,4,1,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,1,1,3,1]=>[1,5,4,1,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,1,3,1,1]=>[1,5,4,3,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,3,1,1,1]=>[4,1,2,2,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,1,1,5]=>[1,6,1,1,1,5]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[3,1,1,1,5,1]=>[1,6,1,1,5,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,1,5,1,1]=>[1,6,1,5,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,5,1,1,1]=>[1,6,5,4,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,5,1,1,1,1]=>[1,3,4,1,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,1,1,1,1,3]=>[1,4,1,1,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,1,1,1,3,1]=>[1,4,1,1,3,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,1,1,3,1,1]=>[1,4,1,3,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,1,3,1,1,1]=>[1,4,3,6,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,1,1,1,1]=>[3,1,1,3,3,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,3,6]=>[1,1,1,1,3,4]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,6,3]=>[1,1,1,1,6,5]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,3,1,6]=>[3,3,3,5,1,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,3,6,1]=>[1,1,1,3,4,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,6,1,3]=>[1,1,1,6,3,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,6,3,1]=>[4,4,4,2,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,3,1,1,6]=>[3,3,5,1,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,3,1,6,1]=>[3,3,5,1,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,3,6,1,1]=>[1,1,3,4,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,6,1,1,3]=>[1,1,6,3,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,6,1,3,1]=>[3,3,1,5,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,6,3,1,1]=>[4,4,2,1,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,1,1,1,6]=>[3,5,1,3,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,3,1,1,6,1]=>[3,5,1,3,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,1,6,1,1]=>[3,5,1,1,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,6,1,1,1]=>[1,3,4,3,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,6,1,1,1,3]=>[1,6,3,1,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,6,1,1,3,1]=>[3,1,5,3,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,6,1,3,1,1]=>[3,1,5,5,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,6,3,1,1,1]=>[4,2,1,2,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,1,1,6]=>[3,1,3,3,3,1]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[3,1,1,1,6,1]=>[3,1,3,3,1,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,1,6,1,1]=>[3,1,3,1,5,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,6,1,1,1]=>[3,1,1,5,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,6,1,1,1,1]=>[1,4,3,1,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[6,1,1,1,1,3]=>[1,3,1,1,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[6,1,1,1,3,1]=>[1,3,1,1,3,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[6,1,1,3,1,1]=>[1,3,1,3,6,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[6,1,3,1,1,1]=>[1,3,3,6,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[6,3,1,1,1,1]=>[1,5,6,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,4,4]=>[1,1,1,1,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,4,1,4]=>[1,1,1,4,5,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,4,4,1]=>[1,1,1,4,1,5]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,4,1,1,4]=>[1,1,4,5,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,4,1,4,1]=>[5,5,1,2,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,4,4,1,1]=>[1,1,4,1,5,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,4,1,1,1,4]=>[1,4,5,1,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,1,1,4,1]=>[5,1,2,5,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,1,4,1,1]=>[5,1,2,1,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,4,1,1,1]=>[1,4,1,5,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,1,1,1,1,4]=>[1,5,1,1,1,4]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,1,1,1,4,1]=>[1,5,1,1,4,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,1,4,1,1]=>[1,5,1,4,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,4,1,1,1]=>[1,5,4,5,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,4,1,1,1,1]=>[1,1,5,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,4,5]=>[1,1,1,1,4,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,5,4]=>[2,2,2,2,6,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,4,1,5]=>[1,1,1,4,5,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,4,5,1]=>[1,1,1,4,2,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,5,1,4]=>[1,1,1,5,4,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,5,4,1]=>[4,4,4,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,4,1,1,5]=>[1,1,4,5,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,4,1,5,1]=>[5,5,1,2,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,4,5,1,1]=>[1,1,4,2,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,5,1,1,4]=>[1,1,5,4,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,5,1,4,1]=>[5,5,2,1,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,5,4,1,1]=>[4,4,1,3,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,1,1,1,5]=>[1,4,5,1,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,1,1,5,1]=>[5,1,2,5,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,1,5,1,1]=>[5,1,2,2,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,5,1,1,1]=>[1,4,2,4,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,5,1,1,1,4]=>[1,5,4,1,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,5,1,1,4,1]=>[5,2,1,5,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,1,4,1,1]=>[5,2,1,1,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,4,1,1,1]=>[4,1,3,1,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,1,1,1,1,5]=>[1,5,1,1,1,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,1,1,5,1]=>[1,5,1,1,5,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,1,5,1,1]=>[1,5,1,5,4,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,5,1,1,1]=>[1,5,5,4,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,5,1,1,1,1]=>[1,2,4,1,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,1,1,1,1,4]=>[1,4,1,1,1,4]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[5,1,1,1,4,1]=>[1,4,1,1,4,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,1,1,4,1,1]=>[1,4,1,4,5,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,1,4,1,1,1]=>[1,4,4,5,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,4,1,1,1,1]=>[2,1,6,2,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,4,6]=>[1,1,1,1,4,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,6,4]=>[3,3,3,3,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,4,1,6]=>[1,1,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,4,6,1]=>[1,1,1,4,3,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,6,1,4]=>[1,1,1,6,3,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,6,4,1]=>[4,4,4,2,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,4,1,1,6]=>[1,1,4,5,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,4,1,6,1]=>[1,1,4,5,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,4,6,1,1]=>[1,1,4,3,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,6,1,1,4]=>[1,1,6,3,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,6,1,4,1]=>[1,1,6,3,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,6,4,1,1]=>[4,4,2,2,1,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,4,1,1,1,6]=>[1,4,5,1,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,1,1,6,1]=>[1,4,5,1,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,1,6,1,1]=>[1,4,5,6,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,6,1,1,1]=>[1,4,3,3,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,6,1,1,1,4]=>[1,6,3,1,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,6,1,1,4,1]=>[1,6,3,1,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,4,1,1]=>[1,6,3,4,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,4,1,1,1]=>[4,2,2,1,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,1,1,1,1,6]=>[1,5,1,1,1,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,1,1,1,6,1]=>[1,5,1,1,6,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,1,1,6,1,1]=>[1,5,1,6,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,1,6,1,1,1]=>[1,5,6,3,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,6,1,1,1,1]=>[1,3,3,1,1,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[6,1,1,1,1,4]=>[1,3,1,1,1,4]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[6,1,1,1,4,1]=>[1,3,1,1,4,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,1,1,4,1,1]=>[1,3,1,4,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,1,4,1,1,1]=>[1,3,4,5,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,4,1,1,1,1]=>[1,6,5,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,5,5]=>[1,1,1,1,5,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,5,1,5]=>[1,1,1,5,4,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,5,5,1]=>[1,1,1,5,1,4]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,5,1,1,5]=>[1,1,5,4,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,5,1,5,1]=>[5,5,2,1,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,5,5,1,1]=>[1,1,5,1,4,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,1,1,1,5]=>[1,5,4,1,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,5,1,1,5,1]=>[5,2,1,5,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,1,5,1,1]=>[5,2,1,2,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,5,1,1,1]=>[1,5,1,4,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[5,1,1,1,1,5]=>[1,4,1,1,1,5]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[5,1,1,1,5,1]=>[1,4,1,1,5,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,1,1,5,1,1]=>[1,4,1,5,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,1,5,1,1,1]=>[1,4,5,4,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,5,1,1,1,1]=>[1,1,4,1,1,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,5,6]=>[1,1,1,1,5,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,6,5]=>[3,3,3,3,1,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,5,1,6]=>[1,1,1,5,4,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,5,6,1]=>[1,1,1,5,2,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,6,1,5]=>[1,1,1,6,3,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,6,5,1]=>[3,3,3,1,2,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,5,1,1,6]=>[1,1,5,4,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,5,1,6,1]=>[1,1,5,4,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,5,6,1,1]=>[1,1,5,2,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,6,1,1,5]=>[1,1,6,3,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,6,1,5,1]=>[1,1,6,3,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,6,5,1,1]=>[3,3,1,2,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,5,1,1,1,6]=>[1,5,4,1,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,5,1,1,6,1]=>[1,5,4,1,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,1,6,1,1]=>[1,5,4,6,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,6,1,1,1]=>[1,5,2,3,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,6,1,1,1,5]=>[1,6,3,1,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,6,1,1,5,1]=>[1,6,3,1,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,5,1,1]=>[1,6,3,5,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,5,1,1,1]=>[3,1,2,6,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,1,1,1,1,6]=>[1,4,1,1,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[5,1,1,1,6,1]=>[1,4,1,1,6,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,1,1,6,1,1]=>[1,4,1,6,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,1,6,1,1,1]=>[1,4,6,3,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,6,1,1,1,1]=>[1,2,3,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[6,1,1,1,1,5]=>[1,3,1,1,1,5]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[6,1,1,1,5,1]=>[1,3,1,1,5,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,1,1,5,1,1]=>[1,3,1,5,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,1,5,1,1,1]=>[1,3,5,4,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,5,1,1,1,1]=>[2,1,5,2,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,2,2,2]=>[1,1,1,2,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,2,1,2,2]=>[2,2,3,1,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,2,1,2]=>[2,2,3,2,1,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,2,2,1]=>[2,2,3,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,2,1,1,2,2]=>[2,3,1,2,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,1,2,1,2]=>[2,3,1,3,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,1,2,2,1]=>[2,3,1,3,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,2,1,1,2]=>[2,3,2,1,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,1,2,1]=>[2,3,2,1,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,2,2,1,1]=>[2,3,2,2,1,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,1,1,2,2]=>[2,1,2,2,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,1,2,1,2]=>[2,1,2,3,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,1,2,2,1]=>[2,1,2,3,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,2,1,1,2]=>[2,1,3,1,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,2,1,2,1]=>[2,1,3,1,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,2,2,1,1]=>[2,1,3,2,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,1,1,2]=>[2,2,1,2,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,1,1,2,1]=>[2,2,1,2,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,2,1,1]=>[2,2,1,3,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,2,1,1,1]=>[2,2,2,1,2,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,2,2,3]=>[1,1,1,2,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,2,3,2]=>[2,2,2,3,3,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,3,2,2]=>[2,2,2,4,1,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,2,1,2,3]=>[2,2,3,1,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,1,3,2]=>[2,2,3,1,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,2,2,1,3]=>[2,2,3,2,1,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,2,2,3,1]=>[1,1,2,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,2,3,1,2]=>[1,1,2,2,6,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,3,2,1]=>[2,2,3,3,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,3,1,2,2]=>[1,1,3,6,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,3,2,1,2]=>[2,2,4,1,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,3,2,2,1]=>[2,2,4,1,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,2,1,1,2,3]=>[2,3,1,2,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,1,3,2]=>[2,3,1,2,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,1,2,1,3]=>[2,3,1,3,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,1,2,3,1]=>[3,4,2,4,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,3,1,2]=>[3,4,2,5,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,3,2,1]=>[2,3,1,4,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,2,1,1,3]=>[2,3,2,1,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,2,1,3,1]=>[3,4,3,2,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,2,3,1,1]=>[1,2,1,2,6,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,3,1,1,2]=>[1,2,2,6,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,3,1,2,1]=>[3,4,4,1,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,3,2,1,1]=>[2,3,3,1,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,1,1,2,2]=>[1,3,6,1,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,1,2,1,2]=>[3,5,1,4,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,1,2,2,1]=>[3,5,1,4,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,1,1,2]=>[2,4,1,1,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,1,2,1]=>[2,4,1,1,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,2,2,1,1]=>[2,4,1,2,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,1,1,2,3]=>[2,1,2,2,3,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,1,1,3,2]=>[2,1,2,2,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,1,2,1,3]=>[2,1,2,3,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,1,2,3,1]=>[3,2,3,4,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,3,1,2]=>[3,2,3,5,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,1,3,2,1]=>[2,1,2,4,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,1,2,1,1,3]=>[2,1,3,1,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,2,1,3,1]=>[3,2,4,2,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,2,3,1,1]=>[3,2,4,4,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,3,1,1,2]=>[3,2,5,1,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,1,2,1]=>[3,2,5,1,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,3,2,1,1]=>[2,1,4,1,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,2,1,1,1,3]=>[2,2,1,2,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,2,1,1,3,1]=>[3,3,2,3,5,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,1,3,1,1]=>[3,3,2,5,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,3,1,1,1]=>[1,1,2,6,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,1,1,2]=>[1,2,6,1,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,1,1,2,1]=>[3,4,1,3,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,1,2,1,1]=>[3,4,1,4,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,2,1,1,1]=>[2,3,1,1,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,1,1,1,2,2]=>[1,6,1,1,2,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,1,2,1,2]=>[3,1,3,4,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,1,2,2,1]=>[3,1,3,4,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,2,1,1,2]=>[3,1,4,2,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,2,1,2,1]=>[3,1,4,2,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,2,1,1]=>[3,1,4,3,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,1,1,1,2]=>[2,1,1,2,2,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,1,1,2,1]=>[2,1,1,2,3,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,1,2,1,1]=>[2,1,1,3,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,2,1,1,1]=>[2,1,2,1,2,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,2,2,4]=>[1,1,1,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,2,4,2]=>[1,1,1,2,3,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,4,2,2]=>[1,1,1,4,6,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,2,1,2,4]=>[2,2,3,1,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,1,4,2]=>[3,3,4,2,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,2,2,1,4]=>[2,2,3,2,1,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,2,2,4,1]=>[1,1,2,1,3,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,2,4,1,2]=>[1,1,2,3,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,2,4,2,1]=>[3,3,4,5,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,4,1,2,2]=>[1,1,4,5,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,4,2,1,2]=>[3,3,6,1,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,4,2,2,1]=>[3,3,6,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,1,1,2,4]=>[2,3,1,2,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,1,4,2]=>[3,4,2,3,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,1,2,1,4]=>[2,3,1,3,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,1,2,4,1]=>[2,3,1,3,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,1,4,1,2]=>[2,3,1,5,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,1,4,2,1]=>[3,4,2,6,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,2,1,1,4]=>[2,3,2,1,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,2,1,4,1]=>[2,3,2,1,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,2,4,1,1]=>[1,2,1,3,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,4,1,1,2]=>[1,2,3,5,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,4,1,2,1]=>[2,3,4,6,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,4,2,1,1]=>[3,4,5,1,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,1,2,2]=>[1,4,5,1,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,1,2,1,2]=>[2,5,6,3,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,1,2,2,1]=>[2,5,6,3,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,2,1,1,2]=>[3,6,1,2,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,1,2,1]=>[3,6,1,2,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,2,2,1,1]=>[3,6,1,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,1,2,4]=>[2,1,2,2,3,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,1,1,4,2]=>[3,2,3,3,6,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,2,1,4]=>[2,1,2,3,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,1,2,4,1]=>[2,1,2,3,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,1,4,1,2]=>[2,1,2,5,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,1,4,2,1]=>[3,2,3,6,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,1,2,1,1,4]=>[2,1,3,1,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,2,1,4,1]=>[2,1,3,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,4,1,1]=>[2,1,3,4,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,1,1,2]=>[2,1,5,6,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,1,2,1]=>[2,1,5,6,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,2,1,1]=>[3,2,6,1,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,1,1,1,4]=>[2,2,1,2,2,5]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,2,1,1,4,1]=>[2,2,1,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,1,4,1,1]=>[2,2,1,5,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,4,1,1,1]=>[1,1,3,5,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,4,1,1,1,2]=>[1,3,5,1,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,1,1,2,1]=>[2,4,6,2,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,1,2,1,1]=>[2,4,6,3,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,2,1,1,1]=>[3,5,1,2,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,1,1,2,2]=>[1,5,1,1,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,1,1,2,1,2]=>[2,6,2,3,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,1,2,2,1]=>[2,6,2,3,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,2,1,1,2]=>[2,6,3,1,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,2,1,2,1]=>[2,6,3,1,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,2,2,1,1]=>[2,6,3,2,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,2,1,1,1,2]=>[3,1,2,3,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,2,1,1,2,1]=>[3,1,2,3,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,1,2,1,1]=>[3,1,2,4,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,2,1,1,1]=>[3,1,3,2,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,2,2,5]=>[1,1,1,2,1,4]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,2,5,2]=>[1,1,1,2,4,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,5,2,2]=>[1,1,1,5,5,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,2,1,2,5]=>[2,2,3,1,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,2,1,5,2]=>[4,4,5,3,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,2,2,1,5]=>[2,2,3,2,1,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,2,2,5,1]=>[1,1,2,1,4,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,2,5,1,2]=>[1,1,2,4,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,2,5,2,1]=>[2,2,3,5,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,5,1,2,2]=>[1,1,5,4,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,5,2,1,2]=>[4,4,1,1,3,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,5,2,2,1]=>[4,4,1,1,4,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,2,1,1,2,5]=>[2,3,1,2,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,1,1,5,2]=>[4,5,3,4,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,1,2,1,5]=>[2,3,1,3,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,1,2,5,1]=>[2,3,1,3,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,1,5,1,2]=>[2,3,1,6,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,1,5,2,1]=>[4,5,3,1,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,2,1,1,5]=>[2,3,2,1,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,2,1,5,1]=>[2,3,2,1,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,2,5,1,1]=>[1,2,1,4,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,5,1,1,2]=>[1,2,4,4,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,5,1,2,1]=>[2,3,5,5,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,5,2,1,1]=>[2,3,5,6,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,1,2,2]=>[1,5,4,1,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,1,2,1,2]=>[2,6,5,3,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,1,2,2,1]=>[2,6,5,3,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,2,1,1,2]=>[4,1,1,3,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,2,1,2,1]=>[4,1,1,3,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,2,2,1,1]=>[4,1,1,4,3,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,1,1,2,5]=>[2,1,2,2,3,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,1,5,2]=>[4,3,4,4,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,1,2,1,5]=>[2,1,2,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,1,2,5,1]=>[2,1,2,3,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,1,5,1,2]=>[2,1,2,6,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,1,5,2,1]=>[4,3,4,1,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,1,2,1,1,5]=>[2,1,3,1,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,2,1,5,1]=>[2,1,3,1,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,2,5,1,1]=>[2,1,3,5,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,5,1,1,2]=>[2,1,6,5,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,1,2,1]=>[2,1,6,5,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,5,2,1,1]=>[4,3,1,1,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,2,1,1,1,5]=>[2,2,1,2,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,2,1,1,5,1]=>[2,2,1,2,6,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,1,5,1,1]=>[2,2,1,6,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,5,1,1,1]=>[1,1,4,4,1,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[2,5,1,1,1,2]=>[1,4,4,1,1,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,5,1,1,2,1]=>[2,5,5,2,3,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,5,1,2,1,1]=>[2,5,5,3,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,5,2,1,1,1]=>[2,5,6,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,1,1,2,2]=>[1,4,1,1,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,1,1,2,1,2]=>[2,5,2,3,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,1,2,2,1]=>[2,5,2,3,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,2,1,1,2]=>[2,5,3,1,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,2,1,2,1]=>[2,5,3,1,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,1,2,2,1,1]=>[2,5,3,2,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,2,1,1,1,2]=>[2,6,1,2,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,2,1,1,2,1]=>[2,6,1,2,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,2,1,2,1,1]=>[2,6,1,3,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,2,2,1,1,1]=>[2,6,2,1,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,2,2,6]=>[1,1,1,2,1,5]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,2,6,2]=>[1,1,1,2,5,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,6,2,2]=>[1,1,1,6,4,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,2,1,2,6]=>[2,2,3,1,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,2,1,6,2]=>[3,3,4,2,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,2,2,1,6]=>[3,3,4,3,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,2,2,6,1]=>[1,1,2,1,5,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,2,6,1,2]=>[1,1,2,5,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,2,6,2,1]=>[2,2,3,6,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,6,1,2,2]=>[1,1,6,3,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,6,2,1,2]=>[3,3,1,6,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,6,2,2,1]=>[3,3,1,6,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,1,1,2,6]=>[2,3,1,2,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,1,1,6,2]=>[3,4,2,3,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,1,2,1,6]=>[3,4,2,4,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,1,2,6,1]=>[2,3,1,3,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,1,6,1,2]=>[3,4,2,1,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,6,2,1]=>[3,4,2,1,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,2,1,1,6]=>[3,4,3,2,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,2,1,6,1]=>[3,4,3,2,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,2,6,1,1]=>[1,2,1,5,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,6,1,1,2]=>[1,2,5,3,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,6,1,2,1]=>[2,3,6,4,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,6,2,1,1]=>[2,3,6,5,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,1,1,2,2]=>[1,6,3,1,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,6,1,2,1,2]=>[3,1,5,4,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,1,2,2,1]=>[3,1,5,4,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,2,1,1,2]=>[3,1,6,2,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,2,1,2,1]=>[3,1,6,2,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,2,2,1,1]=>[3,1,6,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,1,2,6]=>[2,1,2,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,1,1,1,6,2]=>[3,2,3,3,1,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,2,1,6]=>[3,2,3,4,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,1,2,6,1]=>[2,1,2,3,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,1,6,1,2]=>[3,2,3,1,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,1,6,2,1]=>[3,2,3,1,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,1,2,1,1,6]=>[3,2,4,2,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,1,6,1]=>[3,2,4,2,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,2,6,1,1]=>[2,1,3,6,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,1,1,2]=>[3,2,1,5,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,1,2,1]=>[3,2,1,5,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,6,2,1,1]=>[3,2,1,6,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,1,1,1,6]=>[3,3,2,3,3,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,2,1,1,6,1]=>[3,3,2,3,1,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,1,6,1,1]=>[3,3,2,1,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,6,1,1,1]=>[1,1,5,3,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,6,1,1,1,2]=>[1,5,3,1,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,6,1,1,2,1]=>[2,6,4,2,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,6,1,2,1,1]=>[2,6,4,3,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,6,2,1,1,1]=>[2,6,5,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,1,1,1,2,2]=>[1,3,1,1,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[6,1,1,2,1,2]=>[2,4,2,3,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,1,2,2,1]=>[2,4,2,3,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,1,2,1,1,2]=>[2,4,3,1,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,2,1,2,1]=>[2,4,3,1,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,1,2,2,1,1]=>[2,4,3,2,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,2,1,1,1,2]=>[2,5,1,2,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,2,1,1,2,1]=>[2,5,1,2,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,2,1,2,1,1]=>[2,5,1,3,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,2,2,1,1,1]=>[2,5,2,1,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,2,3,3]=>[1,1,1,2,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,3,2,3]=>[2,2,2,4,1,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,3,3,2]=>[2,2,2,4,2,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,2,1,3,3]=>[2,2,3,1,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,2,3,1,3]=>[1,1,2,2,6,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,2,3,3,1]=>[1,1,2,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,3,1,2,3]=>[1,1,3,6,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,3,1,3,2]=>[3,3,5,1,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,3,2,1,3]=>[2,2,4,1,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,3,2,3,1]=>[3,3,5,2,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,3,3,1,2]=>[1,1,3,1,6,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,3,3,2,1]=>[2,2,4,2,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,2,1,1,3,3]=>[2,3,1,2,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,1,3,1,3]=>[3,4,2,5,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,3,3,1]=>[3,4,2,5,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,1,1,3]=>[1,2,2,6,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,3,1,3,1]=>[3,4,4,1,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,3,3,1,1]=>[1,2,2,1,6,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,1,1,2,3]=>[1,3,6,1,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,1,1,3,2]=>[3,5,1,3,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,1,2,1,3]=>[3,5,1,4,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,1,2,3,1]=>[3,5,1,4,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,1,3,1,2]=>[3,5,1,5,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,1,3,2,1]=>[3,5,1,5,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,1,1,3]=>[2,4,1,1,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,2,1,3,1]=>[3,5,2,2,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,3,1,1]=>[3,5,2,4,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,3,1,1,2]=>[1,3,1,6,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,3,1,2,1]=>[3,5,3,1,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,3,2,1,1]=>[2,4,2,1,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,1,1,3,3]=>[2,1,2,2,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,1,3,1,3]=>[3,2,3,5,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,1,3,3,1]=>[3,2,3,5,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,1,3,1,1,3]=>[3,2,5,1,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,1,3,1]=>[3,2,5,1,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,3,3,1,1]=>[3,2,5,3,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,3,1,1,1,3]=>[1,2,6,1,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,1,1,3,1]=>[3,4,1,3,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,1,3,1,1]=>[3,4,1,5,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,3,1,1,1]=>[1,2,1,6,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,1,1,2,3]=>[1,6,1,1,2,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,1,1,1,3,2]=>[3,1,3,3,5,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,1,2,1,3]=>[3,1,3,4,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,1,2,3,1]=>[3,1,3,4,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,1,1,3,1,2]=>[3,1,3,5,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,3,2,1]=>[3,1,3,5,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,1,2,1,1,3]=>[3,1,4,2,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,2,1,3,1]=>[3,1,4,2,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,2,3,1,1]=>[3,1,4,4,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,1,3,1,1,2]=>[3,1,5,1,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,3,1,2,1]=>[3,1,5,1,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,3,2,1,1]=>[3,1,5,2,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,1,1,1,3]=>[2,1,1,2,2,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,2,1,1,3,1]=>[3,2,2,3,5,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,1,3,1,1]=>[3,2,2,5,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,3,1,1,1]=>[3,2,4,1,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,1,1,1,2]=>[1,1,6,1,1,2]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,3,1,1,2,1]=>[3,3,1,3,4,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,1,2,1,1]=>[3,3,1,4,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,2,1,1,1]=>[2,2,1,1,2,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,2,3,4]=>[1,1,1,2,2,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,2,4,3]=>[2,2,2,3,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,3,2,4]=>[2,2,2,4,1,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,3,4,2]=>[1,1,1,3,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,4,2,3]=>[1,1,1,4,6,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,4,3,2]=>[2,2,2,5,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,2,1,3,4]=>[2,2,3,1,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,1,4,3]=>[2,2,3,1,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,2,3,1,4]=>[1,1,2,2,6,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,2,3,4,1]=>[1,1,2,2,2,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,2,4,1,3]=>[1,1,2,3,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,2,4,3,1]=>[3,3,4,5,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,3,1,2,4]=>[1,1,3,6,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,3,1,4,2]=>[3,3,5,1,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,3,2,1,4]=>[2,2,4,1,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,3,2,4,1]=>[2,2,4,1,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,3,4,1,2]=>[1,1,3,2,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,3,4,2,1]=>[3,3,5,4,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,4,1,2,3]=>[1,1,4,5,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,4,1,3,2]=>[2,2,5,6,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,4,2,1,3]=>[3,3,6,1,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,4,2,3,1]=>[3,3,6,1,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,4,3,1,2]=>[3,3,6,2,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,4,3,2,1]=>[2,2,5,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,2,1,1,3,4]=>[2,3,1,2,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,1,4,3]=>[2,3,1,2,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,1,3,1,4]=>[3,4,2,5,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,3,4,1]=>[2,3,1,4,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,1,4,1,3]=>[2,3,1,5,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,4,3,1]=>[3,4,2,6,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,3,1,1,4]=>[1,2,2,6,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,3,1,4,1]=>[1,2,2,6,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,3,4,1,1]=>[1,2,2,2,5,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,4,1,1,3]=>[1,2,3,5,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,4,1,3,1]=>[1,2,3,5,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,4,3,1,1]=>[3,4,5,2,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,1,1,2,4]=>[1,3,6,1,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,1,1,4,2]=>[3,5,1,3,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,1,2,1,4]=>[3,5,1,4,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,2,4,1]=>[1,3,6,2,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,1,4,1,2]=>[1,3,6,4,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,4,2,1]=>[3,5,1,6,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,2,1,1,4]=>[2,4,1,1,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,2,1,4,1]=>[2,4,1,1,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,4,1,1]=>[2,4,1,4,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,4,1,1,2]=>[1,3,2,5,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,4,1,2,1]=>[2,4,3,6,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,4,2,1,1]=>[3,5,4,1,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,1,2,3]=>[1,4,5,1,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,1,1,3,2]=>[2,5,6,2,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,1,2,1,3]=>[2,5,6,3,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,2,3,1]=>[1,4,5,2,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,1,3,1,2]=>[1,4,5,3,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,3,2,1]=>[2,5,6,4,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,2,1,1,3]=>[3,6,1,2,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,2,1,3,1]=>[3,6,1,2,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,2,3,1,1]=>[3,6,1,4,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,4,3,1,1,2]=>[3,6,2,1,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,3,1,2,1]=>[3,6,2,1,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,3,2,1,1]=>[2,5,1,1,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,1,1,1,3,4]=>[2,1,2,2,4,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,1,1,4,3]=>[2,1,2,2,5,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,1,3,1,4]=>[3,2,3,5,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,3,4,1]=>[2,1,2,4,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,1,4,1,3]=>[2,1,2,5,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,1,4,3,1]=>[3,2,3,6,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,1,3,1,1,4]=>[3,2,5,1,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,3,1,4,1]=>[6,5,1,4,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,1,1]=>[2,1,4,3,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,1,1,3]=>[2,1,5,6,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,4,1,3,1]=>[6,5,2,3,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,3,1,1]=>[3,2,6,2,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,1,1,4]=>[1,2,6,1,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,3,1,1,4,1]=>[1,2,6,1,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,1,4,1,1]=>[1,2,6,4,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,4,1,1,1]=>[1,2,2,5,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,4,1,1,1,3]=>[1,3,5,1,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,1,1,3,1]=>[1,3,5,1,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,1,3,1,1]=>[1,3,5,3,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,3,1,1,1]=>[3,5,2,1,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,1,1,2,4]=>[1,6,1,1,2,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,1,1,4,2]=>[3,1,3,3,6,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,1,2,1,4]=>[3,1,3,4,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,1,2,4,1]=>[1,6,1,2,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,4,1,2]=>[1,6,1,4,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,4,2,1]=>[3,1,3,6,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,2,1,1,4]=>[3,1,4,2,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,2,1,4,1]=>[5,3,6,4,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,4,1,1]=>[1,6,2,3,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,1,1,2]=>[1,6,4,5,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,4,1,2,1]=>[5,3,1,2,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,2,1,1]=>[3,1,6,1,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,2,1,1,1,4]=>[2,1,1,2,2,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,2,1,1,4,1]=>[2,1,1,2,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,1,4,1,1]=>[2,1,1,5,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,4,1,1,1]=>[2,1,4,6,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,4,1,1,1,2]=>[1,2,5,1,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,4,1,1,2,1]=>[2,3,6,2,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,4,1,2,1,1]=>[2,3,6,3,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,4,2,1,1,1]=>[3,4,1,2,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,1,1,2,3]=>[1,5,1,1,2,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,1,1,1,3,2]=>[2,6,2,2,4,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,1,1,2,1,3]=>[2,6,2,3,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,1,2,3,1]=>[1,5,1,2,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,1,3,1,2]=>[1,5,1,3,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,1,3,2,1]=>[2,6,2,4,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,1,2,1,1,3]=>[2,6,3,1,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,2,1,3,1]=>[4,1,5,3,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,3,1,1]=>[1,5,2,2,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,3,1,1,2]=>[1,5,3,6,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,3,1,2,1]=>[4,1,6,2,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,2,1,1]=>[2,6,4,1,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,1,1,1,3]=>[3,1,2,3,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,2,1,1,3,1]=>[3,1,2,3,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,1,3,1,1]=>[3,1,2,5,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,3,1,1,1]=>[3,1,4,1,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,3,1,1,1,2]=>[3,2,1,3,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,1,1,2,1]=>[3,2,1,3,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,1,2,1,1]=>[3,2,1,4,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,2,1,1,1]=>[2,1,1,1,2,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,2,3,5]=>[1,1,1,2,2,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,2,5,3]=>[1,1,1,2,4,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,3,2,5]=>[2,2,2,4,1,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,3,5,2]=>[1,1,1,3,3,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,5,2,3]=>[1,1,1,5,5,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,5,3,2]=>[4,4,4,1,2,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,2,1,3,5]=>[2,2,3,1,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,2,1,5,3]=>[4,4,5,3,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,2,3,1,5]=>[1,1,2,2,6,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,2,3,5,1]=>[1,1,2,2,3,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,2,5,1,3]=>[1,1,2,4,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,2,5,3,1]=>[3,3,4,6,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,3,1,2,5]=>[1,1,3,6,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,3,1,5,2]=>[4,4,6,2,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,3,2,1,5]=>[2,2,4,1,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,3,2,5,1]=>[2,2,4,1,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,3,5,1,2]=>[1,1,3,3,4,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,3,5,2,1]=>[2,2,4,4,6,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,5,1,2,3]=>[1,1,5,4,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,5,1,3,2]=>[2,2,6,5,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,5,2,1,3]=>[4,4,1,1,3,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,5,2,3,1]=>[4,4,1,1,5,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,5,3,1,2]=>[4,4,1,2,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,5,3,2,1]=>[4,4,1,2,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,1,1,3,5]=>[2,3,1,2,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,1,1,5,3]=>[4,5,3,4,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,3,1,5]=>[4,5,3,6,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,3,5,1]=>[2,3,1,4,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,5,1,3]=>[2,3,1,6,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,5,3,1]=>[4,5,3,1,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,1,1,5]=>[1,2,2,6,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,3,1,5,1]=>[1,2,2,6,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,3,5,1,1]=>[1,2,2,3,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,5,1,1,3]=>[1,2,4,4,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,5,1,3,1]=>[1,2,4,4,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,3,1,1]=>[3,4,6,1,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,1,2,5]=>[1,3,6,1,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,1,5,2]=>[4,6,2,4,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,1,2,1,5]=>[4,6,2,5,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,2,5,1]=>[1,3,6,2,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,1,5,1,2]=>[1,3,6,5,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,2,1]=>[4,6,2,1,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,2,1,1,5]=>[2,4,1,1,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,2,1,5,1]=>[2,4,1,1,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,5,1,1]=>[2,4,1,5,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,5,1,1,2]=>[1,3,3,4,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,5,1,2,1]=>[2,4,4,5,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,5,2,1,1]=>[2,4,4,6,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,1,1,2,3]=>[1,5,4,1,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,1,1,3,2]=>[2,6,5,2,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,1,2,1,3]=>[2,6,5,3,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,2,3,1]=>[1,5,4,2,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,1,3,1,2]=>[1,5,4,3,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,3,2,1]=>[2,6,5,4,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,2,1,1,3]=>[4,1,1,3,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,2,1,3,1]=>[4,1,1,3,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,2,3,1,1]=>[4,1,1,5,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,3,1,1,2]=>[4,1,2,2,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,3,1,2,1]=>[4,1,2,2,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,3,2,1,1]=>[4,1,2,3,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,1,3,5]=>[2,1,2,2,4,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,1,1,5,3]=>[4,3,4,4,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,1,3,1,5]=>[4,3,4,6,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,1,3,5,1]=>[2,1,2,4,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,1,5,1,3]=>[2,1,2,6,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,1,5,3,1]=>[4,3,4,1,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,3,1,1,5]=>[4,3,6,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,3,1,5,1]=>[6,5,1,4,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,5,1,1]=>[2,1,4,4,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,5,1,1,3]=>[2,1,6,5,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,5,1,3,1]=>[6,5,3,2,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,3,1,1]=>[4,3,1,2,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,1,1,1,5]=>[1,2,6,1,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,3,1,1,5,1]=>[1,2,6,1,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,1,5,1,1]=>[1,2,6,5,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,5,1,1,1]=>[1,2,3,4,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,5,1,1,1,3]=>[1,4,4,1,1,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,5,1,1,3,1]=>[1,4,4,1,3,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,1,3,1,1]=>[1,4,4,3,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,3,1,1,1]=>[3,6,1,1,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,1,1,2,5]=>[1,6,1,1,2,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,1,1,5,2]=>[4,2,4,4,1,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,1,2,1,5]=>[4,2,4,5,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,1,2,5,1]=>[1,6,1,2,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,1,5,1,2]=>[1,6,1,5,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,5,2,1]=>[4,2,4,1,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,1,2,1,1,5]=>[4,2,5,3,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,1,5,1]=>[5,3,6,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,5,1,1]=>[1,6,2,4,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,5,1,1,2]=>[1,6,5,4,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,1,2,1]=>[5,3,2,1,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,2,1,1]=>[4,2,1,1,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,1,1,1,5]=>[2,1,1,2,2,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,2,1,1,5,1]=>[2,1,1,2,6,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,1,5,1,1]=>[2,1,1,6,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,5,1,1,1]=>[2,1,5,5,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,5,1,1,1,2]=>[1,3,4,1,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,5,1,1,2,1]=>[2,4,5,2,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,1,2,1,1]=>[2,4,5,3,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,2,1,1,1]=>[2,4,6,1,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,1,1,2,3]=>[1,4,1,1,2,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,1,1,1,3,2]=>[2,5,2,2,4,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,1,1,2,1,3]=>[2,5,2,3,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,1,2,3,1]=>[1,4,1,2,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,1,3,1,2]=>[1,4,1,3,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,1,3,2,1]=>[2,5,2,4,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,1,2,1,1,3]=>[2,5,3,1,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,1,3,1]=>[3,6,4,2,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,2,3,1,1]=>[1,4,2,2,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,3,1,1,2]=>[1,4,3,6,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,3,1,2,1]=>[3,6,5,1,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,2,1,1]=>[2,5,4,1,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,1,1,1,3]=>[2,6,1,2,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,1,1,3,1]=>[4,1,3,4,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,1,3,1,1]=>[4,1,3,6,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,3,1,1,1]=>[1,5,2,6,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,3,1,1,1,2]=>[3,1,1,3,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,3,1,1,2,1]=>[3,1,1,3,4,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,1,2,1,1]=>[3,1,1,4,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,2,1,1,1]=>[3,1,2,2,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,2,3,6]=>[1,1,1,2,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,2,6,3]=>[1,1,1,2,5,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,3,2,6]=>[2,2,2,4,1,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,3,6,2]=>[1,1,1,3,4,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,6,2,3]=>[1,1,1,6,4,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,6,3,2]=>[4,4,4,2,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,2,1,3,6]=>[2,2,3,1,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,2,1,6,3]=>[4,4,5,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,2,3,1,6]=>[3,3,4,4,1,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,2,3,6,1]=>[1,1,2,2,4,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,2,6,1,3]=>[1,1,2,5,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,2,6,3,1]=>[4,4,5,1,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,3,1,2,6]=>[1,1,3,6,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,1,6,2]=>[3,3,5,1,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,3,2,1,6]=>[3,3,5,2,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,3,2,6,1]=>[2,2,4,1,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,3,6,1,2]=>[1,1,3,4,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,3,6,2,1]=>[2,2,4,5,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,6,1,2,3]=>[1,1,6,3,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,6,1,3,2]=>[3,3,1,5,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,6,2,1,3]=>[3,3,1,6,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,6,2,3,1]=>[3,3,1,6,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,6,3,1,2]=>[4,4,2,1,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,6,3,2,1]=>[4,4,2,1,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,1,1,3,6]=>[2,3,1,2,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,1,1,6,3]=>[4,5,3,4,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,3,1,6]=>[3,4,2,5,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,3,6,1]=>[2,3,1,4,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,6,1,3]=>[3,4,2,1,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,6,3,1]=>[4,5,3,2,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,1,1,6]=>[3,4,4,1,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,2,3,1,6,1]=>[3,4,4,1,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,3,6,1,1]=>[1,2,2,4,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,6,1,1,3]=>[1,2,5,3,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,6,1,3,1]=>[1,2,5,3,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,3,1,1]=>[4,5,1,1,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,1,1,2,6]=>[1,3,6,1,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,1,1,6,2]=>[3,5,1,3,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,1,2,1,6]=>[3,5,1,4,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,1,2,6,1]=>[1,3,6,2,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,1,6,1,2]=>[3,5,1,1,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,1,6,2,1]=>[3,5,1,1,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,2,1,1,6]=>[3,5,2,2,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,2,1,6,1]=>[3,5,2,2,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,2,6,1,1]=>[2,4,1,6,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,6,1,1,2]=>[1,3,4,3,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,6,1,2,1]=>[2,4,5,4,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,6,2,1,1]=>[2,4,5,5,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,1,1,2,3]=>[1,6,3,1,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,6,1,1,3,2]=>[3,1,5,3,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,6,1,2,1,3]=>[3,1,5,4,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,1,2,3,1]=>[3,1,5,4,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,6,1,3,1,2]=>[3,1,5,5,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,1,3,2,1]=>[3,1,5,5,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,6,2,1,1,3]=>[3,1,6,2,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,2,1,3,1]=>[3,1,6,2,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,2,3,1,1]=>[3,1,6,4,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,6,3,1,1,2]=>[4,2,1,2,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,3,1,2,1]=>[4,2,1,2,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,3,2,1,1]=>[4,2,1,3,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,1,3,6]=>[2,1,2,2,4,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,1,1,6,3]=>[4,3,4,4,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,1,3,1,6]=>[3,2,3,5,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,1,3,6,1]=>[2,1,2,4,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,1,6,1,3]=>[3,2,3,1,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,1,6,3,1]=>[4,3,4,2,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,3,1,1,6]=>[3,2,5,1,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,3,1,6,1]=>[3,2,5,1,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,3,6,1,1]=>[2,1,4,5,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,6,1,1,3]=>[3,2,1,5,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,6,1,3,1]=>[3,2,1,5,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,6,3,1,1]=>[4,3,2,1,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,1,1,1,6]=>[3,4,1,3,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,3,1,1,6,1]=>[3,4,1,3,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,1,6,1,1]=>[3,4,1,1,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,6,1,1,1]=>[1,2,4,3,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,6,1,1,1,3]=>[1,5,3,1,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,6,1,1,3,1]=>[1,5,3,1,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,6,1,3,1,1]=>[1,5,3,3,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,6,3,1,1,1]=>[4,1,1,2,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,1,1,2,6]=>[1,6,1,1,2,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,1,1,6,2]=>[3,1,3,3,1,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,1,2,1,6]=>[3,1,3,4,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,1,2,6,1]=>[1,6,1,2,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,6,1,2]=>[3,1,3,1,5,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,6,2,1]=>[3,1,3,1,6,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,2,1,1,6]=>[3,1,4,2,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,2,1,6,1]=>[3,1,4,2,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,2,6,1,1]=>[1,6,2,5,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,6,1,1,2]=>[3,1,1,5,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,6,1,2,1]=>[3,1,1,5,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,6,2,1,1]=>[3,1,1,6,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,2,1,1,1,6]=>[3,2,2,3,3,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,1,1,6,1]=>[3,2,2,3,1,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,1,6,1,1]=>[3,2,2,1,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,6,1,1,1]=>[2,1,6,4,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,6,1,1,1,2]=>[1,4,3,1,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,6,1,1,2,1]=>[2,5,4,2,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,6,1,2,1,1]=>[2,5,4,3,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,6,2,1,1,1]=>[2,5,5,1,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,1,1,1,2,3]=>[1,3,1,1,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[6,1,1,1,3,2]=>[2,4,2,2,4,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[6,1,1,2,1,3]=>[2,4,2,3,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,1,2,3,1]=>[1,3,1,2,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,1,1,3,1,2]=>[1,3,1,3,6,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,1,3,2,1]=>[2,4,2,4,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[6,1,2,1,1,3]=>[2,4,3,1,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,2,1,3,1]=>[3,5,4,2,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,1,2,3,1,1]=>[1,3,2,2,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,1,3,1,1,2]=>[1,3,3,6,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,3,1,2,1]=>[3,5,5,1,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,1,3,2,1,1]=>[2,4,4,1,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[6,2,1,1,1,3]=>[2,5,1,2,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,2,1,1,3,1]=>[3,6,2,3,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,1,3,1,1]=>[3,6,2,5,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,3,1,1,1]=>[1,4,2,6,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,3,1,1,1,2]=>[1,5,6,1,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,3,1,1,2,1]=>[4,1,2,4,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,1,2,1,1]=>[4,1,2,5,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,2,1,1,1]=>[2,6,1,1,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,2,4,4]=>[1,1,1,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,4,2,4]=>[1,1,1,4,6,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,4,4,2]=>[1,1,1,4,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,2,1,4,4]=>[2,2,3,1,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,2,4,1,4]=>[1,1,2,3,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,4,4,1]=>[1,1,2,3,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,4,1,2,4]=>[1,1,4,5,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,4,1,4,2]=>[5,5,1,2,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,4,2,1,4]=>[5,5,1,3,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,4,2,4,1]=>[1,1,4,6,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,4,4,1,2]=>[1,1,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,4,4,2,1]=>[3,3,6,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,1,1,4,4]=>[2,3,1,2,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,1,4,1,4]=>[5,6,4,1,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,4,4,1]=>[2,3,1,5,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,4,1,1,4]=>[1,2,3,5,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,4,1,4,1]=>[1,2,3,5,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,4,1,1]=>[1,2,3,1,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,1,2,4]=>[1,4,5,1,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,4,2]=>[5,1,2,5,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,1,2,1,4]=>[5,1,2,6,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,1,2,4,1]=>[1,4,5,2,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,1,4,1,2]=>[5,1,2,1,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,1,4,2,1]=>[5,1,2,1,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,2,1,1,4]=>[5,1,3,4,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,2,1,4,1]=>[5,1,3,4,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,2,4,1,1]=>[1,4,6,3,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,4,1,1,2]=>[1,4,1,5,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,4,1,2,1]=>[2,5,2,6,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,4,2,1,1]=>[3,6,3,1,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,1,4,4]=>[2,1,2,2,5,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,1,1,4,1,4]=>[5,4,5,1,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,1,4,4,1]=>[2,1,2,5,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,4,1,1,4]=>[5,4,1,2,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,4,1,4,1]=>[5,4,1,2,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,4,4,1,1]=>[2,1,5,2,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,4,1,1,1,4]=>[1,3,5,1,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,4,1,1,4,1]=>[1,3,5,1,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,1,4,1,1]=>[1,3,5,4,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,4,1,1,1]=>[1,3,1,5,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,1,1,2,4]=>[1,5,1,1,2,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,1,4,2]=>[1,5,1,1,4,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,1,2,1,4]=>[2,6,2,3,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,1,2,4,1]=>[1,5,1,2,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,1,4,1,2]=>[1,5,1,4,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,1,4,2,1]=>[5,2,5,1,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,2,1,1,4]=>[2,6,3,1,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,1,4,1]=>[5,2,6,4,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,2,4,1,1]=>[1,5,2,3,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,4,1,1,2]=>[1,5,4,5,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,4,1,2,1]=>[5,2,1,2,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,4,2,1,1]=>[5,2,1,3,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,4]=>[3,1,2,3,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,2,1,1,4,1]=>[5,3,4,5,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,4,1,1]=>[5,3,4,1,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,4,1,1,1]=>[1,6,3,5,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,1,1,1,2]=>[1,1,5,1,1,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,4,1,1,2,1]=>[2,2,6,2,3,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,4,1,2,1,1]=>[2,2,6,3,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,4,2,1,1,1]=>[3,3,1,2,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,2,4,5]=>[1,1,1,2,3,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,2,5,4]=>[2,2,2,3,5,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,4,2,5]=>[1,1,1,4,6,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,4,5,2]=>[1,1,1,4,2,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,5,2,4]=>[1,1,1,5,5,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,5,4,2]=>[4,4,4,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,2,1,4,5]=>[2,2,3,1,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,2,1,5,4]=>[2,2,3,1,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,2,4,1,5]=>[1,1,2,3,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,4,5,1]=>[1,1,2,3,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,2,5,1,4]=>[1,1,2,4,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,2,5,4,1]=>[2,2,3,5,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,4,1,2,5]=>[1,1,4,5,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,4,1,5,2]=>[5,5,1,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,4,2,1,5]=>[5,5,1,3,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,4,2,5,1]=>[5,5,1,3,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,4,5,1,2]=>[1,1,4,2,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,4,5,2,1]=>[2,2,5,3,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,5,1,2,4]=>[1,1,5,4,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,5,1,4,2]=>[5,5,2,1,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,5,2,1,4]=>[5,5,2,2,4,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,5,2,4,1]=>[4,4,1,1,6,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,5,4,1,2]=>[4,4,1,3,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,5,4,2,1]=>[4,4,1,3,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,1,1,4,5]=>[2,3,1,2,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,1,1,5,4]=>[2,3,1,2,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,1,4,1,5]=>[5,6,4,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,1,4,5,1]=>[2,3,1,5,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,1,5,1,4]=>[5,6,4,2,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,1,5,4,1]=>[4,5,3,1,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,2,4,1,1,5]=>[1,2,3,5,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,4,1,5,1]=>[1,2,3,5,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,5,1,1]=>[1,2,3,2,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,5,1,1,4]=>[1,2,4,4,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,2,5,1,4,1]=>[5,6,1,1,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,5,4,1,1]=>[2,3,5,1,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,1,2,5]=>[1,4,5,1,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,1,1,5,2]=>[5,1,2,5,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,4,1,2,1,5]=>[5,1,2,6,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,1,2,5,1]=>[5,1,2,6,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,1,5,1,2]=>[5,1,2,2,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,1,5,2,1]=>[5,1,2,2,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,4,2,1,1,5]=>[5,1,3,4,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,2,1,5,1]=>[5,1,3,4,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,2,5,1,1]=>[5,1,3,1,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,4,5,1,1,2]=>[1,4,2,4,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,4,5,1,2,1]=>[2,5,3,5,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,5,2,1,1]=>[2,5,3,6,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,1,2,4]=>[1,5,4,1,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,1,4,2]=>[5,2,1,5,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,1,2,1,4]=>[5,2,1,6,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,1,2,4,1]=>[1,5,4,2,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,1,4,1,2]=>[5,2,1,1,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,5,1,4,2,1]=>[5,2,1,1,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,2,1,1,4]=>[5,2,2,4,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,2,1,4,1]=>[5,2,2,4,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,2,4,1,1]=>[4,1,1,6,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,5,4,1,1,2]=>[4,1,3,1,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,4,1,2,1]=>[4,1,3,1,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,4,2,1,1]=>[4,1,3,2,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,1,4,5]=>[2,1,2,2,5,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,1,5,4]=>[2,1,2,2,6,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,1,4,1,5]=>[5,4,5,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,1,4,5,1]=>[2,1,2,5,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,1,5,1,4]=>[5,4,5,2,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,1,5,4,1]=>[4,3,4,1,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,1,4,1,1,5]=>[5,4,1,2,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,4,1,5,1]=>[5,4,1,2,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,4,5,1,1]=>[2,1,5,3,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,5,1,1,4]=>[5,4,2,1,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,5,1,4,1]=>[5,4,2,1,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,5,4,1,1]=>[4,3,1,3,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,1,1,1,5]=>[1,3,5,1,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,4,1,1,5,1]=>[1,3,5,1,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,1,5,1,1]=>[1,3,5,5,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,5,1,1,1]=>[1,3,2,4,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,5,1,1,1,4]=>[1,4,4,1,1,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[2,5,1,1,4,1]=>[5,1,1,5,1,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,1,4,1,1]=>[5,1,1,1,2,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,4,1,1,1]=>[2,5,1,6,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,1,1,2,5]=>[1,5,1,1,2,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,1,1,5,2]=>[4,1,4,4,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,1,1,2,1,5]=>[4,1,4,5,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,1,2,5,1]=>[1,5,1,2,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,1,5,1,2]=>[1,5,1,5,4,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,1,5,2,1]=>[4,1,4,1,1,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[4,1,2,1,1,5]=>[4,1,5,3,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,2,1,5,1]=>[5,2,6,4,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,2,5,1,1]=>[1,5,2,4,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,5,1,1,2]=>[1,5,5,4,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,5,1,2,1]=>[5,2,2,1,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,5,2,1,1]=>[4,1,1,1,3,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[4,2,1,1,1,5]=>[4,2,3,4,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,1,1,5,1]=>[5,3,4,5,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,5,1,1]=>[5,3,4,2,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,5,1,1,1]=>[1,6,4,4,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,5,1,1,1,2]=>[1,2,4,1,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,5,1,1,2,1]=>[2,3,5,2,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,5,1,2,1,1]=>[2,3,5,3,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,5,2,1,1,1]=>[2,3,6,1,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,1,1,2,4]=>[1,4,1,1,2,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,1,1,4,2]=>[1,4,1,1,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,1,1,2,1,4]=>[2,5,2,3,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,1,1,2,4,1]=>[1,4,1,2,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,1,4,1,2]=>[1,4,1,4,5,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,1,4,2,1]=>[5,1,5,1,3,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,1,2,1,1,4]=>[2,5,3,1,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,1,2,1,4,1]=>[5,1,6,4,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,2,4,1,1]=>[1,4,2,3,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,4,1,1,2]=>[1,4,4,5,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,4,1,2,1]=>[5,1,1,2,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,4,2,1,1]=>[5,1,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,1,1,1,4]=>[2,6,1,2,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,2,1,1,4,1]=>[5,2,4,5,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,1,4,1,1]=>[5,2,4,1,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,4,1,1,1]=>[1,5,3,5,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,4,1,1,1,2]=>[2,1,6,2,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,4,1,1,2,1]=>[2,1,6,2,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,1,2,1,1]=>[2,1,6,3,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,2,1,1,1]=>[3,2,1,2,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,2,4,6]=>[1,1,1,2,3,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,2,6,4]=>[1,1,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,4,2,6]=>[1,1,1,4,6,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,4,6,2]=>[1,1,1,4,3,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,6,2,4]=>[1,1,1,6,4,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,6,4,2]=>[3,3,3,1,1,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,2,1,4,6]=>[2,2,3,1,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,2,1,6,4]=>[3,3,4,2,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,2,4,1,6]=>[1,1,2,3,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,4,6,1]=>[1,1,2,3,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,2,6,1,4]=>[1,1,2,5,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,6,4,1]=>[4,4,5,1,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,4,1,2,6]=>[1,1,4,5,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,4,1,6,2]=>[5,5,1,2,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,4,2,1,6]=>[3,3,6,1,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,4,2,6,1]=>[1,1,4,6,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,4,6,1,2]=>[1,1,4,3,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,4,6,2,1]=>[2,2,5,4,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,6,1,2,4]=>[1,1,6,3,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,6,1,4,2]=>[3,3,1,5,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,6,2,1,4]=>[5,5,3,1,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,6,2,4,1]=>[1,1,6,4,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,6,4,1,2]=>[4,4,2,2,1,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,6,4,2,1]=>[3,3,1,1,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,1,1,4,6]=>[2,3,1,2,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,1,1,6,4]=>[3,4,2,3,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,1,4,1,6]=>[5,6,4,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,4,6,1]=>[2,3,1,5,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,6,1,4]=>[3,4,2,1,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,6,4,1]=>[4,5,3,2,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,4,1,1,6]=>[1,2,3,5,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,4,1,6,1]=>[1,2,3,5,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,4,6,1,1]=>[1,2,3,3,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,6,1,1,4]=>[1,2,5,3,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,6,1,4,1]=>[1,2,5,3,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,6,4,1,1]=>[4,5,1,2,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,1,1,2,6]=>[1,4,5,1,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,1,1,6,2]=>[5,1,2,5,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,1,2,1,6]=>[5,1,2,6,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,2,6,1]=>[1,4,5,2,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,1,6,1,2]=>[1,4,5,6,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,6,2,1]=>[5,1,2,3,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,2,1,1,6]=>[3,6,1,2,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,2,1,6,1]=>[3,6,1,2,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,2,6,1,1]=>[1,4,6,5,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,6,1,1,2]=>[1,4,3,3,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,4,6,1,2,1]=>[2,5,4,4,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,4,6,2,1,1]=>[2,5,4,5,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,1,1,2,4]=>[1,6,3,1,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,6,1,1,4,2]=>[3,1,5,3,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,1,2,1,4]=>[3,1,5,4,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,2,4,1]=>[1,6,3,2,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,1,4,1,2]=>[1,6,3,4,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,4,2,1]=>[3,1,5,6,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,2,1,1,4]=>[5,3,1,4,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,2,1,4,1]=>[5,3,1,4,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,6,2,4,1,1]=>[1,6,4,3,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,4,1,1,2]=>[4,2,2,1,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,4,1,2,1]=>[4,2,2,1,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,4,2,1,1]=>[3,1,1,1,2,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,1,1,4,6]=>[2,1,2,2,5,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,1,1,6,4]=>[3,2,3,3,1,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,1,1,4,1,6]=>[5,4,5,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,4,6,1]=>[2,1,2,5,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,1,6,1,4]=>[3,2,3,1,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,6,4,1]=>[4,3,4,2,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,4,1,1,6]=>[5,4,1,2,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,1,6,1]=>[6,5,2,3,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,6,1,1]=>[2,1,5,4,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,6,1,1,4]=>[3,2,1,5,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,6,1,4,1]=>[6,5,4,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,4,1,1]=>[4,3,2,2,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,4,1,1,1,6]=>[1,3,5,1,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,4,1,1,6,1]=>[1,3,5,1,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,1,6,1,1]=>[1,3,5,6,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,6,1,1,1]=>[1,3,3,3,1,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[2,6,1,1,1,4]=>[1,5,3,1,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,6,1,1,4,1]=>[1,5,3,1,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,1,4,1,1]=>[1,5,3,4,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,4,1,1,1]=>[4,1,2,1,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,1,1,1,2,6]=>[1,5,1,1,2,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[4,1,1,1,6,2]=>[1,5,1,1,6,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,1,2,1,6]=>[4,1,4,5,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,1,1,2,6,1]=>[1,5,1,2,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,1,6,1,2]=>[1,5,1,6,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,1,6,2,1]=>[5,2,5,3,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,2,1,1,6]=>[4,1,5,3,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,1,2,1,6,1]=>[4,1,5,3,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,6,1,1]=>[1,5,2,5,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,6,1,1,2]=>[1,5,6,3,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,6,1,2,1]=>[4,1,2,6,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,2,1,1]=>[5,2,3,1,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,1,6]=>[3,1,2,3,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,2,1,1,6,1]=>[3,1,2,3,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,1,6,1,1]=>[3,1,2,1,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,6,1,1,1]=>[1,6,5,3,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,6,1,1,1,2]=>[1,3,3,1,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,6,1,1,2,1]=>[2,4,4,2,3,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,6,1,2,1,1]=>[2,4,4,3,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,6,2,1,1,1]=>[2,4,5,1,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,1,1,1,2,4]=>[1,3,1,1,2,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,1,1,4,2]=>[1,3,1,1,4,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[6,1,1,2,1,4]=>[2,4,2,3,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,1,2,4,1]=>[1,3,1,2,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,1,4,1,2]=>[1,3,1,4,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,1,4,2,1]=>[3,5,3,6,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,1,2,1,1,4]=>[2,4,3,1,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,2,1,4,1]=>[2,4,3,1,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,2,4,1,1]=>[1,3,2,3,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,4,1,1,2]=>[1,3,4,5,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,4,1,2,1]=>[2,4,5,6,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,2,1,1]=>[3,5,6,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,1,1,1,4]=>[2,5,1,2,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,2,1,1,4,1]=>[5,1,4,5,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,1,4,1,1]=>[5,1,4,1,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,4,1,1,1]=>[1,4,3,5,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,4,1,1,1,2]=>[1,6,5,1,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,4,1,1,2,1]=>[4,2,1,4,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,1,2,1,1]=>[4,2,1,5,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,2,1,1,1]=>[3,1,1,2,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,2,5,5]=>[1,1,1,2,4,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,5,2,5]=>[1,1,1,5,5,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,5,5,2]=>[1,1,1,5,1,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,2,1,5,5]=>[2,2,3,1,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,2,5,1,5]=>[1,1,2,4,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,5,5,1]=>[1,1,2,4,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,5,1,2,5]=>[1,1,5,4,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,5,1,5,2]=>[5,5,2,1,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,5,2,1,5]=>[4,4,1,1,3,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,5,2,5,1]=>[5,5,2,2,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,5,5,1,2]=>[1,1,5,1,4,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,5,5,2,1]=>[4,4,1,4,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,2,1,1,5,5]=>[2,3,1,2,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,1,5,1,5]=>[5,6,4,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,1,5,5,1]=>[2,3,1,6,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,5,1,1,5]=>[1,2,4,4,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,5,1,5,1]=>[5,6,1,1,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,5,5,1,1]=>[1,2,4,1,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,5,1,1,2,5]=>[1,5,4,1,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,1,1,5,2]=>[5,2,1,5,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,5,1,2,1,5]=>[5,2,1,6,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,1,2,5,1]=>[5,2,1,6,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,5,1,5,1,2]=>[5,2,1,2,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,5,1,5,2,1]=>[5,2,1,2,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,2,1,1,5]=>[4,1,1,3,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,5,2,1,5,1]=>[5,2,2,4,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,2,5,1,1]=>[5,2,2,1,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,5,1,1,2]=>[1,5,1,4,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,5,1,2,1]=>[2,6,2,5,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,5,2,1,1]=>[4,1,4,1,3,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,1,1,5,5]=>[2,1,2,2,6,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,1,1,5,1,5]=>[5,4,5,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,1,5,5,1]=>[2,1,2,6,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,5,1,1,5]=>[5,4,2,1,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,5,1,5,1]=>[5,4,2,1,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,5,5,1,1]=>[2,1,6,2,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,1,1,5]=>[1,4,4,1,1,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,5,1,1,5,1]=>[5,1,1,5,2,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,1,5,1,1]=>[5,1,1,2,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,5,1,1,1]=>[1,4,1,4,1,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[5,1,1,1,2,5]=>[1,4,1,1,2,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,1,1,1,5,2]=>[1,4,1,1,5,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[5,1,1,2,1,5]=>[2,5,2,3,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,1,2,5,1]=>[1,4,1,2,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[5,1,1,5,1,2]=>[1,4,1,5,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,1,5,2,1]=>[5,1,5,2,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,2,1,1,5]=>[2,5,3,1,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,2,1,5,1]=>[5,1,6,4,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,2,5,1,1]=>[1,4,2,4,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[5,1,5,1,1,2]=>[1,4,5,4,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,5,1,2,1]=>[5,1,2,1,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,5,2,1,1]=>[5,1,2,2,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,1,1,1,5]=>[4,1,3,4,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,2,1,1,5,1]=>[5,2,4,5,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,1,5,1,1]=>[5,2,4,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,5,1,1,1]=>[1,5,4,4,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,5,1,1,1,2]=>[1,1,4,1,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,5,1,1,2,1]=>[2,2,5,2,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,5,1,2,1,1]=>[2,2,5,3,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,5,2,1,1,1]=>[2,2,6,1,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,2,5,6]=>[1,1,1,2,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,2,6,5]=>[2,2,2,3,6,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,5,2,6]=>[4,4,4,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,5,6,2]=>[1,1,1,5,2,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,6,2,5]=>[1,1,1,6,4,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,6,5,2]=>[4,4,4,2,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,2,1,5,6]=>[2,2,3,1,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,2,1,6,5]=>[3,3,4,2,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,5,1,6]=>[1,1,2,4,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,2,5,6,1]=>[1,1,2,4,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,2,6,1,5]=>[1,1,2,5,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,6,5,1]=>[2,2,3,6,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,5,1,2,6]=>[1,1,5,4,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,5,1,6,2]=>[5,5,2,1,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,5,2,1,6]=>[4,4,1,1,3,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,5,2,6,1]=>[4,4,1,1,1,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,5,6,1,2]=>[1,1,5,2,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,5,6,2,1]=>[2,2,6,3,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,6,1,2,5]=>[1,1,6,3,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,6,1,5,2]=>[4,4,2,6,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,6,2,1,5]=>[5,5,3,1,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,6,2,5,1]=>[5,5,3,1,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,6,5,1,2]=>[3,3,1,2,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,6,5,2,1]=>[4,4,2,3,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,1,1,5,6]=>[2,3,1,2,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,1,1,6,5]=>[3,4,2,3,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,5,1,6]=>[5,6,4,2,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,5,6,1]=>[2,3,1,6,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,1,6,1,5]=>[4,5,3,2,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,6,5,1]=>[3,4,2,1,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,5,1,1,6]=>[1,2,4,4,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,5,1,6,1]=>[1,2,4,4,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,6,1,1]=>[1,2,4,2,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,6,1,1,5]=>[1,2,5,3,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,6,1,5,1]=>[1,2,5,3,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,6,5,1,1]=>[2,3,6,1,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,1,2,6]=>[1,5,4,1,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,1,1,6,2]=>[5,2,1,5,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,1,2,1,6]=>[5,2,1,6,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,2,6,1]=>[1,5,4,2,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,1,6,1,2]=>[1,5,4,6,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,6,2,1]=>[5,2,1,3,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,2,1,1,6]=>[4,1,1,3,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,5,2,1,6,1]=>[4,1,1,3,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,2,6,1,1]=>[4,1,1,1,6,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,5,6,1,1,2]=>[1,5,2,3,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,5,6,1,2,1]=>[2,6,3,4,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,6,2,1,1]=>[2,6,3,5,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,1,1,2,5]=>[1,6,3,1,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,1,1,5,2]=>[4,2,6,4,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,6,1,2,1,5]=>[4,2,6,5,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,2,5,1]=>[1,6,3,2,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,1,5,1,2]=>[1,6,3,5,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,5,2,1]=>[4,2,6,1,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,2,1,1,5]=>[5,3,1,4,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,2,1,5,1]=>[5,3,1,4,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,6,2,5,1,1]=>[5,3,1,1,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,6,5,1,1,2]=>[3,1,2,6,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,5,1,2,1]=>[3,1,2,6,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,5,2,1,1]=>[4,2,3,1,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,1,5,6]=>[2,1,2,2,6,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,1,1,1,6,5]=>[3,2,3,3,1,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,5,1,6]=>[5,4,5,2,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,5,6,1]=>[2,1,2,6,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,1,6,1,5]=>[4,3,4,2,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,1,6,5,1]=>[3,2,3,1,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,1,5,1,1,6]=>[5,4,2,1,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,5,1,6,1]=>[6,5,3,2,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,6,1,1]=>[2,1,6,3,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,1,1,5]=>[4,3,2,6,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,6,1,5,1]=>[6,5,4,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,5,1,1]=>[3,2,1,2,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,5,1,1,1,6]=>[1,4,4,1,1,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,5,1,1,6,1]=>[1,4,4,1,6,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,1,6,1,1]=>[1,4,4,6,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,6,1,1,1]=>[1,4,2,3,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,6,1,1,1,5]=>[1,5,3,1,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,6,1,1,5,1]=>[1,5,3,1,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,1,5,1,1]=>[1,5,3,5,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,5,1,1,1]=>[2,6,1,5,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,1,1,2,6]=>[1,4,1,1,2,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,1,1,1,6,2]=>[1,4,1,1,6,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,1,1,2,1,6]=>[3,6,3,4,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,1,2,6,1]=>[1,4,1,2,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,1,6,1,2]=>[1,4,1,6,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,1,6,2,1]=>[5,1,5,3,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,1,2,1,1,6]=>[3,6,4,2,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,2,1,6,1]=>[3,6,4,2,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,2,6,1,1]=>[1,4,2,5,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,6,1,1,2]=>[1,4,6,3,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,6,1,2,1]=>[3,6,1,5,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,6,2,1,1]=>[5,1,3,1,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,1,1,1,6]=>[4,1,3,4,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,2,1,1,6,1]=>[4,1,3,4,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,1,6,1,1]=>[4,1,3,2,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,6,1,1,1]=>[1,5,5,3,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,6,1,1,1,2]=>[1,2,3,1,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[5,6,1,1,2,1]=>[2,3,4,2,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,6,1,2,1,1]=>[2,3,4,3,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,6,2,1,1,1]=>[2,3,5,1,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,1,1,1,2,5]=>[1,3,1,1,2,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[6,1,1,1,5,2]=>[1,3,1,1,5,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[6,1,1,2,1,5]=>[2,4,2,3,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,1,2,5,1]=>[1,3,1,2,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,1,5,1,2]=>[1,3,1,5,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,1,5,2,1]=>[4,6,4,1,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,1,2,1,1,5]=>[2,4,3,1,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,2,1,5,1]=>[2,4,3,1,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,2,5,1,1]=>[1,3,2,4,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,5,1,1,2]=>[1,3,5,4,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,5,1,2,1]=>[2,4,6,5,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,5,2,1,1]=>[4,6,1,1,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,2,1,1,1,5]=>[2,5,1,2,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,2,1,1,5,1]=>[5,1,4,5,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,1,5,1,1]=>[5,1,4,2,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,5,1,1,1]=>[1,4,4,4,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[6,5,1,1,1,2]=>[2,1,5,2,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,5,1,1,2,1]=>[2,1,5,2,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,5,1,2,1,1]=>[2,1,5,3,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,5,2,1,1,1]=>[2,1,6,1,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,3,3,3]=>[1,1,1,3,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,3,1,3,3]=>[1,1,3,6,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,3,3,1,3]=>[1,1,3,1,6,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,3,3,3,1]=>[1,1,3,1,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,3,1,1,3,3]=>[1,3,6,1,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,1,3,1,3]=>[6,1,4,1,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,3,1,3,3,1]=>[3,5,1,5,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,3,1,1,3]=>[1,3,1,6,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,3,1,3,1]=>[3,5,3,1,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,3,3,1,1]=>[1,3,1,1,6,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,1,1,3,3]=>[1,6,1,1,3,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,1,3,1,3]=>[3,1,3,5,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,1,3,3,1]=>[3,1,3,5,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,3,1,1,3]=>[3,1,5,1,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,3,1,3,1]=>[3,1,5,1,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,1,3,3,1,1]=>[3,1,5,3,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,1,1,1,3]=>[1,1,6,1,1,3]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,3,1,1,3,1]=>[3,3,1,3,5,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,1,3,1,1]=>[3,3,1,5,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,3,1,1,1]=>[1,1,1,6,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,3,3,4]=>[1,1,1,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,3,4,3]=>[2,2,2,4,3,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,4,3,3]=>[2,2,2,5,1,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,3,1,3,4]=>[1,1,3,6,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,3,1,4,3]=>[3,3,5,1,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,3,3,1,4]=>[1,1,3,1,6,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,3,3,4,1]=>[1,1,3,1,2,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,3,4,1,3]=>[1,1,3,2,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,3,4,3,1]=>[3,3,5,4,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,4,1,3,3]=>[1,1,4,5,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,4,3,1,3]=>[3,3,6,2,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,4,3,3,1]=>[3,3,6,2,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,3,1,1,3,4]=>[1,3,6,1,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,1,1,4,3]=>[3,5,1,3,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,1,3,1,4]=>[6,1,4,1,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,1,3,4,1]=>[1,3,6,3,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,1,4,1,3]=>[6,1,4,2,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,4,3,1]=>[3,5,1,6,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,3,1,1,4]=>[1,3,1,6,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,3,1,4,1]=>[1,3,1,6,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,3,4,1,1]=>[1,3,1,2,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,4,1,1,3]=>[1,3,2,5,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,4,1,3,1]=>[1,3,2,5,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,4,3,1,1]=>[3,5,4,2,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,1,3,3]=>[1,4,5,1,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,1,3,1,3]=>[6,2,3,1,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,1,3,3,1]=>[1,4,5,3,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,3,1,1,3]=>[3,6,2,1,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,1,3,1]=>[3,6,2,1,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,3,3,1,1]=>[3,6,2,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,1,1,3,4]=>[1,6,1,1,3,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,1,1,4,3]=>[3,1,3,3,6,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,1,3,1,4]=>[3,1,3,5,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,1,3,4,1]=>[1,6,1,3,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,4,1,3]=>[1,6,1,4,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,1,4,3,1]=>[3,1,3,6,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,3,1,1,4]=>[3,1,5,1,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,3,1,4,1]=>[6,4,1,4,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,3,4,1,1]=>[1,6,3,2,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,1,1,3]=>[1,6,4,5,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,1,3,1]=>[6,4,2,3,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,4,3,1,1]=>[3,1,6,2,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,1,1,1,4]=>[1,1,6,1,1,4]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[3,3,1,1,4,1]=>[1,1,6,1,4,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,1,4,1,1]=>[1,1,6,4,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,4,1,1,1]=>[1,1,2,5,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[3,4,1,1,1,3]=>[1,2,5,1,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,4,1,1,3,1]=>[1,2,5,1,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,1,3,1,1]=>[1,2,5,3,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,3,1,1,1]=>[3,4,2,1,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,1,1,3,3]=>[1,5,1,1,3,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,1,3,1,3]=>[1,5,1,3,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,1,3,3,1]=>[1,5,1,3,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,1,3,1,1,3]=>[1,5,3,6,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,3,1,3,1]=>[6,3,1,4,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,1,3,3,1,1]=>[1,5,3,1,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,3,1,1,1,3]=>[3,2,1,3,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,3,1,1,3,1]=>[3,2,1,3,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,1,3,1,1]=>[3,2,1,5,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,3,1,1,1]=>[3,2,3,1,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,3,3,5]=>[1,1,1,3,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,3,5,3]=>[1,1,1,3,3,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,5,3,3]=>[1,1,1,5,6,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,3,1,3,5]=>[1,1,3,6,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,3,1,5,3]=>[4,4,6,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,3,3,1,5]=>[1,1,3,1,6,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,3,3,5,1]=>[1,1,3,1,3,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,5,1,3]=>[1,1,3,3,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,3,5,3,1]=>[3,3,5,5,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,5,1,3,3]=>[1,1,5,4,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,5,3,1,3]=>[4,4,1,2,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,5,3,3,1]=>[4,4,1,2,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,1,1,3,5]=>[1,3,6,1,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,3,1,1,5,3]=>[4,6,2,4,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,1,3,1,5]=>[6,1,4,1,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,1,3,5,1]=>[6,1,4,1,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,1,5,1,3]=>[6,1,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,5,3,1]=>[4,6,2,1,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,3,3,1,1,5]=>[1,3,1,6,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,3,1,5,1]=>[1,3,1,6,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,3,5,1,1]=>[1,3,1,3,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,5,1,1,3]=>[1,3,3,4,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,5,1,3,1]=>[6,1,1,2,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,5,3,1,1]=>[3,5,5,1,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,5,1,1,3,3]=>[1,5,4,1,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,1,3,1,3]=>[6,3,2,1,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,1,3,3,1]=>[1,5,4,3,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,3,1,1,3]=>[4,1,2,2,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,3,1,3,1]=>[4,1,2,2,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,5,3,3,1,1]=>[4,1,2,4,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,1,3,5]=>[1,6,1,1,3,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[3,1,1,1,5,3]=>[4,2,4,4,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,3,1,5]=>[4,2,4,6,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,1,3,5,1]=>[1,6,1,3,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,5,1,3]=>[1,6,1,5,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,1,5,3,1]=>[4,2,4,1,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,1,3,1,1,5]=>[4,2,6,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,3,1,5,1]=>[6,4,1,4,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,3,5,1,1]=>[1,6,3,3,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,5,1,1,3]=>[1,6,5,4,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,5,1,3,1]=>[6,4,3,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,5,3,1,1]=>[4,2,1,2,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,1,1,1,5]=>[1,1,6,1,1,5]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[3,3,1,1,5,1]=>[1,1,6,1,5,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,1,5,1,1]=>[1,1,6,5,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,5,1,1,1]=>[1,1,3,4,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[3,5,1,1,1,3]=>[1,3,4,1,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,5,1,1,3,1]=>[1,3,4,1,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,1,3,1,1]=>[1,3,4,3,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,3,1,1,1]=>[3,5,1,1,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,1,1,1,3,3]=>[1,4,1,1,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,1,1,3,1,3]=>[1,4,1,3,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,1,3,3,1]=>[1,4,1,3,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,1,3,1,1,3]=>[1,4,3,6,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,3,1,3,1]=>[6,2,1,4,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,3,3,1,1]=>[1,4,3,1,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,1,1,1,3]=>[3,1,1,3,3,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,3,1,1,3,1]=>[3,1,1,3,5,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,3,1,3,1,1]=>[3,1,1,5,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,3,3,1,1,1]=>[3,1,3,1,3,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,3,3,6]=>[1,1,1,3,1,4]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,3,6,3]=>[1,1,1,3,4,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,6,3,3]=>[1,1,1,6,5,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,3,1,3,6]=>[1,1,3,6,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,3,1,6,3]=>[4,4,6,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,3,3,1,6]=>[3,3,5,3,1,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,3,3,6,1]=>[1,1,3,1,4,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,3,6,1,3]=>[1,1,3,4,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,3,6,3,1]=>[1,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,6,1,3,3]=>[1,1,6,3,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,6,3,1,3]=>[4,4,2,1,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,6,3,3,1]=>[4,4,2,1,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,1,1,3,6]=>[1,3,6,1,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,1,6,3]=>[4,6,2,4,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,1,3,1,6]=>[3,5,1,5,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,1,3,6,1]=>[6,1,4,1,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,1,6,1,3]=>[6,1,4,4,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,3,1,6,3,1]=>[4,6,2,2,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,3,3,1,1,6]=>[3,5,3,1,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,3,3,1,6,1]=>[3,5,3,1,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,3,6,1,1]=>[1,3,1,4,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,6,1,1,3]=>[1,3,4,3,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,6,1,3,1]=>[6,1,2,1,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,6,3,1,1]=>[1,3,4,5,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,1,3,3]=>[1,6,3,1,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,6,1,3,1,3]=>[6,4,1,1,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,6,1,3,3,1]=>[3,1,5,5,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,6,3,1,1,3]=>[4,2,1,2,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,3,1,3,1]=>[4,2,1,2,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,6,3,3,1,1]=>[4,2,1,4,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,1,3,6]=>[1,6,1,1,3,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,1,1,6,3]=>[4,2,4,4,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,3,1,6]=>[3,1,3,5,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,1,1,3,6,1]=>[1,6,1,3,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,6,1,3]=>[3,1,3,1,5,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,1,6,3,1]=>[4,2,4,2,1,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,1,3,1,1,6]=>[3,1,5,1,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,1,3,1,6,1]=>[3,1,5,1,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,1,3,6,1,1]=>[1,6,3,4,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,6,1,1,3]=>[3,1,1,5,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,6,1,3,1]=>[3,1,1,5,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,1,6,3,1,1]=>[4,2,2,1,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,1,1,1,6]=>[3,3,1,3,3,1]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[3,3,1,1,6,1]=>[3,3,1,3,1,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,1,6,1,1]=>[3,3,1,1,5,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,6,1,1,1]=>[1,1,4,3,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[3,6,1,1,1,3]=>[1,4,3,1,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,6,1,1,3,1]=>[1,4,3,1,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,6,1,3,1,1]=>[1,4,3,3,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,6,3,1,1,1]=>[1,4,5,6,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,1,1,1,3,3]=>[1,3,1,1,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[6,1,1,3,1,3]=>[1,3,1,3,6,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[6,1,1,3,3,1]=>[1,3,1,3,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[6,1,3,1,1,3]=>[1,3,3,6,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[6,1,3,1,3,1]=>[6,1,1,4,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[6,1,3,3,1,1]=>[1,3,3,1,6,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[6,3,1,1,1,3]=>[1,5,6,1,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,3,1,1,3,1]=>[4,1,2,4,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,3,1,3,1,1]=>[4,1,2,6,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,3,3,1,1,1]=>[1,5,1,6,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,3,4,4]=>[1,1,1,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,4,3,4]=>[2,2,2,5,1,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,4,4,3]=>[2,2,2,5,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,3,1,4,4]=>[1,1,3,6,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,3,4,1,4]=>[1,1,3,2,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,3,4,4,1]=>[1,1,3,2,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,4,1,3,4]=>[1,1,4,5,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,4,1,4,3]=>[5,5,1,2,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,4,3,1,4]=>[5,5,1,4,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,4,3,4,1]=>[2,2,5,1,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,4,4,1,3]=>[1,1,4,1,5,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,4,4,3,1]=>[3,3,6,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,3,1,1,4,4]=>[1,3,6,1,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,1,4,1,4]=>[6,1,4,2,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,1,4,4,1]=>[1,3,6,4,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,4,1,1,4]=>[1,3,2,5,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,4,1,4,1]=>[1,3,2,5,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,4,1,1]=>[1,3,2,1,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,1,3,4]=>[1,4,5,1,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,1,4,3]=>[5,1,2,5,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,1,3,1,4]=>[6,2,3,1,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,1,3,4,1]=>[1,4,5,3,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,1,4,1,3]=>[6,2,3,2,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,4,1,4,3,1]=>[5,1,2,1,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,3,1,1,4]=>[5,1,4,3,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,3,1,4,1]=>[5,1,4,3,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,3,4,1,1]=>[2,5,1,3,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,4,1,1,3]=>[1,4,1,5,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,4,1,3,1]=>[1,4,1,5,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,4,3,1,1]=>[3,6,3,2,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,1,1,4,4]=>[1,6,1,1,4,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,1,4,1,4]=>[5,3,5,1,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,1,4,4,1]=>[1,6,1,4,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,4,1,1,4]=>[5,3,1,2,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,4,1,4,1]=>[5,3,1,2,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,1,4,4,1,1]=>[1,6,4,1,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,4,1,1,1,4]=>[1,2,5,1,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,4,1,1,4,1]=>[1,2,5,1,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,1,4,1,1]=>[1,2,5,4,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,4,1,1,1]=>[1,2,1,5,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,1,1,1,3,4]=>[1,5,1,1,3,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,1,4,3]=>[2,6,2,2,5,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,1,3,1,4]=>[1,5,1,3,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,1,3,4,1]=>[1,5,1,3,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,1,4,1,3]=>[1,5,1,4,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,1,4,3,1]=>[5,2,5,1,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,3,1,1,4]=>[1,5,3,6,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,3,1,4,1]=>[6,3,1,4,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,3,4,1,1]=>[1,5,3,2,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,4,1,1,3]=>[1,5,4,5,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,4,1,3,1]=>[6,3,2,3,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,4,3,1,1]=>[5,2,1,4,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,1,4]=>[3,2,1,3,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,3,1,1,4,1]=>[5,4,3,5,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,4,1,1]=>[5,4,3,1,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,4,1,1,1]=>[2,1,3,6,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,4,1,1,1,3]=>[1,1,5,1,1,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,4,1,1,3,1]=>[1,1,5,1,3,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,1,3,1,1]=>[1,1,5,3,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,3,1,1,1]=>[3,3,2,1,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,3,4,5]=>[1,1,1,3,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,3,5,4]=>[2,2,2,4,4,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,4,3,5]=>[2,2,2,5,1,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,4,5,3]=>[1,1,1,4,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,5,3,4]=>[1,1,1,5,6,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,5,4,3]=>[2,2,2,6,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,3,1,4,5]=>[1,1,3,6,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,3,1,5,4]=>[4,4,6,2,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,3,4,1,5]=>[1,1,3,2,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,3,4,5,1]=>[1,1,3,2,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,3,5,1,4]=>[1,1,3,3,4,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,3,5,4,1]=>[2,2,4,4,1,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,4,1,3,5]=>[1,1,4,5,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,4,1,5,3]=>[5,5,1,2,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,4,3,1,5]=>[5,5,1,4,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,4,3,5,1]=>[2,2,5,1,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,4,5,1,3]=>[1,1,4,2,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,4,5,3,1]=>[3,3,6,4,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,5,1,3,4]=>[1,1,5,4,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,5,1,4,3]=>[5,5,2,1,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,5,3,1,4]=>[5,5,2,3,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,5,3,4,1]=>[4,4,1,2,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,5,4,1,3]=>[4,4,1,3,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,5,4,3,1]=>[4,4,1,3,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,1,1,4,5]=>[1,3,6,1,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,1,5,4]=>[4,6,2,4,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,1,4,1,5]=>[6,1,4,2,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,1,4,5,1]=>[1,3,6,4,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,1,5,1,4]=>[6,1,4,3,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,1,5,4,1]=>[4,6,2,1,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,4,1,1,5]=>[1,3,2,5,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,4,1,5,1]=>[1,3,2,5,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,5,1,1]=>[1,3,2,2,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,5,1,1,4]=>[1,3,3,4,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,5,1,4,1]=>[6,1,1,2,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,5,4,1,1]=>[2,4,4,1,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,4,1,1,3,5]=>[1,4,5,1,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,1,1,5,3]=>[5,1,2,5,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,1,3,1,5]=>[6,2,3,1,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,1,3,5,1]=>[6,2,3,1,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,1,5,1,3]=>[6,2,3,3,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,4,1,5,3,1]=>[5,1,2,2,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,4,3,1,1,5]=>[5,1,4,3,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,3,1,5,1]=>[5,1,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,3,5,1,1]=>[2,5,1,4,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,5,1,1,3]=>[1,4,2,4,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,5,1,3,1]=>[1,4,2,4,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,5,3,1,1]=>[3,6,4,1,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,1,1,3,4]=>[1,5,4,1,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,1,4,3]=>[5,2,1,5,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,1,3,1,4]=>[6,3,2,1,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,3,4,1]=>[1,5,4,3,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,1,4,1,3]=>[6,3,2,2,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,5,1,4,3,1]=>[5,2,1,1,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,3,1,1,4]=>[5,2,3,3,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,3,1,4,1]=>[5,2,3,3,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,3,4,1,1]=>[4,1,2,5,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,4,1,1,3]=>[4,1,3,1,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,4,1,3,1]=>[4,1,3,1,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,4,3,1,1]=>[4,1,3,3,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,1,1,4,5]=>[1,6,1,1,4,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,1,1,5,4]=>[4,2,4,4,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,1,4,1,5]=>[5,3,5,1,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,1,4,5,1]=>[1,6,1,4,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,1,5,1,4]=>[5,3,5,2,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,1,5,4,1]=>[4,2,4,1,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,1,4,1,1,5]=>[5,3,1,2,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,4,1,5,1]=>[5,3,1,2,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,1,4,5,1,1]=>[1,6,4,2,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,5,1,1,4]=>[5,3,2,1,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,5,1,4,1]=>[5,3,2,1,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,1,5,4,1,1]=>[4,2,1,3,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,1,1,5]=>[1,2,5,1,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[3,4,1,1,5,1]=>[1,2,5,1,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,1,5,1,1]=>[1,2,5,5,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,5,1,1,1]=>[1,2,2,4,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,5,1,1,1,4]=>[1,3,4,1,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,5,1,1,4,1]=>[1,3,4,1,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,1,4,1,1]=>[1,3,4,4,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,4,1,1,1]=>[2,4,1,6,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,1,1,1,3,5]=>[1,5,1,1,3,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[4,1,1,1,5,3]=>[4,1,4,4,1,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,1,1,3,1,5]=>[4,1,4,6,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,1,3,5,1]=>[1,5,1,3,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,1,5,1,3]=>[1,5,1,5,4,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,1,5,3,1]=>[4,1,4,1,2,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,1,3,1,1,5]=>[4,1,6,2,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,3,1,5,1]=>[6,3,1,4,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,3,5,1,1]=>[1,5,3,3,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,5,1,1,3]=>[1,5,5,4,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,5,1,3,1]=>[6,3,3,2,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,5,3,1,1]=>[4,1,1,2,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,3,1,1,1,5]=>[4,3,2,4,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,1,1,5,1]=>[5,4,3,5,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,5,1,1]=>[5,4,3,2,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,5,1,1,1]=>[2,1,4,5,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,5,1,1,1,3]=>[1,2,4,1,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,5,1,1,3,1]=>[1,2,4,1,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,1,3,1,1]=>[1,2,4,3,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,3,1,1,1]=>[3,4,1,1,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,1,1,1,3,4]=>[1,4,1,1,3,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,1,1,4,3]=>[2,5,2,2,5,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[5,1,1,3,1,4]=>[1,4,1,3,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,1,3,4,1]=>[1,4,1,3,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,1,4,1,3]=>[1,4,1,4,5,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,1,4,3,1]=>[5,1,5,1,4,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,1,3,1,1,4]=>[1,4,3,6,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,3,1,4,1]=>[6,2,1,4,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,3,4,1,1]=>[1,4,3,2,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,4,1,1,3]=>[1,4,4,5,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,4,1,3,1]=>[6,2,2,3,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,4,3,1,1]=>[5,1,1,4,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,1,1,1,4]=>[3,1,1,3,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[5,3,1,1,4,1]=>[5,3,3,5,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,4,1,1]=>[5,3,3,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,4,1,1,1]=>[1,6,2,5,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,4,1,1,1,3]=>[2,1,6,2,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,4,1,1,3,1]=>[4,3,1,4,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,1,3,1,1]=>[4,3,1,6,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,3,1,1,1]=>[3,2,2,1,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,3,4,6]=>[1,1,1,3,2,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,3,6,4]=>[1,1,1,3,4,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,4,3,6]=>[2,2,2,5,1,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,4,6,3]=>[1,1,1,4,3,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,6,3,4]=>[1,1,1,6,5,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,6,4,3]=>[3,3,3,1,1,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,1,4,6]=>[1,1,3,6,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,3,1,6,4]=>[3,3,5,1,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,3,4,1,6]=>[1,1,3,2,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,4,6,1]=>[1,1,3,2,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,6,1,4]=>[1,1,3,4,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,3,6,4,1]=>[1,1,3,4,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,4,1,3,6]=>[1,1,4,5,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,4,1,6,3]=>[5,5,1,2,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,4,3,1,6]=>[3,3,6,2,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,4,3,6,1]=>[2,2,5,1,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,4,6,1,3]=>[1,1,4,3,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,4,6,3,1]=>[1,1,4,3,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,6,1,3,4]=>[1,1,6,3,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,6,1,4,3]=>[3,3,1,5,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,6,3,1,4]=>[5,5,3,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,6,3,4,1]=>[4,4,2,1,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,6,4,1,3]=>[4,4,2,2,1,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,6,4,3,1]=>[3,3,1,1,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,1,1,4,6]=>[1,3,6,1,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,1,6,4]=>[3,5,1,3,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,1,4,1,6]=>[6,1,4,2,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,1,4,6,1]=>[6,1,4,2,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,1,6,1,4]=>[6,1,4,4,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,1,6,4,1]=>[4,6,2,2,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,3,4,1,1,6]=>[1,3,2,5,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,4,1,6,1]=>[1,3,2,5,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,4,6,1,1]=>[1,3,2,3,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,6,1,1,4]=>[1,3,4,3,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,6,1,4,1]=>[6,1,2,1,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,6,4,1,1]=>[1,3,4,6,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,1,1,3,6]=>[1,4,5,1,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,1,1,6,3]=>[5,1,2,5,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,1,3,1,6]=>[6,2,3,1,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,1,3,6,1]=>[6,2,3,1,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,1,6,1,3]=>[6,2,3,4,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,1,6,3,1]=>[5,1,2,3,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,4,3,1,1,6]=>[3,6,2,1,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,3,1,6,1]=>[3,6,2,1,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,3,6,1,1]=>[2,5,1,5,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,6,1,1,3]=>[1,4,3,3,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,4,6,1,3,1]=>[6,2,1,1,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,6,3,1,1]=>[1,4,3,5,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,1,3,4]=>[1,6,3,1,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,6,1,1,4,3]=>[3,1,5,3,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,1,3,1,4]=>[6,4,1,1,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,6,1,3,4,1]=>[1,6,3,3,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,1,4,1,3]=>[6,4,1,2,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,1,4,3,1]=>[3,1,5,6,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,3,1,1,4]=>[5,3,2,3,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,6,3,1,4,1]=>[5,3,2,3,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,6,3,4,1,1]=>[4,2,1,5,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,6,4,1,1,3]=>[4,2,2,1,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,4,1,3,1]=>[4,2,2,1,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,6,4,3,1,1]=>[3,1,1,2,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,1,1,1,4,6]=>[1,6,1,1,4,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,1,1,6,4]=>[3,1,3,3,1,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,1,1,4,1,6]=>[5,3,5,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,1,4,6,1]=>[1,6,1,4,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,6,1,4]=>[3,1,3,1,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,1,6,4,1]=>[4,2,4,2,2,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,1,4,1,1,6]=>[5,3,1,2,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,4,1,6,1]=>[6,4,2,3,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,4,6,1,1]=>[1,6,4,3,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,6,1,1,4]=>[3,1,1,5,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,6,1,4,1]=>[6,4,4,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,6,4,1,1]=>[4,2,2,2,1,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,4,1,1,1,6]=>[1,2,5,1,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,4,1,1,6,1]=>[1,2,5,1,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,1,6,1,1]=>[1,2,5,6,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,6,1,1,1]=>[1,2,3,3,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,6,1,1,1,4]=>[1,4,3,1,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,6,1,1,4,1]=>[1,4,3,1,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,1,4,1,1]=>[1,4,3,4,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,4,1,1,1]=>[1,4,6,5,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,1,1,3,6]=>[1,5,1,1,3,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,1,1,6,3]=>[4,1,4,4,2,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,1,1,3,1,6]=>[4,1,4,6,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,1,3,6,1]=>[1,5,1,3,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,1,6,1,3]=>[1,5,1,6,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,1,6,3,1]=>[4,1,4,2,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,1,3,1,1,6]=>[4,1,6,2,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,3,1,6,1]=>[6,3,1,4,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,1,3,6,1,1]=>[1,5,3,4,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,6,1,1,3]=>[1,5,6,3,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,6,1,3,1]=>[6,3,4,1,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,1,6,3,1,1]=>[4,1,2,1,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,3,1,1,1,6]=>[3,2,1,3,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,3,1,1,6,1]=>[3,2,1,3,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,1,6,1,1]=>[3,2,1,1,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,6,1,1,1]=>[2,1,5,4,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,6,1,1,1,3]=>[1,3,3,1,1,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[4,6,1,1,3,1]=>[1,3,3,1,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[4,6,1,3,1,1]=>[1,3,3,3,6,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[4,6,3,1,1,1]=>[1,3,5,6,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,1,1,3,4]=>[1,3,1,1,3,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,1,1,4,3]=>[2,4,2,2,5,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,1,1,3,1,4]=>[1,3,1,3,6,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,1,3,4,1]=>[1,3,1,3,2,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,1,4,1,3]=>[1,3,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,1,1,4,3,1]=>[3,5,3,6,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,1,3,1,1,4]=>[1,3,3,6,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,3,1,4,1]=>[6,1,1,4,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,3,4,1,1]=>[1,3,3,2,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,4,1,1,3]=>[1,3,4,5,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,1,4,1,3,1]=>[6,1,2,3,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,4,3,1,1]=>[3,5,6,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,1,1,4]=>[1,5,6,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,3,1,1,4,1]=>[5,2,3,5,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,1,4,1,1]=>[5,2,3,1,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,4,1,1,1]=>[1,5,2,5,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[6,4,1,1,1,3]=>[1,6,5,1,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,4,1,1,3,1]=>[4,2,1,4,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,4,1,3,1,1]=>[4,2,1,6,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,4,3,1,1,1]=>[3,1,2,1,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,3,5,5]=>[1,1,1,3,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,5,3,5]=>[1,1,1,5,6,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,5,5,3]=>[1,1,1,5,1,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,3,1,5,5]=>[1,1,3,6,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,3,5,1,5]=>[1,1,3,3,4,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,5,5,1]=>[1,1,3,3,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,5,1,3,5]=>[1,1,5,4,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,5,1,5,3]=>[5,5,2,1,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,5,3,1,5]=>[4,4,1,2,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,5,3,5,1]=>[1,1,5,6,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,5,5,1,3]=>[1,1,5,1,4,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,5,5,3,1]=>[4,4,1,4,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,1,1,5,5]=>[1,3,6,1,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,1,5,1,5]=>[6,1,4,3,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,1,5,5,1]=>[1,3,6,5,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,5,1,1,5]=>[1,3,3,4,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,5,1,5,1]=>[6,1,1,2,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,5,5,1,1]=>[1,3,3,1,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,5,1,1,3,5]=>[1,5,4,1,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,1,1,5,3]=>[5,2,1,5,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,1,3,1,5]=>[6,3,2,1,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,1,3,5,1]=>[6,3,2,1,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,5,1,5,1,3]=>[6,3,2,3,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,5,1,5,3,1]=>[5,2,1,2,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,3,1,1,5]=>[4,1,2,2,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,5,3,1,5,1]=>[5,2,3,3,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,3,5,1,1]=>[1,5,6,3,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,5,1,1,3]=>[1,5,1,4,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,5,1,3,1]=>[1,5,1,4,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,5,3,1,1]=>[4,1,4,2,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,1,5,5]=>[1,6,1,1,5,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[3,1,1,5,1,5]=>[5,3,5,2,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,1,5,5,1]=>[1,6,1,5,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,5,1,1,5]=>[5,3,2,1,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,5,1,5,1]=>[5,3,2,1,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,1,5,5,1,1]=>[1,6,5,1,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,5,1,1,1,5]=>[1,3,4,1,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,5,1,1,5,1]=>[1,3,4,1,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,1,5,1,1]=>[1,3,4,5,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,5,1,1,1]=>[1,3,1,4,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,1,1,1,3,5]=>[1,4,1,1,3,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[5,1,1,1,5,3]=>[1,4,1,1,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[5,1,1,3,1,5]=>[1,4,1,3,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,1,3,5,1]=>[1,4,1,3,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,1,5,1,3]=>[1,4,1,5,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,1,5,3,1]=>[5,1,5,2,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,1,3,1,1,5]=>[1,4,3,6,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,3,1,5,1]=>[6,2,1,4,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,3,5,1,1]=>[1,4,3,3,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,5,1,1,3]=>[1,4,5,4,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,5,1,3,1]=>[6,2,3,2,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,5,3,1,1]=>[5,1,2,3,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,1,1,5]=>[4,2,2,4,4,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[5,3,1,1,5,1]=>[5,3,3,5,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,5,1,1]=>[5,3,3,2,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,5,1,1,1]=>[1,6,3,4,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,5,1,1,1,3]=>[1,1,4,1,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,5,1,1,3,1]=>[1,1,4,1,3,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,5,1,3,1,1]=>[1,1,4,3,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,5,3,1,1,1]=>[3,3,1,1,3,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,3,5,6]=>[1,1,1,3,3,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,3,6,5]=>[2,2,2,4,5,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,5,3,6]=>[1,1,1,5,6,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,5,6,3]=>[1,1,1,5,2,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,6,3,5]=>[1,1,1,6,5,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,6,5,3]=>[3,3,3,1,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,1,5,6]=>[1,1,3,6,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,1,6,5]=>[3,3,5,1,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,3,5,1,6]=>[1,1,3,3,4,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,3,5,6,1]=>[1,1,3,3,2,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,6,1,5]=>[1,1,3,4,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,6,5,1]=>[2,2,4,5,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,5,1,3,6]=>[1,1,5,4,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,5,1,6,3]=>[5,5,2,1,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,5,3,1,6]=>[4,4,1,2,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,5,3,6,1]=>[1,1,5,6,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,5,6,1,3]=>[1,1,5,2,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,5,6,3,1]=>[4,4,1,5,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,6,1,3,5]=>[1,1,6,3,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,6,1,5,3]=>[4,4,2,6,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,6,3,1,5]=>[4,4,2,1,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,6,3,5,1]=>[1,1,6,5,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,6,5,1,3]=>[3,3,1,2,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,6,5,3,1]=>[3,3,1,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,3,1,1,5,6]=>[1,3,6,1,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,1,1,6,5]=>[3,5,1,3,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,1,5,1,6]=>[6,1,4,3,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,1,5,6,1]=>[1,3,6,5,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,1,6,1,5]=>[6,1,4,4,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,1,6,5,1]=>[3,5,1,1,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,5,1,1,6]=>[1,3,3,4,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,5,1,6,1]=>[6,1,1,2,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,5,6,1,1]=>[1,3,3,2,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,6,1,1,5]=>[1,3,4,3,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,6,1,5,1]=>[6,1,2,1,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,6,5,1,1]=>[2,4,5,1,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,1,1,3,6]=>[1,5,4,1,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,1,1,6,3]=>[5,2,1,5,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,1,3,1,6]=>[6,3,2,1,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,1,3,6,1]=>[6,3,2,1,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,5,1,6,1,3]=>[6,3,2,4,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,1,6,3,1]=>[5,2,1,3,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,3,1,1,6]=>[4,1,2,2,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,5,3,1,6,1]=>[4,1,2,2,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,5,3,6,1,1]=>[1,5,6,4,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,6,1,1,3]=>[1,5,2,3,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,5,6,1,3,1]=>[1,5,2,3,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,6,3,1,1]=>[4,1,5,1,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,6,1,1,3,5]=>[1,6,3,1,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,6,1,1,5,3]=>[4,2,6,4,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,1,3,1,5]=>[6,4,1,1,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,6,1,3,5,1]=>[6,4,1,1,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,6,1,5,1,3]=>[6,4,1,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,1,5,3,1]=>[4,2,6,1,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,6,3,1,1,5]=>[4,2,1,2,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,6,3,1,5,1]=>[5,3,2,3,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,6,3,5,1,1]=>[1,6,5,3,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,5,1,1,3]=>[3,1,2,6,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,5,1,3,1]=>[3,1,2,6,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,5,3,1,1]=>[3,1,2,1,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,1,1,1,5,6]=>[1,6,1,1,5,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,1,1,6,5]=>[3,1,3,3,1,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,1,1,5,1,6]=>[5,3,5,2,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,1,5,6,1]=>[1,6,1,5,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,1,6,1,5]=>[4,2,4,2,6,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,1,6,5,1]=>[3,1,3,1,2,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,5,1,1,6]=>[5,3,2,1,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,5,1,6,1]=>[6,4,3,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,5,6,1,1]=>[1,6,5,2,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,6,1,1,5]=>[4,2,2,6,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,6,1,5,1]=>[6,4,4,1,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,6,5,1,1]=>[3,1,1,2,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,5,1,1,1,6]=>[1,3,4,1,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,5,1,1,6,1]=>[1,3,4,1,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,1,6,1,1]=>[1,3,4,6,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,6,1,1,1]=>[1,3,2,3,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,6,1,1,1,5]=>[1,4,3,1,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,6,1,1,5,1]=>[1,4,3,1,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,1,5,1,1]=>[1,4,3,5,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,5,1,1,1]=>[2,5,1,5,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[5,1,1,1,3,6]=>[1,4,1,1,3,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,1,1,1,6,3]=>[1,4,1,1,6,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[5,1,1,3,1,6]=>[3,6,3,5,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,1,1,3,6,1]=>[1,4,1,3,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,1,6,1,3]=>[1,4,1,6,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,1,6,3,1]=>[5,1,5,3,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,1,3,1,1,6]=>[3,6,5,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,1,3,1,6,1]=>[6,2,1,4,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,3,6,1,1]=>[1,4,3,4,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,6,1,1,3]=>[1,4,6,3,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,6,1,3,1]=>[6,2,4,1,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,6,3,1,1]=>[5,1,3,2,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,1,1,6]=>[3,1,1,3,3,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[5,3,1,1,6,1]=>[3,1,1,3,1,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,3,1,6,1,1]=>[3,1,1,1,5,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,3,6,1,1,1]=>[1,6,4,3,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,6,1,1,1,3]=>[1,2,3,1,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[5,6,1,1,3,1]=>[1,2,3,1,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,6,1,3,1,1]=>[1,2,3,3,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,6,3,1,1,1]=>[1,2,5,6,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,1,1,1,3,5]=>[1,3,1,1,3,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[6,1,1,1,5,3]=>[1,3,1,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,1,3,1,5]=>[1,3,1,3,6,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,1,1,3,5,1]=>[1,3,1,3,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[6,1,1,5,1,3]=>[1,3,1,5,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,1,1,5,3,1]=>[4,6,4,1,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,1,3,1,1,5]=>[1,3,3,6,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,1,3,1,5,1]=>[6,1,1,4,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,3,5,1,1]=>[1,3,3,3,4,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[6,1,5,1,1,3]=>[1,3,5,4,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,1,5,1,3,1]=>[6,1,3,2,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,5,3,1,1]=>[4,6,1,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,3,1,1,1,5]=>[4,1,2,4,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,3,1,1,5,1]=>[5,2,3,5,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,1,5,1,1]=>[5,2,3,2,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,5,1,1,1]=>[1,5,3,4,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,5,1,1,1,3]=>[2,1,5,2,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,5,1,1,3,1]=>[3,2,6,3,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,5,1,3,1,1]=>[3,2,6,5,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,5,3,1,1,1]=>[3,2,1,1,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,4,4,4]=>[1,1,1,4,1,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,4,1,4,4]=>[1,1,4,5,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,4,4,1,4]=>[1,1,4,1,5,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,4,4,4,1]=>[1,1,4,1,1,5]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,4,1,1,4,4]=>[1,4,5,1,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,1,4,1,4]=>[5,1,2,1,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,4,1,4,4,1]=>[5,1,2,1,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,4,1,1,4]=>[1,4,1,5,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,4,1,4,1]=>[5,1,5,2,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,4,4,1,1]=>[1,4,1,1,5,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,1,1,1,4,4]=>[1,5,1,1,4,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,1,1,4,1,4]=>[5,2,5,1,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,1,1,4,4,1]=>[1,5,1,4,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,4,1,1,4]=>[5,2,1,2,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,1,4,1,4,1]=>[5,2,1,2,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,4,4,1,1]=>[1,5,4,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,4,1,1,1,4]=>[1,1,5,1,1,4]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,4,1,1,4,1]=>[1,1,5,1,4,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,4,1,4,1,1]=>[1,1,5,4,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,4,4,1,1,1]=>[1,1,1,5,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,4,4,5]=>[1,1,1,4,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,4,5,4]=>[2,2,2,5,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,5,4,4]=>[2,2,2,6,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,4,1,4,5]=>[1,1,4,5,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,4,1,5,4]=>[5,5,1,2,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,4,4,1,5]=>[1,1,4,1,5,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,4,4,5,1]=>[1,1,4,1,2,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,4,5,1,4]=>[1,1,4,2,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,4,5,4,1]=>[2,2,5,3,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,5,1,4,4]=>[1,1,5,4,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,5,4,1,4]=>[5,5,2,4,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,5,4,4,1]=>[4,4,1,3,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,1,1,4,5]=>[1,4,5,1,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,1,1,5,4]=>[5,1,2,5,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,1,4,1,5]=>[5,1,2,1,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,1,4,5,1]=>[5,1,2,1,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,1,5,1,4]=>[5,1,2,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,4,1,5,4,1]=>[5,1,2,2,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,4,4,1,1,5]=>[1,4,1,5,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,4,1,5,1]=>[5,1,5,2,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,4,5,1,1]=>[1,4,1,2,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,4,5,1,1,4]=>[1,4,2,4,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,4,5,1,4,1]=>[5,1,6,1,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,5,4,1,1]=>[2,5,3,1,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,1,4,4]=>[1,5,4,1,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,5,1,4,1,4]=>[5,2,1,1,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,5,1,4,4,1]=>[5,2,1,1,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,4,1,1,4]=>[5,2,4,2,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,4,1,4,1]=>[5,2,4,2,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,4,4,1,1]=>[4,1,3,4,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,1,1,1,4,5]=>[1,5,1,1,4,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,1,1,5,4]=>[4,1,4,4,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,1,1,4,1,5]=>[5,2,5,1,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,1,1,4,5,1]=>[1,5,1,4,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,1,5,1,4]=>[5,2,5,2,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,1,1,5,4,1]=>[4,1,4,1,3,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[4,1,4,1,1,5]=>[5,2,1,2,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,1,4,1,5,1]=>[5,2,1,2,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,4,5,1,1]=>[1,5,4,2,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,5,1,1,4]=>[5,2,2,1,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,1,5,1,4,1]=>[5,2,2,1,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,5,4,1,1]=>[4,1,1,3,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[4,4,1,1,1,5]=>[1,1,5,1,1,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,4,1,1,5,1]=>[1,1,5,1,5,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,4,1,5,1,1]=>[1,1,5,5,4,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,4,5,1,1,1]=>[1,1,2,4,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[4,5,1,1,1,4]=>[1,2,4,1,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[4,5,1,1,4,1]=>[1,2,4,1,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,5,1,4,1,1]=>[1,2,4,4,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,5,4,1,1,1]=>[2,3,1,6,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,1,1,4,4]=>[1,4,1,1,4,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[5,1,1,4,1,4]=>[5,1,5,1,2,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,1,1,4,4,1]=>[1,4,1,4,1,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,1,4,1,1,4]=>[5,1,1,2,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,1,4,1,4,1]=>[5,1,1,2,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[5,1,4,4,1,1]=>[1,4,4,1,5,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,4,1,1,1,4]=>[2,1,6,2,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,4,1,1,4,1]=>[5,4,2,5,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,1,4,1,1]=>[5,4,2,1,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,4,1,1,1]=>[2,1,2,6,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,4,4,6]=>[1,1,1,4,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,4,6,4]=>[1,1,1,4,3,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,6,4,4]=>[3,3,3,1,1,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,4,1,4,6]=>[1,1,4,5,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,4,1,6,4]=>[5,5,1,2,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,4,4,1,6]=>[1,1,4,1,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,4,4,6,1]=>[1,1,4,1,3,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,4,6,1,4]=>[1,1,4,3,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,4,6,4,1]=>[1,1,4,3,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,6,1,4,4]=>[1,1,6,3,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,6,4,1,4]=>[5,5,3,3,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,6,4,4,1]=>[4,4,2,2,4,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,4,1,1,4,6]=>[1,4,5,1,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,1,1,6,4]=>[5,1,2,5,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,1,4,1,6]=>[5,1,2,1,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,1,4,6,1]=>[6,2,3,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,1,6,1,4]=>[6,2,3,4,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,1,6,4,1]=>[5,1,2,3,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,4,4,1,1,6]=>[1,4,1,5,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,4,1,6,1]=>[1,4,1,5,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,4,6,1,1]=>[1,4,1,3,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,4,6,1,1,4]=>[1,4,3,3,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,4,6,1,4,1]=>[6,2,1,1,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,6,4,1,1]=>[1,4,3,6,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,1,4,4]=>[1,6,3,1,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,6,1,4,1,4]=>[6,4,1,2,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,1,4,4,1]=>[1,6,3,4,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,4,1,1,4]=>[5,3,3,2,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,6,4,1,4,1]=>[5,3,3,2,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,6,4,4,1,1]=>[4,2,2,4,1,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,1,1,1,4,6]=>[1,5,1,1,4,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,1,1,6,4]=>[4,1,4,4,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,1,1,4,1,6]=>[5,2,5,1,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,1,4,6,1]=>[1,5,1,4,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,1,6,1,4]=>[1,5,1,6,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,1,6,4,1]=>[4,1,4,2,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,1,4,1,1,6]=>[5,2,1,2,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,4,1,6,1]=>[6,3,2,3,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,4,6,1,1]=>[1,5,4,3,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,6,1,1,4]=>[1,5,6,3,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,6,1,4,1]=>[6,3,4,1,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,6,4,1,1]=>[4,1,2,2,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,4,1,1,1,6]=>[1,1,5,1,1,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,4,1,1,6,1]=>[1,1,5,1,6,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,1,6,1,1]=>[1,1,5,6,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,6,1,1,1]=>[1,1,3,3,1,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[4,6,1,1,1,4]=>[1,3,3,1,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[4,6,1,1,4,1]=>[1,3,3,1,4,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,6,1,4,1,1]=>[1,3,3,4,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,6,4,1,1,1]=>[1,3,6,5,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,1,1,4,4]=>[1,3,1,1,4,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[6,1,1,4,1,4]=>[1,3,1,4,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,1,1,4,4,1]=>[1,3,1,4,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,1,4,1,1,4]=>[1,3,4,5,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,1,4,1,4,1]=>[6,1,2,3,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,4,4,1,1]=>[1,3,4,1,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,4,1,1,1,4]=>[1,6,5,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,4,1,1,4,1]=>[5,3,2,5,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,4,1,4,1,1]=>[5,3,2,1,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,4,4,1,1,1]=>[1,6,1,5,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,4,5,5]=>[1,1,1,4,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,5,4,5]=>[2,2,2,6,1,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,5,5,4]=>[2,2,2,6,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,4,1,5,5]=>[1,1,4,5,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,4,5,1,5]=>[1,1,4,2,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,4,5,5,1]=>[1,1,4,2,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,5,1,4,5]=>[1,1,5,4,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,5,1,5,4]=>[5,5,2,1,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,5,4,1,5]=>[4,4,1,3,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,5,4,5,1]=>[2,2,6,1,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,5,5,1,4]=>[1,1,5,1,4,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,5,5,4,1]=>[4,4,1,4,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,1,1,5,5]=>[1,4,5,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,1,5,1,5]=>[5,1,2,2,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,1,5,5,1]=>[5,1,2,2,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,5,1,1,5]=>[1,4,2,4,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,5,1,5,1]=>[5,1,6,1,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,5,5,1,1]=>[1,4,2,1,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,5,1,1,4,5]=>[1,5,4,1,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,1,1,5,4]=>[5,2,1,5,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,1,4,1,5]=>[5,2,1,1,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,5,1,4,5,1]=>[5,2,1,1,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,5,1,5,1,4]=>[5,2,1,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,5,1,5,4,1]=>[5,2,1,2,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,4,1,1,5]=>[4,1,3,1,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,5,4,1,5,1]=>[5,2,4,2,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,4,5,1,1]=>[2,6,1,3,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,5,1,1,4]=>[1,5,1,4,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,5,5,1,4,1]=>[5,2,5,1,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,5,4,1,1]=>[4,1,4,3,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,1,1,1,5,5]=>[1,5,1,1,5,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[4,1,1,5,1,5]=>[5,2,5,2,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,1,1,5,5,1]=>[1,5,1,5,1,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,5,1,1,5]=>[5,2,2,1,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,1,5,1,5,1]=>[5,2,2,1,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,5,5,1,1]=>[1,5,5,1,4,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,5,1,1,1,5]=>[1,2,4,1,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,5,1,1,5,1]=>[1,2,4,1,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,5,1,5,1,1]=>[1,2,4,5,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,5,5,1,1,1]=>[1,2,1,4,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,1,1,1,4,5]=>[1,4,1,1,4,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,1,1,1,5,4]=>[2,5,2,2,6,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,1,4,1,5]=>[5,1,5,1,2,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,1,1,4,5,1]=>[1,4,1,4,2,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[5,1,1,5,1,4]=>[5,1,5,2,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,1,1,5,4,1]=>[5,1,5,2,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,4,1,1,5]=>[5,1,1,2,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,1,4,1,5,1]=>[5,1,1,2,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[5,1,4,5,1,1]=>[1,4,4,2,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[5,1,5,1,1,4]=>[5,1,2,1,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,1,5,1,4,1]=>[5,1,2,1,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[5,1,5,4,1,1]=>[5,1,2,4,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,1,1,1,5]=>[4,3,1,4,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,4,1,1,5,1]=>[5,4,2,5,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,1,5,1,1]=>[5,4,2,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,5,1,1,1]=>[2,1,3,5,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,5,1,1,1,4]=>[1,1,4,1,1,4]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[5,5,1,1,4,1]=>[1,1,4,1,4,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,5,1,4,1,1]=>[1,1,4,4,5,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,5,4,1,1,1]=>[2,2,1,6,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,4,5,6]=>[1,1,1,4,2,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,4,6,5]=>[2,2,2,5,4,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,5,4,6]=>[2,2,2,6,1,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,5,6,4]=>[1,1,1,5,2,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,6,4,5]=>[3,3,3,1,1,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,6,5,4]=>[3,3,3,1,2,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,4,1,5,6]=>[1,1,4,5,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,4,1,6,5]=>[5,5,1,2,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,4,5,1,6]=>[1,1,4,2,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,4,5,6,1]=>[1,1,4,2,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,4,6,1,5]=>[1,1,4,3,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,4,6,5,1]=>[2,2,5,4,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,5,1,4,6]=>[1,1,5,4,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,5,1,6,4]=>[5,5,2,1,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,5,4,1,6]=>[4,4,1,3,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,5,4,6,1]=>[2,2,6,1,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,5,6,1,4]=>[1,1,5,2,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,5,6,4,1]=>[4,4,1,5,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,6,1,4,5]=>[1,1,6,3,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,6,1,5,4]=>[4,4,2,6,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,6,4,1,5]=>[4,4,2,2,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,6,4,5,1]=>[3,3,1,1,4,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,6,5,1,4]=>[5,5,3,4,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,6,5,4,1]=>[4,4,2,3,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,4,1,1,5,6]=>[1,4,5,1,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,1,1,6,5]=>[5,1,2,5,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,1,5,1,6]=>[5,1,2,2,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,1,5,6,1]=>[1,4,5,5,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,1,6,1,5]=>[6,2,3,4,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,1,6,5,1]=>[5,1,2,3,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,5,1,1,6]=>[1,4,2,4,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,4,5,1,6,1]=>[1,4,2,4,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,5,6,1,1]=>[1,4,2,2,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,4,6,1,1,5]=>[1,4,3,3,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,6,1,5,1]=>[6,2,1,1,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,6,5,1,1]=>[2,5,4,1,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,1,1,4,6]=>[1,5,4,1,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,1,1,6,4]=>[5,2,1,5,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,1,4,1,6]=>[5,2,1,1,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,5,1,4,6,1]=>[6,3,2,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,5,1,6,1,4]=>[6,3,2,4,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,6,4,1]=>[5,2,1,3,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,4,1,1,6]=>[4,1,3,1,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,5,4,1,6,1]=>[4,1,3,1,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,4,6,1,1]=>[2,6,1,4,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,6,1,1,4]=>[1,5,2,3,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,6,1,4,1]=>[1,5,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,6,4,1,1]=>[4,1,5,2,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,6,1,1,4,5]=>[1,6,3,1,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,1,1,5,4]=>[4,2,6,4,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,1,4,1,5]=>[6,4,1,2,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,1,4,5,1]=>[1,6,3,4,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,1,5,1,4]=>[6,4,1,3,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,1,5,4,1]=>[4,2,6,1,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,4,1,1,5]=>[4,2,2,1,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,6,4,1,5,1]=>[5,3,3,2,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,6,4,5,1,1]=>[3,1,1,4,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,6,5,1,1,4]=>[5,3,4,1,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,5,1,4,1]=>[5,3,4,1,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,6,5,4,1,1]=>[4,2,3,3,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,1,1,1,5,6]=>[1,5,1,1,5,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[4,1,1,1,6,5]=>[4,1,4,4,2,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,1,1,5,1,6]=>[5,2,5,2,1,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,1,5,6,1]=>[1,5,1,5,2,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,1,6,1,5]=>[4,1,4,2,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,1,6,5,1]=>[5,2,5,3,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,5,1,1,6]=>[5,2,2,1,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,5,1,6,1]=>[6,3,3,2,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,5,6,1,1]=>[1,5,5,2,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,6,1,1,5]=>[4,1,2,6,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,6,1,5,1]=>[6,3,4,1,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,6,5,1,1]=>[5,2,3,4,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,5,1,1,1,6]=>[1,2,4,1,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,5,1,1,6,1]=>[1,2,4,1,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,1,6,1,1]=>[1,2,4,6,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,6,1,1,1]=>[1,2,2,3,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,6,1,1,1,5]=>[1,3,3,1,1,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[4,6,1,1,5,1]=>[1,3,3,1,5,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,6,1,5,1,1]=>[1,3,3,5,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,6,5,1,1,1]=>[2,4,1,5,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,1,1,1,4,6]=>[1,4,1,1,4,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,1,1,1,6,4]=>[3,6,3,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[5,1,1,4,1,6]=>[5,1,5,1,2,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,1,1,4,6,1]=>[1,4,1,4,3,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,1,6,1,4]=>[1,4,1,6,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,1,6,4,1]=>[5,1,5,3,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,1,4,1,1,6]=>[5,1,1,2,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,1,4,1,6,1]=>[6,2,2,3,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,4,6,1,1]=>[1,4,4,3,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,6,1,1,4]=>[1,4,6,3,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,6,1,4,1]=>[6,2,4,1,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,6,4,1,1]=>[5,1,3,3,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,4,1,1,1,6]=>[4,3,1,4,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,4,1,1,6,1]=>[4,3,1,4,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,1,6,1,1]=>[4,3,1,2,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,6,1,1,1]=>[2,1,4,4,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[5,6,1,1,1,4]=>[1,2,3,1,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,6,1,1,4,1]=>[1,2,3,1,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,6,1,4,1,1]=>[1,2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,6,4,1,1,1]=>[1,2,6,5,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,1,1,1,4,5]=>[1,3,1,1,4,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[6,1,1,1,5,4]=>[2,4,2,2,6,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[6,1,1,4,1,5]=>[1,3,1,4,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,1,1,4,5,1]=>[1,3,1,4,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,1,5,1,4]=>[1,3,1,5,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,1,1,5,4,1]=>[4,6,4,1,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,1,4,1,1,5]=>[1,3,4,5,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,1,4,1,5,1]=>[6,1,2,3,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,4,5,1,1]=>[1,3,4,2,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,5,1,1,4]=>[1,3,5,4,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,1,5,1,4,1]=>[6,1,3,2,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,5,4,1,1]=>[4,6,1,3,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,4,1,1,1,5]=>[4,2,1,4,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,4,1,1,5,1]=>[5,3,2,5,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,4,1,5,1,1]=>[5,3,2,2,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,4,5,1,1,1]=>[1,6,2,4,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,5,1,1,1,4]=>[2,1,5,2,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,5,1,1,4,1]=>[5,4,1,5,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,5,1,4,1,1]=>[5,4,1,1,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,5,4,1,1,1]=>[2,1,1,6,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,2,2,2]=>[1,1,2,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,2,1,2,2,2]=>[2,3,1,3,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,1,2,2]=>[2,3,2,1,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,2,1,2]=>[2,3,2,2,1,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,2,2,1]=>[2,3,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,1,2,2,2]=>[2,1,2,3,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,2,1,2,2]=>[2,1,3,1,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,2,2,1,2]=>[2,1,3,2,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,2,2,2,1]=>[2,1,3,2,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,1,2,2]=>[2,2,1,2,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,1,2,1,2]=>[2,2,1,3,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,1,2,2,1]=>[2,2,1,3,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,2,1,1,2]=>[2,2,2,1,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,2,1,2,1]=>[2,2,2,1,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,2,2,1,1]=>[2,2,2,2,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,2,2,2,3]=>[1,1,2,1,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,2,2,3,2]=>[2,2,3,2,3,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,3,2,2]=>[2,2,3,3,1,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,3,2,2,2]=>[2,2,4,1,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,2,1,2,2,3]=>[2,3,1,3,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,2,3,2]=>[2,3,1,3,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,1,3,2,2]=>[2,3,1,4,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,2,1,2,3]=>[2,3,2,1,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,1,3,2]=>[2,3,2,1,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,2,2,1,3]=>[2,3,2,2,1,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,2,2,3,1]=>[1,2,1,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,2,3,1,2]=>[1,2,1,2,6,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,2,3,2,1]=>[2,3,2,3,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,3,1,2,2]=>[1,2,2,6,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,3,2,1,2]=>[2,3,3,1,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,3,2,2,1]=>[2,3,3,1,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,1,2,2,2]=>[1,3,6,2,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,2,1,2,2]=>[2,4,1,1,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,2,1,2]=>[2,4,1,2,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,2,2,1]=>[2,4,1,2,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,1,2,2,3]=>[2,1,2,3,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,1,2,3,2]=>[2,1,2,3,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,1,3,2,2]=>[2,1,2,4,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,2,1,2,3]=>[2,1,3,1,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,1,2,1,3,2]=>[2,1,3,1,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,2,2,1,3]=>[2,1,3,2,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,2,2,3,1]=>[3,2,4,3,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,2,3,1,2]=>[3,2,4,4,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,3,2,1]=>[2,1,3,3,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,3,1,2,2]=>[3,2,5,1,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,2,1,2]=>[2,1,4,1,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,3,2,2,1]=>[2,1,4,1,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,2,1,1,2,3]=>[2,2,1,2,3,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,1,1,3,2]=>[2,2,1,2,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,1,2,1,3]=>[2,2,1,3,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,1,2,3,1]=>[3,3,2,4,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,3,1,2]=>[3,3,2,5,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,1,3,2,1]=>[2,2,1,4,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,2,2,1,1,3]=>[2,2,2,1,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,2,2,1,3,1]=>[3,3,3,2,5,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,2,3,1,1]=>[1,1,1,2,6,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,2,3,1,1,2]=>[1,1,2,6,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,2,3,1,2,1]=>[3,3,4,1,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,3,2,1,1]=>[2,2,3,1,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,3,1,1,2,2]=>[1,2,6,1,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,1,2,1,2]=>[3,4,1,4,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,1,2,2,1]=>[3,4,1,4,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,2,1,1,2]=>[2,3,1,1,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,2,1,2,1]=>[2,3,1,1,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,3,2,2,1,1]=>[2,3,1,2,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,1,1,2,2,2]=>[1,6,1,2,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,2,1,2,2]=>[3,1,4,2,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,2,2,1,2]=>[3,1,4,3,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,2,2,2,1]=>[3,1,4,3,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,1,1,2,2]=>[2,1,1,2,3,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,1,2,1,2]=>[2,1,1,3,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,2,1,2,2,1]=>[2,1,1,3,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,2,1,1,2]=>[2,1,2,1,2,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,2,1,2,1]=>[2,1,2,1,3,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,2,2,1,1]=>[2,1,2,2,1,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,2,2,2,4]=>[1,1,2,1,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,2,4,2]=>[1,1,2,1,3,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,2,4,2,2]=>[1,1,2,3,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,4,2,2,2]=>[1,1,4,6,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,1,2,2,4]=>[2,3,1,3,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,2,4,2]=>[3,4,2,4,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,4,2,2]=>[3,4,2,6,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,2,1,2,4]=>[2,3,2,1,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,1,4,2]=>[3,4,3,2,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,2,2,1,4]=>[2,3,2,2,1,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,2,2,4,1]=>[1,2,1,1,3,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,2,4,1,2]=>[1,2,1,3,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,2,4,2,1]=>[3,4,3,5,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,1,2,2]=>[1,2,3,5,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,4,2,1,2]=>[3,4,5,1,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,2,2,1]=>[3,4,5,1,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,2,2,2]=>[1,4,5,2,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,2,1,2,2]=>[3,6,1,2,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,2,1,2]=>[3,6,1,3,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,2,2,1]=>[3,6,1,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,2,2,4]=>[2,1,2,3,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,1,2,4,2]=>[3,2,3,4,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,1,4,2,2]=>[3,2,3,6,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,2,1,2,4]=>[2,1,3,1,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,2,1,4,2]=>[3,2,4,2,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,2,2,1,4]=>[2,1,3,2,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,2,2,4,1]=>[2,1,3,2,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,2,4,1,2]=>[2,1,3,4,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,2,4,2,1]=>[3,2,4,5,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,4,1,2,2]=>[2,1,5,6,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,2,1,2]=>[3,2,6,1,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,2,2,1]=>[3,2,6,1,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,1,1,2,4]=>[2,2,1,2,3,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,1,4,2]=>[3,3,2,3,6,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,1,2,1,4]=>[2,2,1,3,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,1,2,4,1]=>[2,2,1,3,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,1,4,1,2]=>[2,2,1,5,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,1,4,2,1]=>[3,3,2,6,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,2,1,1,4]=>[2,2,2,1,2,5]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,2,2,1,4,1]=>[2,2,2,1,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,2,4,1,1]=>[1,1,1,3,5,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,2,4,1,1,2]=>[1,1,3,5,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,4,1,2,1]=>[2,2,4,6,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,4,2,1,1]=>[3,3,5,1,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,4,1,1,2,2]=>[1,3,5,1,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,1,2,1,2]=>[2,4,6,3,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,1,2,2,1]=>[2,4,6,3,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,2,1,1,2]=>[3,5,1,2,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,2,1,2,1]=>[3,5,1,2,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,2,2,1,1]=>[3,5,1,3,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,1,2,2,2]=>[1,5,1,2,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,1,2,1,2,2]=>[2,6,3,1,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,2,2,1,2]=>[2,6,3,2,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,2,2,2,1]=>[2,6,3,2,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,2,1,1,2,2]=>[3,1,2,3,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,2,1,2,1,2]=>[3,1,2,4,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,1,2,2,1]=>[3,1,2,4,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,2,1,1,2]=>[3,1,3,2,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,2,2,1,2,1]=>[3,1,3,2,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,2,2,1,1]=>[3,1,3,3,2,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,2,2,2,5]=>[1,1,2,1,1,4]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,2,2,5,2]=>[1,1,2,1,4,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,5,2,2]=>[1,1,2,4,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,5,2,2,2]=>[1,1,5,5,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,2,1,2,2,5]=>[2,3,1,3,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,1,2,5,2]=>[2,3,1,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,1,5,2,2]=>[4,5,3,1,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,2,1,2,5]=>[2,3,2,1,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,2,1,5,2]=>[4,5,4,3,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,2,2,1,5]=>[2,3,2,2,1,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,2,2,5,1]=>[1,2,1,1,4,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,2,5,1,2]=>[1,2,1,4,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,2,5,2,1]=>[2,3,2,5,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,5,1,2,2]=>[1,2,4,4,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,5,2,1,2]=>[2,3,5,6,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,5,2,2,1]=>[2,3,5,6,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,2,2,2]=>[1,5,4,2,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,2,1,2,2]=>[4,1,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,2,2,1,2]=>[4,1,1,4,3,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,2,2,2,1]=>[4,1,1,4,4,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,1,2,2,5]=>[2,1,2,3,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,2,5,2]=>[2,1,2,3,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,1,5,2,2]=>[4,3,4,1,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,2,1,2,5]=>[2,1,3,1,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,2,1,5,2]=>[4,3,5,3,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,2,2,1,5]=>[2,1,3,2,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,2,2,5,1]=>[2,1,3,2,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,2,5,1,2]=>[2,1,3,5,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,2,5,2,1]=>[2,1,3,5,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,5,1,2,2]=>[2,1,6,5,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,2,1,2]=>[4,3,1,1,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,5,2,2,1]=>[4,3,1,1,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,2,1,1,2,5]=>[2,2,1,2,3,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,1,1,5,2]=>[4,4,3,4,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,1,2,1,5]=>[2,2,1,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,1,2,5,1]=>[2,2,1,3,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,1,5,1,2]=>[2,2,1,6,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,1,5,2,1]=>[4,4,3,1,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,2,2,1,1,5]=>[2,2,2,1,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,2,2,1,5,1]=>[2,2,2,1,6,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,2,5,1,1]=>[1,1,1,4,4,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[2,2,5,1,1,2]=>[1,1,4,4,1,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,5,1,2,1]=>[2,2,5,5,3,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,5,2,1,1]=>[2,2,5,6,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,1,2,2]=>[1,4,4,1,2,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,5,1,2,1,2]=>[2,5,5,3,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,5,1,2,2,1]=>[2,5,5,3,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,5,2,1,1,2]=>[2,5,6,1,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,2,1,2,1]=>[2,5,6,1,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,2,2,1,1]=>[2,5,6,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,1,2,2,2]=>[1,4,1,2,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,1,2,1,2,2]=>[2,5,3,1,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,2,2,1,2]=>[2,5,3,2,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,2,2,2,1]=>[2,5,3,2,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,2,1,1,2,2]=>[2,6,1,2,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,2,1,2,1,2]=>[2,6,1,3,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,2,1,2,2,1]=>[2,6,1,3,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,2,2,1,1,2]=>[2,6,2,1,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,2,2,1,2,1]=>[2,6,2,1,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,2,2,2,1,1]=>[2,6,2,2,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,2,2,2,6]=>[1,1,2,1,1,5]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,2,2,6,2]=>[1,1,2,1,5,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,2,6,2,2]=>[1,1,2,5,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,6,2,2,2]=>[1,1,6,4,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,1,2,2,6]=>[2,3,1,3,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,1,2,6,2]=>[2,3,1,3,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,1,6,2,2]=>[3,4,2,1,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,2,1,2,6]=>[2,3,2,1,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,2,1,6,2]=>[3,4,3,2,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,2,2,1,6]=>[3,4,3,3,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,2,2,6,1]=>[1,2,1,1,5,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,2,6,1,2]=>[1,2,1,5,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,2,6,2,1]=>[2,3,2,6,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,6,1,2,2]=>[1,2,5,3,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,6,2,1,2]=>[2,3,6,5,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,2,2,1]=>[2,3,6,5,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,1,2,2,2]=>[1,6,3,2,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,6,2,1,2,2]=>[3,1,6,2,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,2,2,1,2]=>[3,1,6,3,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,2,2,2,1]=>[3,1,6,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,2,2,6]=>[2,1,2,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,1,1,2,6,2]=>[2,1,2,3,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,1,6,2,2]=>[3,2,3,1,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,2,1,2,6]=>[2,1,3,1,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,1,2,1,6,2]=>[3,2,4,2,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,2,2,1,6]=>[3,2,4,3,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,2,6,1]=>[2,1,3,2,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,2,6,1,2]=>[2,1,3,6,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,2,6,2,1]=>[2,1,3,6,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,6,1,2,2]=>[3,2,1,5,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,2,1,2]=>[3,2,1,6,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,2,2,1]=>[3,2,1,6,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,1,1,2,6]=>[2,2,1,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,2,1,1,6,2]=>[3,3,2,3,1,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,1,2,1,6]=>[3,3,2,4,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,1,2,6,1]=>[2,2,1,3,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,1,6,1,2]=>[3,3,2,1,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,1,6,2,1]=>[3,3,2,1,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,2,1,1,6]=>[3,3,3,2,3,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,2,2,1,6,1]=>[3,3,3,2,1,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,2,6,1,1]=>[1,1,1,5,3,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,2,6,1,1,2]=>[1,1,5,3,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,6,1,2,1]=>[2,2,6,4,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,6,2,1,1]=>[2,2,6,5,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,6,1,1,2,2]=>[1,5,3,1,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,6,1,2,1,2]=>[2,6,4,3,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,6,1,2,2,1]=>[2,6,4,3,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,6,2,1,1,2]=>[2,6,5,1,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,2,1,2,1]=>[2,6,5,1,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,2,2,1,1]=>[2,6,5,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,1,1,2,2,2]=>[1,3,1,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[6,1,2,1,2,2]=>[2,4,3,1,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,2,2,1,2]=>[2,4,3,2,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,2,2,2,1]=>[2,4,3,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,2,1,1,2,2]=>[2,5,1,2,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,2,1,2,1,2]=>[2,5,1,3,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,2,1,2,2,1]=>[2,5,1,3,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,2,2,1,1,2]=>[2,5,2,1,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,2,2,1,2,1]=>[2,5,2,1,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,2,2,2,1,1]=>[2,5,2,2,1,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,2,2,3,3]=>[1,1,2,1,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,2,3,2,3]=>[2,2,3,3,1,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,3,3,2]=>[2,2,3,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,3,2,2,3]=>[2,2,4,1,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,3,2,3,2]=>[2,2,4,1,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,3,3,2,2]=>[2,2,4,2,1,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,2,1,2,3,3]=>[2,3,1,3,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,1,3,2,3]=>[2,3,1,4,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,1,3,3,2]=>[2,3,1,4,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,2,1,3,3]=>[2,3,2,1,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,2,3,1,3]=>[1,2,1,2,6,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,2,3,3,1]=>[1,2,1,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,3,1,2,3]=>[1,2,2,6,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,3,1,3,2]=>[3,4,4,1,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,2,1,3]=>[2,3,3,1,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,2,3,1]=>[3,4,4,2,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,3,3,1,2]=>[1,2,2,1,6,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,3,3,2,1]=>[2,3,3,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,3,1,2,2,3]=>[1,3,6,2,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,1,2,3,2]=>[3,5,1,4,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,1,3,2,2]=>[3,5,1,5,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,1,2,3]=>[2,4,1,1,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,2,1,3,2]=>[2,4,1,1,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,3,2,2,1,3]=>[2,4,1,2,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,2,2,3,1]=>[3,5,2,3,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,3,1,2]=>[3,5,2,4,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,3,2,1]=>[2,4,1,3,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,3,1,2,2]=>[1,3,1,6,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,3,2,1,2]=>[2,4,2,1,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,3,2,2,1]=>[2,4,2,1,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,1,2,3,3]=>[2,1,2,3,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,1,3,2,3]=>[2,1,2,4,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,1,3,3,2]=>[2,1,2,4,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,2,1,3,3]=>[2,1,3,1,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,2,3,1,3]=>[3,2,4,4,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,2,3,3,1]=>[3,2,4,4,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,3,1,2,3]=>[3,2,5,1,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,1,3,2]=>[3,2,5,1,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,3,2,1,3]=>[2,1,4,1,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,3,2,3,1]=>[3,2,5,2,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,3,3,1,2]=>[3,2,5,3,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,3,2,1]=>[2,1,4,2,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,2,1,1,3,3]=>[2,2,1,2,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,2,1,3,1,3]=>[3,3,2,5,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,2,1,3,3,1]=>[3,3,2,5,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,3,1,1,3]=>[1,1,2,6,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,2,3,1,3,1]=>[3,3,4,1,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,3,3,1,1]=>[1,1,2,1,6,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,1,2,3]=>[1,2,6,1,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,3,1,1,3,2]=>[3,4,1,3,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,1,2,1,3]=>[3,4,1,4,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,2,3,1]=>[3,4,1,4,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,3,1,3,1,2]=>[3,4,1,5,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,3,1,3,2,1]=>[3,4,1,5,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,2,1,1,3]=>[2,3,1,1,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,2,1,3,1]=>[3,4,2,2,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,2,3,1,1]=>[3,4,2,4,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,3,1,1,2]=>[1,2,1,6,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,3,1,2,1]=>[3,4,3,1,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,3,2,1,1]=>[2,3,2,1,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,1,1,2,2,3]=>[1,6,1,2,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,1,1,2,3,2]=>[3,1,3,4,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,1,3,2,2]=>[3,1,3,5,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,2,1,2,3]=>[3,1,4,2,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,2,1,3,2]=>[3,1,4,2,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,2,2,1,3]=>[3,1,4,3,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,2,2,3,1]=>[3,1,4,3,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,1,2,3,1,2]=>[3,1,4,4,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,1,2,3,2,1]=>[3,1,4,4,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,3,1,2,2]=>[3,1,5,1,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,3,2,1,2]=>[3,1,5,2,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,3,2,2,1]=>[3,1,5,2,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,1,1,2,3]=>[2,1,1,2,3,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,1,1,3,2]=>[2,1,1,2,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,2,1,2,1,3]=>[2,1,1,3,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,1,2,3,1]=>[3,2,2,4,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,3,1,2]=>[3,2,2,5,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,1,3,2,1]=>[2,1,1,4,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[3,2,2,1,1,3]=>[2,1,2,1,2,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,2,2,1,3,1]=>[3,2,3,2,5,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,2,3,1,1]=>[3,2,3,4,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,3,1,1,2]=>[3,2,4,1,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,1,2,1]=>[3,2,4,1,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,3,2,1,1]=>[2,1,3,1,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,3,1,1,2,2]=>[1,1,6,1,2,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,3,1,2,1,2]=>[3,3,1,4,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,3,1,2,2,1]=>[3,3,1,4,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,2,1,1,2]=>[2,2,1,1,2,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,3,2,1,2,1]=>[2,2,1,1,3,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,3,2,2,1,1]=>[2,2,1,2,1,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,2,2,3,4]=>[1,1,2,1,2,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,2,4,3]=>[2,2,3,2,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,2,3,2,4]=>[2,2,3,3,1,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,3,4,2]=>[1,1,2,2,2,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,4,2,3]=>[1,1,2,3,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,2,4,3,2]=>[2,2,3,4,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,3,2,2,4]=>[2,2,4,1,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,3,2,4,2]=>[3,3,5,2,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,3,4,2,2]=>[1,1,3,2,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,4,2,2,3]=>[1,1,4,6,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,4,2,3,2]=>[3,3,6,1,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,4,3,2,2]=>[2,2,5,1,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,1,2,3,4]=>[2,3,1,3,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,1,2,4,3]=>[2,3,1,3,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,1,3,2,4]=>[2,3,1,4,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,1,3,4,2]=>[3,4,2,5,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,1,4,2,3]=>[3,4,2,6,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,1,4,3,2]=>[2,3,1,5,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,2,1,3,4]=>[2,3,2,1,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,1,4,3]=>[2,3,2,1,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,2,3,1,4]=>[1,2,1,2,6,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,2,3,4,1]=>[1,2,1,2,2,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,2,4,1,3]=>[1,2,1,3,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,2,4,3,1]=>[3,4,3,5,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,3,1,2,4]=>[1,2,2,6,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,1,4,2]=>[3,4,4,1,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,2,3,2,1,4]=>[2,3,3,1,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,3,2,4,1]=>[2,3,3,1,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,3,4,1,2]=>[1,2,2,2,5,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,2,3,4,2,1]=>[3,4,4,4,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,4,1,2,3]=>[1,2,3,5,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,4,1,3,2]=>[2,3,4,6,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,4,2,1,3]=>[3,4,5,1,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,2,3,1]=>[3,4,5,1,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,4,3,1,2]=>[3,4,5,2,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,3,2,1]=>[2,3,4,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,3,1,2,2,4]=>[1,3,6,2,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,1,2,4,2]=>[3,5,1,4,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,1,4,2,2]=>[3,5,1,6,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,1,2,4]=>[2,4,1,1,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,2,1,4,2]=>[3,5,2,2,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,2,2,1,4]=>[2,4,1,2,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,2,2,4,1]=>[2,4,1,2,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,2,4,1,2]=>[2,4,1,4,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,2,4,2,1]=>[3,5,2,5,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,4,1,2,2]=>[1,3,2,5,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,4,2,1,2]=>[3,5,4,1,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,2,2,1]=>[3,5,4,1,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,2,2,3]=>[1,4,5,2,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,1,2,3,2]=>[2,5,6,3,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,1,3,2,2]=>[2,5,6,4,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,2,1,2,3]=>[3,6,1,2,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,1,3,2]=>[3,6,1,2,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,2,2,1,3]=>[3,6,1,3,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,2,2,3,1]=>[3,6,1,3,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,4,2,3,1,2]=>[3,6,1,4,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,4,2,3,2,1]=>[3,6,1,4,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,3,1,2,2]=>[3,6,2,1,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,3,2,1,2]=>[2,5,1,1,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,3,2,2,1]=>[2,5,1,1,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,1,1,2,3,4]=>[2,1,2,3,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,1,2,4,3]=>[2,1,2,3,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,1,3,2,4]=>[2,1,2,4,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,1,3,4,2]=>[3,2,3,5,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,1,4,2,3]=>[3,2,3,6,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,1,4,3,2]=>[2,1,2,5,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,1,2,1,3,4]=>[2,1,3,1,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,2,1,4,3]=>[2,1,3,1,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,2,3,1,4]=>[3,2,4,4,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,2,3,4,1]=>[2,1,3,3,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,2,4,1,3]=>[2,1,3,4,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,2,4,3,1]=>[3,2,4,5,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,3,1,2,4]=>[3,2,5,1,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,3,1,4,2]=>[3,2,5,1,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,2,1,4]=>[2,1,4,1,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,3,2,4,1]=>[2,1,4,1,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,3,4,1,2]=>[2,1,4,3,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,3,4,2,1]=>[3,2,5,4,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,4,1,2,3]=>[2,1,5,6,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,4,1,3,2]=>[2,1,5,6,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,2,1,3]=>[3,2,6,1,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,2,3,1]=>[3,2,6,1,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,4,3,1,2]=>[3,2,6,2,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,3,2,1]=>[2,1,5,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[2,2,1,1,3,4]=>[2,2,1,2,4,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,1,4,3]=>[2,2,1,2,5,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,2,1,3,1,4]=>[3,3,2,5,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,1,3,4,1]=>[2,2,1,4,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,1,4,1,3]=>[2,2,1,5,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,1,4,3,1]=>[3,3,2,6,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,3,1,1,4]=>[1,1,2,6,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,2,3,1,4,1]=>[1,1,2,6,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,3,4,1,1]=>[1,1,2,2,5,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,4,1,1,3]=>[1,1,3,5,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,4,1,3,1]=>[1,1,3,5,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,4,3,1,1]=>[3,3,5,2,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,3,1,1,2,4]=>[1,2,6,1,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,1,1,4,2]=>[3,4,1,3,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,3,1,2,1,4]=>[3,4,1,4,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,1,2,4,1]=>[1,2,6,2,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,4,1,2]=>[1,2,6,4,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,4,2,1]=>[3,4,1,6,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,2,1,1,4]=>[2,3,1,1,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,2,1,4,1]=>[2,3,1,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,2,4,1,1]=>[2,3,1,4,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,4,1,1,2]=>[1,2,2,5,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,4,1,2,1]=>[2,3,3,6,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,3,4,2,1,1]=>[3,4,4,1,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,1,1,2,3]=>[1,3,5,1,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,4,1,1,3,2]=>[2,4,6,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,4,1,2,1,3]=>[2,4,6,3,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,1,2,3,1]=>[1,3,5,2,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,1,3,1,2]=>[1,3,5,3,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,1,3,2,1]=>[2,4,6,4,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,2,1,1,3]=>[3,5,1,2,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,2,1,3,1]=>[3,5,1,2,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,2,3,1,1]=>[3,5,1,4,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,3,1,1,2]=>[3,5,2,1,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,3,1,2,1]=>[3,5,2,1,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,3,2,1,1]=>[2,4,1,1,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,1,1,2,2,4]=>[1,6,1,2,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,1,2,4,2]=>[3,1,3,4,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,4,2,2]=>[3,1,3,6,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,2,1,2,4]=>[3,1,4,2,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,1,4,2]=>[3,1,4,2,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,2,2,1,4]=>[3,1,4,3,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,2,2,4,1]=>[1,6,2,1,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,2,4,1,2]=>[1,6,2,3,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,2,4,2,1]=>[3,1,4,5,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,4,1,2,2]=>[1,6,4,5,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,4,2,1,2]=>[3,1,6,1,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,4,2,2,1]=>[3,1,6,1,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,2,1,1,2,4]=>[2,1,1,2,3,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,1,4,2]=>[3,2,2,3,6,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,1,2,1,4]=>[2,1,1,3,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,2,1,2,4,1]=>[2,1,1,3,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,1,4,1,2]=>[2,1,1,5,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,4,2,1]=>[3,2,2,6,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,2,2,1,1,4]=>[2,1,2,1,2,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,2,2,1,4,1]=>[2,1,2,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,2,4,1,1]=>[2,1,2,4,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,2,4,1,1,2]=>[2,1,4,6,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,4,1,2,1]=>[2,1,4,6,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,4,2,1,1]=>[3,2,5,1,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,4,1,1,2,2]=>[1,2,5,1,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,4,1,2,1,2]=>[2,3,6,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,1,2,2,1]=>[2,3,6,3,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,4,2,1,1,2]=>[3,4,1,2,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,2,1,2,1]=>[3,4,1,2,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,4,2,2,1,1]=>[3,4,1,3,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,1,2,2,3]=>[1,5,1,2,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,1,1,2,3,2]=>[2,6,2,3,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,1,3,2,2]=>[2,6,2,4,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,1,2,1,2,3]=>[2,6,3,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,1,2,1,3,2]=>[2,6,3,1,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,2,2,1,3]=>[2,6,3,2,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,2,2,3,1]=>[1,5,2,1,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,2,3,1,2]=>[1,5,2,2,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,2,3,2,1]=>[2,6,3,3,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,3,1,2,2]=>[1,5,3,6,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,3,2,1,2]=>[2,6,4,1,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,2,2,1]=>[2,6,4,1,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,1,1,2,3]=>[3,1,2,3,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,2,1,1,3,2]=>[3,1,2,3,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,2,1,2,1,3]=>[3,1,2,4,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,2,3,1]=>[3,1,2,4,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,3,1,2]=>[3,1,2,5,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,3,2,1]=>[3,1,2,5,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,2,2,1,1,3]=>[3,1,3,2,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,2,2,1,3,1]=>[3,1,3,2,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,2,3,1,1]=>[3,1,3,4,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,2,3,1,1,2]=>[3,1,4,1,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,2,3,1,2,1]=>[3,1,4,1,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,3,2,1,1]=>[3,1,4,2,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,1,1,2,2]=>[3,2,1,3,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,1,2,1,2]=>[3,2,1,4,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,1,2,2,1]=>[3,2,1,4,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,2,1,1,2]=>[2,1,1,1,2,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,3,2,1,2,1]=>[2,1,1,1,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[4,3,2,2,1,1]=>[2,1,1,2,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,2,3,5]=>[1,1,2,1,2,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,2,2,5,3]=>[1,1,2,1,4,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,2,3,2,5]=>[2,2,3,3,1,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,2,3,5,2]=>[1,1,2,2,3,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,2,5,2,3]=>[1,1,2,4,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,2,5,3,2]=>[3,3,4,6,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,3,2,2,5]=>[2,2,4,1,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,3,2,5,2]=>[2,2,4,1,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,3,5,2,2]=>[1,1,3,3,5,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,5,2,2,3]=>[1,1,5,5,1,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,5,2,3,2]=>[4,4,1,1,5,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,5,3,2,2]=>[4,4,1,2,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,2,3,5]=>[2,3,1,3,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,1,2,5,3]=>[3,4,2,4,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,1,3,2,5]=>[2,3,1,4,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,3,5,2]=>[2,3,1,4,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,1,5,2,3]=>[4,5,3,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,1,5,3,2]=>[4,5,3,1,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,2,1,3,5]=>[2,3,2,1,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,2,1,5,3]=>[4,5,4,3,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,2,3,1,5]=>[1,2,1,2,6,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,2,3,5,1]=>[1,2,1,2,3,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,2,5,1,3]=>[1,2,1,4,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,2,5,3,1]=>[3,4,3,6,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,2,3,1,2,5]=>[1,2,2,6,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,2,3,1,5,2]=>[4,5,5,2,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,3,2,1,5]=>[2,3,3,1,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,3,2,5,1]=>[2,3,3,1,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,3,5,1,2]=>[1,2,2,3,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,5,2,1]=>[2,3,3,4,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,5,1,2,3]=>[1,2,4,4,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,2,5,1,3,2]=>[2,3,5,5,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,5,2,1,3]=>[2,3,5,6,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,2,3,1]=>[1,2,4,5,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,5,3,1,2]=>[3,4,6,1,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,2,5,3,2,1]=>[3,4,6,1,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,1,2,2,5]=>[1,3,6,2,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,2,5,2]=>[1,3,6,2,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,2,2]=>[4,6,2,1,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,2,1,2,5]=>[2,4,1,1,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,1,5,2]=>[4,6,3,3,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,2,2,1,5]=>[2,4,1,2,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,2,2,5,1]=>[2,4,1,2,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,2,5,1,2]=>[2,4,1,5,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,2,5,2,1]=>[2,4,1,5,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,5,1,2,2]=>[1,3,3,4,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,5,2,1,2]=>[2,4,4,6,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,5,2,2,1]=>[2,4,4,6,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,1,2,2,3]=>[1,5,4,2,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,1,2,3,2]=>[2,6,5,3,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,1,3,2,2]=>[2,6,5,4,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,2,1,2,3]=>[4,1,1,3,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,5,2,1,3,2]=>[4,1,1,3,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,2,2,1,3]=>[4,1,1,4,3,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,2,2,3,1]=>[4,1,1,4,5,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,2,3,1,2]=>[4,1,1,5,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,2,3,2,1]=>[4,1,1,5,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,3,1,2,2]=>[4,1,2,2,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,3,2,1,2]=>[4,1,2,3,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,3,2,2,1]=>[4,1,2,3,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,2,3,5]=>[2,1,2,3,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,1,2,5,3]=>[3,2,3,4,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,1,3,2,5]=>[2,1,2,4,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,1,3,5,2]=>[2,1,2,4,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,1,1,5,2,3]=>[4,3,4,1,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,1,5,3,2]=>[4,3,4,1,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,2,1,3,5]=>[2,1,3,1,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,2,1,5,3]=>[4,3,5,3,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,2,3,1,5]=>[4,3,5,5,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,2,3,5,1]=>[2,1,3,3,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,2,5,1,3]=>[2,1,3,5,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,2,5,3,1]=>[3,2,4,6,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,3,1,2,5]=>[3,2,5,1,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,1,5,2]=>[4,3,6,2,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,3,2,1,5]=>[2,1,4,1,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,1,3,2,5,1]=>[2,1,4,1,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,3,5,1,2]=>[2,1,4,4,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,5,2,1]=>[2,1,4,4,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,5,1,2,3]=>[2,1,6,5,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,5,1,3,2]=>[2,1,6,5,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,5,2,1,3]=>[4,3,1,1,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,5,2,3,1]=>[4,3,1,1,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,5,3,1,2]=>[4,3,1,2,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,5,3,2,1]=>[4,3,1,2,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,2,1,1,3,5]=>[2,2,1,2,4,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,2,1,1,5,3]=>[4,4,3,4,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,2,1,3,1,5]=>[4,4,3,6,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,2,1,3,5,1]=>[2,2,1,4,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,1,5,1,3]=>[2,2,1,6,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,1,5,3,1]=>[4,4,3,1,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,2,3,1,1,5]=>[1,1,2,6,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,2,3,1,5,1]=>[1,1,2,6,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,3,5,1,1]=>[1,1,2,3,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,5,1,1,3]=>[1,1,4,4,1,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,2,5,1,3,1]=>[1,1,4,4,3,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,5,3,1,1]=>[3,3,6,1,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[2,3,1,1,2,5]=>[1,2,6,1,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,1,1,5,2]=>[4,5,2,4,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,3,1,2,1,5]=>[4,5,2,5,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,1,2,5,1]=>[1,2,6,2,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,3,1,5,1,2]=>[1,2,6,5,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,5,2,1]=>[4,5,2,1,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,2,1,1,5]=>[2,3,1,1,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,2,1,5,1]=>[2,3,1,1,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,2,5,1,1]=>[2,3,1,5,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,3,5,1,1,2]=>[1,2,3,4,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,5,1,2,1]=>[2,3,4,5,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,5,2,1,1]=>[2,3,4,6,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,1,2,3]=>[1,4,4,1,2,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,5,1,1,3,2]=>[2,5,5,2,4,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,1,2,1,3]=>[2,5,5,3,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,1,2,3,1]=>[1,4,4,2,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,5,1,3,1,2]=>[1,4,4,3,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,5,1,3,2,1]=>[2,5,5,4,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,2,1,1,3]=>[2,5,6,1,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,2,1,3,1]=>[6,2,3,5,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,2,3,1,1]=>[1,4,5,2,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,3,1,1,2]=>[3,6,1,1,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,5,3,1,2,1]=>[3,6,1,1,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,5,3,2,1,1]=>[3,6,1,2,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,1,2,2,5]=>[1,6,1,2,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,1,2,5,2]=>[1,6,1,2,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,5,2,2]=>[4,2,4,1,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,2,1,2,5]=>[3,1,4,2,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,2,1,5,2]=>[4,2,5,3,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,2,2,1,5]=>[4,2,5,4,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,2,5,1]=>[1,6,2,1,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,2,5,1,2]=>[1,6,2,4,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,2,5,2,1]=>[5,3,6,1,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,2,2]=>[1,6,5,4,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,1,2]=>[4,2,1,1,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,5,2,2,1]=>[4,2,1,1,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,1,1,2,5]=>[2,1,1,2,3,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,1,5,2]=>[4,3,3,4,1,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,2,1,2,1,5]=>[2,1,1,3,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,2,1,2,5,1]=>[2,1,1,3,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,1,5,1,2]=>[2,1,1,6,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,5,2,1]=>[4,3,3,1,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,2,2,1,1,5]=>[2,1,2,1,2,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,2,2,1,5,1]=>[2,1,2,1,6,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,2,5,1,1]=>[2,1,2,5,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,2,5,1,1,2]=>[2,1,5,5,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,5,1,2,1]=>[2,1,5,5,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,5,2,1,1]=>[2,1,5,6,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,5,1,1,2,2]=>[1,3,4,1,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,5,1,2,1,2]=>[2,4,5,3,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,1,2,2,1]=>[2,4,5,3,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,2,1,1,2]=>[2,4,6,1,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,2,1,2,1]=>[2,4,6,1,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,2,2,1,1]=>[2,4,6,2,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,1,2,2,3]=>[1,4,1,2,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,1,1,2,3,2]=>[2,5,2,3,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,1,3,2,2]=>[2,5,2,4,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,1,2,1,2,3]=>[2,5,3,1,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,1,2,1,3,2]=>[2,5,3,1,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,2,2,1,3]=>[2,5,3,2,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,2,3,1]=>[1,4,2,1,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,2,3,1,2]=>[1,4,2,2,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,2,3,2,1]=>[2,5,3,3,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,1,3,1,2,2]=>[1,4,3,6,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,3,2,1,2]=>[2,5,4,1,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,3,2,2,1]=>[2,5,4,1,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,1,1,2,3]=>[2,6,1,2,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,2,1,1,3,2]=>[2,6,1,2,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,2,1,2,1,3]=>[2,6,1,3,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,1,2,3,1]=>[4,1,3,5,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,3,1,2]=>[4,1,3,6,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,3,2,1]=>[2,6,1,4,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,2,2,1,1,3]=>[2,6,2,1,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,2,1,3,1]=>[4,1,4,3,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,2,3,1,1]=>[1,5,1,2,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,2,3,1,1,2]=>[1,5,2,6,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,3,1,2,1]=>[4,1,5,2,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,3,2,1,1]=>[2,6,3,1,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,1,1,2,2]=>[3,1,1,3,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,3,1,2,1,2]=>[3,1,1,4,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,3,1,2,2,1]=>[3,1,1,4,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,2,1,1,2]=>[3,1,2,2,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,3,2,1,2,1]=>[3,1,2,2,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,3,2,2,1,1]=>[3,1,2,3,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,2,3,6]=>[1,1,2,1,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,2,2,6,3]=>[1,1,2,1,5,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,2,3,2,6]=>[2,2,3,3,1,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,2,3,6,2]=>[1,1,2,2,4,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,2,6,2,3]=>[1,1,2,5,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,2,6,3,2]=>[4,4,5,1,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,3,2,2,6]=>[2,2,4,1,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,3,2,6,2]=>[2,2,4,1,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,3,6,2,2]=>[1,1,3,4,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,6,2,2,3]=>[1,1,6,4,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,6,2,3,2]=>[3,3,1,6,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,6,3,2,2]=>[4,4,2,1,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,2,3,6]=>[2,3,1,3,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,1,2,6,3]=>[4,5,3,5,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,1,3,2,6]=>[2,3,1,4,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,3,6,2]=>[2,3,1,4,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,6,2,3]=>[3,4,2,1,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,1,6,3,2]=>[4,5,3,2,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,2,1,3,6]=>[2,3,2,1,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,2,1,6,3]=>[4,5,4,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,2,3,1,6]=>[3,4,3,4,1,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,2,2,3,6,1]=>[1,2,1,2,4,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,2,6,1,3]=>[1,2,1,5,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,2,6,3,1]=>[4,5,4,1,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,3,1,2,6]=>[1,2,2,6,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,2,3,1,6,2]=>[3,4,4,1,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,2,3,2,1,6]=>[3,4,4,2,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,3,2,6,1]=>[2,3,3,1,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,3,6,1,2]=>[1,2,2,4,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,6,2,1]=>[2,3,3,5,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,6,1,2,3]=>[1,2,5,3,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,6,1,3,2]=>[2,3,6,4,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,6,2,1,3]=>[2,3,6,5,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,6,2,3,1]=>[1,2,5,4,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,3,1,2]=>[4,5,1,1,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,6,3,2,1]=>[4,5,1,1,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,1,2,2,6]=>[1,3,6,2,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,1,2,6,2]=>[1,3,6,2,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,6,2,2]=>[3,5,1,1,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,1,2,6]=>[2,4,1,1,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,2,1,6,2]=>[3,5,2,2,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,2,2,1,6]=>[3,5,2,3,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,2,2,6,1]=>[2,4,1,2,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,2,6,1,2]=>[2,4,1,6,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,2,6,2,1]=>[2,4,1,6,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,6,1,2,2]=>[1,3,4,3,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,6,2,1,2]=>[2,4,5,5,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,6,2,2,1]=>[2,4,5,5,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,1,2,2,3]=>[1,6,3,2,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,6,1,2,3,2]=>[3,1,5,4,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,1,3,2,2]=>[3,1,5,5,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,6,2,1,2,3]=>[3,1,6,2,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,2,1,3,2]=>[3,1,6,2,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,2,2,1,3]=>[3,1,6,3,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,2,2,3,1]=>[3,1,6,3,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,6,2,3,1,2]=>[3,1,6,4,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,6,2,3,2,1]=>[3,1,6,4,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,3,1,2,2]=>[4,2,1,2,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,3,2,1,2]=>[4,2,1,3,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,3,2,2,1]=>[4,2,1,3,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,2,3,6]=>[2,1,2,3,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,1,1,2,6,3]=>[4,3,4,5,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,1,3,2,6]=>[2,1,2,4,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,1,1,3,6,2]=>[2,1,2,4,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,1,6,2,3]=>[3,2,3,1,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,1,6,3,2]=>[4,3,4,2,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,2,1,3,6]=>[2,1,3,1,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,1,6,3]=>[4,3,5,3,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,2,3,1,6]=>[3,2,4,4,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,2,3,6,1]=>[2,1,3,3,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,2,6,1,3]=>[2,1,3,6,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,2,6,3,1]=>[4,3,5,1,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,1,2,6]=>[4,3,6,2,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,1,6,2]=>[3,2,5,1,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,2,1,6]=>[3,2,5,2,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,3,2,6,1]=>[2,1,4,1,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,3,6,1,2]=>[2,1,4,5,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,6,2,1]=>[2,1,4,5,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,6,1,2,3]=>[3,2,1,5,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,6,1,3,2]=>[3,2,1,5,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,6,2,1,3]=>[3,2,1,6,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,6,2,3,1]=>[3,2,1,6,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,6,3,1,2]=>[4,3,2,1,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,6,3,2,1]=>[4,3,2,1,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,2,1,1,3,6]=>[2,2,1,2,4,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,2,1,1,6,3]=>[4,4,3,4,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,2,1,3,1,6]=>[3,3,2,5,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,2,1,3,6,1]=>[2,2,1,4,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,1,6,1,3]=>[3,3,2,1,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,2,1,6,3,1]=>[4,4,3,2,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,2,3,1,1,6]=>[3,3,4,1,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,2,3,1,6,1]=>[3,3,4,1,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,3,6,1,1]=>[1,1,2,4,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,6,1,1,3]=>[1,1,5,3,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,6,1,3,1]=>[1,1,5,3,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,6,3,1,1]=>[4,4,1,1,2,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,3,1,1,2,6]=>[1,2,6,1,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,1,1,6,2]=>[3,4,1,3,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,3,1,2,1,6]=>[3,4,1,4,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,1,2,6,1]=>[1,2,6,2,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,6,1,2]=>[3,4,1,1,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,3,1,6,2,1]=>[3,4,1,1,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,2,1,1,6]=>[3,4,2,2,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,2,1,6,1]=>[3,4,2,2,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,2,6,1,1]=>[2,3,1,6,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,6,1,1,2]=>[1,2,4,3,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,6,1,2,1]=>[2,3,5,4,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,6,2,1,1]=>[2,3,5,5,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,1,1,2,3]=>[1,5,3,1,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,6,1,1,3,2]=>[2,6,4,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,6,1,2,1,3]=>[2,6,4,3,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,6,1,2,3,1]=>[1,5,3,2,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,1,3,1,2]=>[1,5,3,3,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,6,1,3,2,1]=>[2,6,4,4,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,2,1,1,3]=>[2,6,5,1,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,2,1,3,1]=>[6,3,2,5,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,2,3,1,1]=>[1,5,4,2,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,3,1,1,2]=>[4,1,1,2,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,3,1,2,1]=>[4,1,1,2,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,3,2,1,1]=>[4,1,1,3,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,1,1,2,2,6]=>[1,6,1,2,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,1,2,6,2]=>[1,6,1,2,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,6,2,2]=>[3,1,3,1,6,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,2,1,2,6]=>[4,2,5,3,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,2,1,6,2]=>[3,1,4,2,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,2,2,1,6]=>[3,1,4,3,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,1,2,2,6,1]=>[1,6,2,1,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,2,6,1,2]=>[1,6,2,5,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,2,6,2,1]=>[5,3,6,2,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,6,1,2,2]=>[3,1,1,5,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,6,2,1,2]=>[3,1,1,6,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,6,2,2,1]=>[3,1,1,6,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,2,1,1,2,6]=>[2,1,1,2,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,2,1,1,6,2]=>[3,2,2,3,1,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,1,2,1,6]=>[3,2,2,4,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[3,2,1,2,6,1]=>[2,1,1,3,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,1,6,1,2]=>[3,2,2,1,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,1,6,2,1]=>[3,2,2,1,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,2,2,1,1,6]=>[3,2,3,2,3,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,2,1,6,1]=>[3,2,3,2,1,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,2,6,1,1]=>[2,1,2,6,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,2,6,1,1,2]=>[2,1,6,4,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,6,1,2,1]=>[2,1,6,4,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,6,2,1,1]=>[2,1,6,5,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,6,1,1,2,2]=>[1,4,3,1,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,6,1,2,1,2]=>[2,5,4,3,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,6,1,2,2,1]=>[2,5,4,3,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,6,2,1,1,2]=>[2,5,5,1,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,6,2,1,2,1]=>[2,5,5,1,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,6,2,2,1,1]=>[2,5,5,2,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,1,1,2,2,3]=>[1,3,1,2,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[6,1,1,2,3,2]=>[2,4,2,3,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,1,3,2,2]=>[2,4,2,4,1,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[6,1,2,1,2,3]=>[2,4,3,1,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[6,1,2,1,3,2]=>[2,4,3,1,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,2,2,1,3]=>[2,4,3,2,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,2,2,3,1]=>[1,3,2,1,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,1,2,3,1,2]=>[1,3,2,2,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[6,1,2,3,2,1]=>[2,4,3,3,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,1,3,1,2,2]=>[1,3,3,6,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,3,2,1,2]=>[2,4,4,1,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,3,2,2,1]=>[2,4,4,1,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[6,2,1,1,2,3]=>[2,5,1,2,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,2,1,1,3,2]=>[2,5,1,2,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,1,2,1,3]=>[2,5,1,3,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,1,2,3,1]=>[3,6,2,4,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,1,3,1,2]=>[3,6,2,5,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,1,3,2,1]=>[2,5,1,4,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,2,2,1,1,3]=>[2,5,2,1,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,2,2,1,3,1]=>[3,6,3,2,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,2,3,1,1]=>[1,4,1,2,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,2,3,1,1,2]=>[1,4,2,6,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,2,3,1,2,1]=>[3,6,4,1,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,3,2,1,1]=>[2,5,3,1,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,3,1,1,2,2]=>[1,5,6,1,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,3,1,2,1,2]=>[4,1,2,5,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,1,2,2,1]=>[4,1,2,5,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,2,1,1,2]=>[2,6,1,1,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,3,2,1,2,1]=>[2,6,1,1,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,3,2,2,1,1]=>[2,6,1,2,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,2,4,4]=>[1,1,2,1,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,2,4,2,4]=>[1,1,2,3,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,2,4,4,2]=>[1,1,2,3,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,4,2,2,4]=>[1,1,4,6,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,4,2,4,2]=>[3,3,6,1,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,4,4,2,2]=>[1,1,4,1,6,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,1,2,4,4]=>[2,3,1,3,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,4,2,4]=>[3,4,2,6,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,4,4,2]=>[3,4,2,6,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,2,1,4,4]=>[2,3,2,1,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,2,4,1,4]=>[1,2,1,3,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,4,4,1]=>[1,2,1,3,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,2,4,1,2,4]=>[1,2,3,5,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,4,1,4,2]=>[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,2,1,4]=>[3,4,5,1,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,2,4,1]=>[1,2,3,6,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,4,4,1,2]=>[1,2,3,1,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,4,4,2,1]=>[3,4,5,3,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,2,2,4]=>[1,4,5,2,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,2,4,2]=>[1,4,5,2,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,4,2,2]=>[5,1,2,1,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,2,1,2,4]=>[3,6,1,2,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,1,4,2]=>[5,1,3,4,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,2,2,1,4]=>[5,1,3,5,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,2,2,4,1]=>[1,4,6,1,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,4,1,2]=>[1,4,6,3,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,4,2,1]=>[3,6,1,5,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,4,1,2,2]=>[1,4,1,5,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,4,2,1,2]=>[3,6,3,1,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,4,2,2,1]=>[3,6,3,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,2,4,4]=>[2,1,2,3,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,1,4,2,4]=>[3,2,3,6,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,4,4,2]=>[3,2,3,6,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,2,1,4,4]=>[2,1,3,1,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,2,4,1,4]=>[2,1,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,4,4,1]=>[2,1,3,4,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,1,2,4]=>[2,1,5,6,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,1,4,2]=>[5,4,1,2,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,4,2,1,4]=>[5,4,1,3,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,2,4,1]=>[6,5,2,4,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,4,1,2]=>[2,1,5,2,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,4,2,1]=>[3,2,6,3,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,1,1,4,4]=>[2,2,1,2,5,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,2,1,4,1,4]=>[5,5,4,1,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,2,1,4,4,1]=>[2,2,1,5,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,4,1,1,4]=>[1,1,3,5,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,4,1,4,1]=>[1,1,3,5,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,4,4,1,1]=>[1,1,3,1,5,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,4,1,1,2,4]=>[1,3,5,1,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,1,1,4,2]=>[1,3,5,1,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,1,2,1,4]=>[2,4,6,3,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,2,4,1]=>[1,3,5,2,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,1,4,1,2]=>[1,3,5,4,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,1,4,2,1]=>[6,1,3,2,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,1,1,4]=>[3,5,1,2,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,2,1,4,1]=>[6,1,4,5,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,4,1,1]=>[1,3,6,3,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,4,1,1,2]=>[1,3,1,5,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,4,1,2,1]=>[2,4,2,6,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,4,2,1,1]=>[3,5,3,1,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,1,2,2,4]=>[1,5,1,2,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,2,4,2]=>[1,5,1,2,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,1,4,2,2]=>[1,5,1,4,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,2,1,2,4]=>[2,6,3,1,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,2,1,4,2]=>[5,2,6,4,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,2,1,4]=>[2,6,3,2,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,2,4,1]=>[1,5,2,1,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,2,4,1,2]=>[1,5,2,3,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,2,4,2,1]=>[4,1,5,6,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,1,2,2]=>[1,5,4,5,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,4,2,1,2]=>[5,2,1,3,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,2,2,1]=>[5,2,1,3,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,2,4]=>[3,1,2,3,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,1,4,2]=>[3,1,2,3,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,2,1,2,1,4]=>[3,1,2,4,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,1,2,4,1]=>[4,2,3,5,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,4,1,2]=>[5,3,4,1,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,4,2,1]=>[3,1,2,6,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,2,1,1,4]=>[3,1,3,2,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,2,2,1,4,1]=>[5,3,5,4,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,4,1,1]=>[1,6,1,3,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,2,4,1,1,2]=>[1,6,3,5,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,4,1,2,1]=>[4,2,6,1,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,4,2,1,1]=>[3,1,5,1,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,1,1,2,2]=>[1,1,5,1,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,4,1,2,1,2]=>[2,2,6,3,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,4,1,2,2,1]=>[2,2,6,3,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,4,2,1,1,2]=>[3,3,1,2,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,2,1,2,1]=>[3,3,1,2,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,2,2,1,1]=>[3,3,1,3,2,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,2,2,4,5]=>[1,1,2,1,3,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,2,2,5,4]=>[2,2,3,2,5,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,2,4,2,5]=>[1,1,2,3,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,2,4,5,2]=>[1,1,2,3,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,2,5,2,4]=>[1,1,2,4,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,5,4,2]=>[3,3,4,6,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,4,2,2,5]=>[1,1,4,6,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,4,2,5,2]=>[5,5,1,3,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,4,5,2,2]=>[1,1,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,5,2,2,4]=>[1,1,5,5,1,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,5,2,4,2]=>[4,4,1,1,6,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,5,4,2,2]=>[4,4,1,3,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,2,4,5]=>[2,3,1,3,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,1,2,5,4]=>[2,3,1,3,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,1,4,2,5]=>[5,6,4,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,4,5,2]=>[2,3,1,5,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,1,5,2,4]=>[4,5,3,1,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,5,4,2]=>[4,5,3,1,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,2,1,4,5]=>[2,3,2,1,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,2,1,5,4]=>[2,3,2,1,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,2,4,1,5]=>[1,2,1,3,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,2,4,5,1]=>[1,2,1,3,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,2,5,1,4]=>[1,2,1,4,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,2,2,5,4,1]=>[2,3,2,5,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,4,1,2,5]=>[1,2,3,5,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,4,1,5,2]=>[4,5,6,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,4,2,1,5]=>[4,5,6,2,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,2,5,1]=>[1,2,3,6,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,4,5,1,2]=>[1,2,3,2,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,4,5,2,1]=>[2,3,4,3,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,5,1,2,4]=>[1,2,4,4,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,5,1,4,2]=>[5,6,1,1,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,2,5,2,1,4]=>[5,6,1,2,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,5,2,4,1]=>[1,2,4,5,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,5,4,1,2]=>[2,3,5,1,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,5,4,2,1]=>[3,4,6,2,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,1,2,2,5]=>[1,4,5,2,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,1,2,5,2]=>[5,1,2,6,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,1,5,2,2]=>[5,1,2,2,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,4,2,1,2,5]=>[5,1,3,4,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,1,5,2]=>[5,1,3,4,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,2,2,1,5]=>[5,1,3,5,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,2,2,5,1]=>[5,1,3,5,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,4,2,5,1,2]=>[5,1,3,1,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,2,5,2,1]=>[5,1,3,1,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,5,1,2,2]=>[1,4,2,4,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,4,5,2,1,2]=>[2,5,3,6,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,5,2,2,1]=>[2,5,3,6,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,2,2,4]=>[1,5,4,2,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,2,4,2]=>[1,5,4,2,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,4,2,2]=>[5,2,1,1,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,2,1,2,4]=>[4,1,1,3,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,2,1,4,2]=>[5,2,2,4,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,2,2,1,4]=>[5,2,2,5,4,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,2,2,4,1]=>[4,1,1,4,6,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,5,2,4,1,2]=>[4,1,1,6,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,5,2,4,2,1]=>[4,1,1,6,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,4,1,2,2]=>[4,1,3,1,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,4,2,1,2]=>[4,1,3,2,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,4,2,2,1]=>[4,1,3,2,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,2,4,5]=>[2,1,2,3,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,1,2,5,4]=>[2,1,2,3,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,1,4,2,5]=>[5,4,5,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,1,4,5,2]=>[2,1,2,5,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,1,5,2,4]=>[4,3,4,1,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,1,1,5,4,2]=>[4,3,4,1,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,2,1,4,5]=>[2,1,3,1,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,2,1,5,4]=>[2,1,3,1,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,1,2,4,1,5]=>[4,3,5,6,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,2,4,5,1]=>[2,1,3,4,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,2,5,1,4]=>[5,4,6,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,2,5,4,1]=>[2,1,3,5,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,1,2,5]=>[5,4,1,2,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,1,5,2]=>[5,4,1,2,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,4,2,1,5]=>[5,4,1,3,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,4,2,5,1]=>[5,4,1,3,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,1,4,5,1,2]=>[2,1,5,3,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,5,2,1]=>[2,1,5,3,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,5,1,2,4]=>[2,1,6,5,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,1,4,2]=>[5,4,2,1,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,5,2,1,4]=>[5,4,2,2,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,5,2,4,1]=>[4,3,1,1,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,1,5,4,1,2]=>[4,3,1,3,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,5,4,2,1]=>[4,3,1,3,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,2,1,1,4,5]=>[2,2,1,2,5,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,1,1,5,4]=>[2,2,1,2,6,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,2,1,4,1,5]=>[5,5,4,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,1,4,5,1]=>[2,2,1,5,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,1,5,1,4]=>[5,5,4,2,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,2,1,5,4,1]=>[4,4,3,1,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,2,4,1,1,5]=>[1,1,3,5,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,4,1,5,1]=>[1,1,3,5,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,4,5,1,1]=>[1,1,3,2,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,5,1,1,4]=>[1,1,4,4,1,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,5,1,4,1]=>[5,5,1,1,1,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,2,5,4,1,1]=>[2,2,5,1,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,4,1,1,2,5]=>[1,3,5,1,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,4,1,1,5,2]=>[4,6,1,4,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,4,1,2,1,5]=>[4,6,1,5,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,1,2,5,1]=>[1,3,5,2,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,1,5,1,2]=>[1,3,5,5,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,1,5,2,1]=>[4,6,1,1,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,2,1,1,5]=>[4,6,2,3,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,2,1,5,1]=>[6,1,4,5,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,5,1,1]=>[1,3,6,4,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,4,5,1,1,2]=>[1,3,2,4,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,4,5,1,2,1]=>[2,4,3,5,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,5,2,1,1]=>[2,4,3,6,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,1,2,4]=>[1,4,4,1,2,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,1,1,4,2]=>[5,1,1,5,1,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,5,1,2,1,4]=>[5,1,1,6,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,5,1,2,4,1]=>[1,4,4,2,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,1,4,1,2]=>[5,1,1,1,2,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,5,1,4,2,1]=>[5,1,1,1,3,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,5,2,1,1,4]=>[5,1,2,4,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,2,1,4,1]=>[5,1,2,4,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,2,4,1,1]=>[1,4,5,3,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,5,4,1,1,2]=>[2,5,1,6,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,4,1,2,1]=>[2,5,1,6,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,4,2,1,1]=>[3,6,2,1,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,1,2,2,5]=>[1,5,1,2,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,1,2,5,2]=>[1,5,1,2,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,1,5,2,2]=>[4,1,4,1,1,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,1,2,1,2,5]=>[2,6,3,1,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,2,1,5,2]=>[4,1,5,3,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,2,2,1,5]=>[4,1,5,4,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,2,2,5,1]=>[1,5,2,1,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,2,5,1,2]=>[1,5,2,4,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,1,2,5,2,1]=>[5,2,6,1,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,5,1,2,2]=>[1,5,5,4,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,5,2,1,2]=>[4,1,1,1,3,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,5,2,2,1]=>[4,1,1,1,4,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[4,2,1,1,2,5]=>[3,1,2,3,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,1,1,5,2]=>[4,2,3,4,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,2,1,5]=>[4,2,3,5,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,2,5,1]=>[5,3,4,6,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,1,5,1,2]=>[5,3,4,2,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,5,2,1]=>[4,2,3,1,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,2,2,1,1,5]=>[4,2,4,3,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,2,1,5,1]=>[5,3,5,4,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,2,5,1,1]=>[1,6,1,4,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,2,5,1,1,2]=>[1,6,4,4,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,5,1,2,1]=>[5,3,1,1,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,5,2,1,1]=>[5,3,1,2,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,5,1,1,2,2]=>[1,2,4,1,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,5,1,2,1,2]=>[2,3,5,3,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,5,1,2,2,1]=>[2,3,5,3,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,5,2,1,1,2]=>[2,3,6,1,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,5,2,1,2,1]=>[2,3,6,1,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,5,2,2,1,1]=>[2,3,6,2,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,1,2,2,4]=>[1,4,1,2,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,1,2,4,2]=>[1,4,1,2,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,1,4,2,2]=>[1,4,1,4,6,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,1,2,1,2,4]=>[2,5,3,1,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,1,4,2]=>[5,1,6,4,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,2,2,1,4]=>[2,5,3,2,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,1,2,2,4,1]=>[1,4,2,1,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,2,4,1,2]=>[1,4,2,3,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,4,2,1]=>[3,6,4,5,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,4,1,2,2]=>[1,4,4,5,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,4,2,1,2]=>[5,1,1,3,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,4,2,2,1]=>[5,1,1,3,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,1,1,2,4]=>[2,6,1,2,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,1,1,4,2]=>[5,2,4,5,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,2,1,4]=>[2,6,1,3,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,1,2,4,1]=>[4,1,3,5,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,1,4,1,2]=>[5,2,4,1,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,4,2,1]=>[5,2,4,1,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,2,1,1,4]=>[2,6,2,1,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,2,2,1,4,1]=>[5,2,5,4,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,2,4,1,1]=>[1,5,1,3,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,2,4,1,1,2]=>[1,5,3,5,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,2,4,1,2,1]=>[4,1,6,1,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,4,2,1,1]=>[4,1,6,2,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,1,1,2,2]=>[2,1,6,2,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,4,1,2,1,2]=>[2,1,6,3,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,4,1,2,2,1]=>[2,1,6,3,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,2,1,1,2]=>[3,2,1,2,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,2,1,2,1]=>[3,2,1,2,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,4,2,2,1,1]=>[3,2,1,3,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,2,4,6]=>[1,1,2,1,3,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,2,2,6,4]=>[1,1,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,2,4,2,6]=>[1,1,2,3,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,2,4,6,2]=>[1,1,2,3,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,2,6,2,4]=>[1,1,2,5,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,2,6,4,2]=>[4,4,5,1,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,4,2,2,6]=>[1,1,4,6,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,4,2,6,2]=>[5,5,1,3,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,4,6,2,2]=>[1,1,4,3,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,6,2,2,4]=>[1,1,6,4,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,6,2,4,2]=>[3,3,1,6,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,6,4,2,2]=>[3,3,1,1,1,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,1,2,4,6]=>[2,3,1,3,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,1,2,6,4]=>[4,5,3,5,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,4,2,6]=>[5,6,4,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,4,6,2]=>[2,3,1,5,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,6,2,4]=>[3,4,2,1,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,6,4,2]=>[3,4,2,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,2,2,1,4,6]=>[2,3,2,1,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,2,1,6,4]=>[3,4,3,2,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,2,4,1,6]=>[1,2,1,3,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,2,4,6,1]=>[1,2,1,3,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,2,6,1,4]=>[1,2,1,5,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,6,4,1]=>[4,5,4,1,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,4,1,2,6]=>[1,2,3,5,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,1,6,2]=>[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,2,1,6]=>[3,4,5,1,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,4,2,6,1]=>[1,2,3,6,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,4,6,1,2]=>[1,2,3,3,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,4,6,2,1]=>[2,3,4,4,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,6,1,2,4]=>[1,2,5,3,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,6,1,4,2]=>[1,2,5,3,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,6,2,1,4]=>[5,6,2,1,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,6,2,4,1]=>[1,2,5,4,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,6,4,1,2]=>[4,5,1,2,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,6,4,2,1]=>[4,5,1,2,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,1,2,2,6]=>[1,4,5,2,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,1,2,6,2]=>[5,1,2,6,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,1,6,2,2]=>[5,1,2,3,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,2,1,2,6]=>[5,1,3,4,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,1,6,2]=>[5,1,3,4,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,2,2,1,6]=>[3,6,1,3,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,2,2,6,1]=>[1,4,6,1,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,6,1,2]=>[1,4,6,5,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,6,2,1]=>[5,1,3,2,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,6,1,2,2]=>[1,4,3,3,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,4,6,2,1,2]=>[2,5,4,5,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,6,2,2,1]=>[2,5,4,5,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,1,2,2,4]=>[1,6,3,2,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,6,1,2,4,2]=>[3,1,5,4,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,1,4,2,2]=>[3,1,5,6,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,2,1,2,4]=>[3,1,6,2,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,1,4,2]=>[5,3,1,4,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,6,2,2,1,4]=>[5,3,1,5,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,2,2,4,1]=>[1,6,4,1,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,4,1,2]=>[1,6,4,3,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,4,2,1]=>[3,1,6,5,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,4,1,2,2]=>[4,2,2,1,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,4,2,1,2]=>[3,1,1,1,2,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,6,4,2,2,1]=>[3,1,1,1,3,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,1,2,4,6]=>[2,1,2,3,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,1,2,6,4]=>[4,3,4,5,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,1,4,2,6]=>[5,4,5,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,4,6,2]=>[2,1,2,5,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,1,6,2,4]=>[3,2,3,1,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,6,4,2]=>[3,2,3,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,2,1,4,6]=>[2,1,3,1,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,1,6,4]=>[3,2,4,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,2,4,1,6]=>[4,3,5,6,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,4,6,1]=>[2,1,3,4,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,6,1,4]=>[2,1,3,6,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,6,4,1]=>[4,3,5,1,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,4,1,2,6]=>[5,4,1,2,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,4,1,6,2]=>[5,4,1,2,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,4,2,1,6]=>[3,2,6,1,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,4,2,6,1]=>[6,5,2,4,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,6,1,2]=>[2,1,5,4,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,4,6,2,1]=>[2,1,5,4,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,6,1,2,4]=>[3,2,1,5,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,6,1,4,2]=>[3,2,1,5,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,6,2,1,4]=>[5,4,3,1,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,6,2,4,1]=>[6,5,4,2,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,4,1,2]=>[4,3,2,2,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,6,4,2,1]=>[3,2,1,1,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[2,2,1,1,4,6]=>[2,2,1,2,5,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,2,1,1,6,4]=>[3,3,2,3,1,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,2,1,4,1,6]=>[5,5,4,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,4,6,1]=>[2,2,1,5,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,1,6,1,4]=>[3,3,2,1,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,1,6,4,1]=>[4,4,3,2,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,2,4,1,1,6]=>[1,1,3,5,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,2,4,1,6,1]=>[1,1,3,5,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,4,6,1,1]=>[1,1,3,3,3,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[2,2,6,1,1,4]=>[1,1,5,3,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,6,1,4,1]=>[1,1,5,3,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,6,4,1,1]=>[4,4,1,2,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,4,1,1,2,6]=>[1,3,5,1,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,1,1,6,2]=>[1,3,5,1,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,1,2,1,6]=>[4,6,1,5,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,2,6,1]=>[1,3,5,2,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,1,6,1,2]=>[1,3,5,6,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,1,6,2,1]=>[6,1,3,4,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,1,1,6]=>[3,5,1,2,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,2,1,6,1]=>[3,5,1,2,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,2,6,1,1]=>[1,3,6,5,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,6,1,1,2]=>[1,3,3,3,1,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,4,6,1,2,1]=>[2,4,4,4,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,4,6,2,1,1]=>[2,4,4,5,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,6,1,1,2,4]=>[1,5,3,1,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,1,1,4,2]=>[1,5,3,1,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,6,1,2,1,4]=>[2,6,4,3,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,1,2,4,1]=>[1,5,3,2,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,6,1,4,1,2]=>[1,5,3,4,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,6,1,4,2,1]=>[6,3,1,2,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,2,1,1,4]=>[5,2,1,4,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,6,2,1,4,1]=>[5,2,1,4,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,6,2,4,1,1]=>[1,5,4,3,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,4,1,1,2]=>[4,1,2,1,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,4,1,2,1]=>[4,1,2,1,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,4,2,1,1]=>[4,1,2,2,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,1,1,2,2,6]=>[1,5,1,2,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[4,1,1,2,6,2]=>[1,5,1,2,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,1,6,2,2]=>[1,5,1,6,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,2,1,2,6]=>[4,1,5,3,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,2,1,6,2]=>[5,2,6,4,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,2,1,6]=>[4,1,5,4,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,1,2,2,6,1]=>[1,5,2,1,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,2,6,1,2]=>[1,5,2,5,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,2,6,2,1]=>[5,2,6,2,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,6,1,2,2]=>[1,5,6,3,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,6,2,1,2]=>[5,2,3,1,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,2,2,1]=>[5,2,3,1,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,2,6]=>[4,2,3,4,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,1,1,6,2]=>[3,1,2,3,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,2,1,2,1,6]=>[3,1,2,4,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,2,1,2,6,1]=>[4,2,3,5,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,6,1,2]=>[3,1,2,1,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,6,2,1]=>[3,1,2,1,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,2,1,1,6]=>[3,1,3,2,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,2,2,1,6,1]=>[3,1,3,2,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,2,6,1,1]=>[1,6,1,5,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,2,6,1,1,2]=>[1,6,5,3,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,6,1,2,1]=>[4,2,1,6,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,6,2,1,1]=>[5,3,2,1,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,6,1,1,2,2]=>[1,3,3,1,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,6,1,2,1,2]=>[2,4,4,3,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,6,1,2,2,1]=>[2,4,4,3,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,6,2,1,1,2]=>[2,4,5,1,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,6,2,1,2,1]=>[2,4,5,1,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,6,2,2,1,1]=>[2,4,5,2,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,1,1,2,2,4]=>[1,3,1,2,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,1,2,4,2]=>[1,3,1,2,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,1,4,2,2]=>[1,3,1,4,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[6,1,2,1,2,4]=>[2,4,3,1,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,2,1,4,2]=>[3,5,4,2,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,2,2,1,4]=>[2,4,3,2,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,2,2,4,1]=>[1,3,2,1,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,2,4,1,2]=>[1,3,2,3,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,1,2,4,2,1]=>[3,5,4,5,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,1,4,1,2,2]=>[1,3,4,5,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,4,2,1,2]=>[3,5,6,1,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,2,2,1]=>[3,5,6,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,1,1,2,4]=>[2,5,1,2,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,1,1,4,2]=>[5,1,4,5,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,2,1,2,1,4]=>[2,5,1,3,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,2,1,2,4,1]=>[2,5,1,3,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,1,4,1,2]=>[5,1,4,1,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,1,4,2,1]=>[5,1,4,1,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,2,2,1,1,4]=>[2,5,2,1,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,2,2,1,4,1]=>[5,1,5,4,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,2,4,1,1]=>[1,4,1,3,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,2,4,1,1,2]=>[1,4,3,5,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,4,1,2,1]=>[2,5,4,6,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,4,2,1,1]=>[3,6,5,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,4,1,1,2,2]=>[1,6,5,1,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,4,1,2,1,2]=>[4,2,1,5,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,4,1,2,2,1]=>[4,2,1,5,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,2,1,1,2]=>[3,1,1,2,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,2,1,2,1]=>[3,1,1,2,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,2,2,1,1]=>[3,1,1,3,2,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,2,2,5,5]=>[1,1,2,1,4,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,2,5,2,5]=>[1,1,2,4,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,5,5,2]=>[1,1,2,4,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,5,2,2,5]=>[1,1,5,5,1,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,5,2,5,2]=>[5,5,2,2,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,5,5,2,2]=>[1,1,5,1,5,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,2,1,2,5,5]=>[2,3,1,3,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,1,5,2,5]=>[5,6,4,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,1,5,5,2]=>[4,5,3,1,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,2,1,5,5]=>[2,3,2,1,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,2,5,1,5]=>[1,2,1,4,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,5,5,1]=>[1,2,1,4,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,2,5,1,2,5]=>[1,2,4,4,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,2,5,1,5,2]=>[5,6,1,1,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,5,2,1,5]=>[5,6,1,2,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,5,2,5,1]=>[5,6,1,2,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,5,5,1,2]=>[1,2,4,1,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,5,5,2,1]=>[2,3,5,2,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,2,2,5]=>[1,5,4,2,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,1,2,5,2]=>[5,2,1,6,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,5,1,5,2,2]=>[5,2,1,2,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,5,2,1,2,5]=>[5,2,2,4,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,2,1,5,2]=>[4,1,1,3,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,2,2,1,5]=>[4,1,1,4,3,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,5,2,2,5,1]=>[5,2,2,5,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,2,5,1,2]=>[5,2,2,1,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,5,2,5,2,1]=>[5,2,2,1,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,5,1,2,2]=>[1,5,1,4,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,5,2,1,2]=>[4,1,4,1,3,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,5,2,2,1]=>[4,1,4,1,4,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,1,2,5,5]=>[2,1,2,3,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,5,2,5]=>[5,4,5,2,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,1,5,5,2]=>[4,3,4,1,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,1,2,1,5,5]=>[2,1,3,1,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,2,5,1,5]=>[5,4,6,1,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,2,5,5,1]=>[2,1,3,5,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,5,1,2,5]=>[5,4,2,1,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,5,1,5,2]=>[5,4,2,1,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,5,2,1,5]=>[4,3,1,1,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,5,2,5,1]=>[5,4,2,2,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,5,5,1,2]=>[2,1,6,2,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,5,2,1]=>[4,3,1,4,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,2,1,1,5,5]=>[2,2,1,2,6,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,2,1,5,1,5]=>[5,5,4,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,1,5,5,1]=>[2,2,1,6,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,5,1,1,5]=>[1,1,4,4,1,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,2,5,1,5,1]=>[5,5,1,1,2,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,2,5,5,1,1]=>[1,1,4,1,4,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[2,5,1,1,2,5]=>[1,4,4,1,2,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,5,1,1,5,2]=>[5,1,1,5,2,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,5,1,2,1,5]=>[5,1,1,6,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,1,2,5,1]=>[5,1,1,6,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[2,5,1,5,1,2]=>[5,1,1,2,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,5,1,5,2,1]=>[5,1,1,2,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,2,1,1,5]=>[5,1,2,4,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,2,1,5,1]=>[5,1,2,4,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,2,5,1,1]=>[5,1,2,1,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,5,1,1,2]=>[1,4,1,4,1,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,5,5,1,2,1]=>[2,5,2,5,3,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,5,5,2,1,1]=>[2,5,2,6,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,1,2,2,5]=>[1,4,1,2,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,1,1,2,5,2]=>[1,4,1,2,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,1,5,2,2]=>[1,4,1,5,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[5,1,2,1,2,5]=>[2,5,3,1,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,1,2,1,5,2]=>[5,1,6,4,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,2,2,1,5]=>[2,5,3,2,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,2,2,5,1]=>[1,4,2,1,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[5,1,2,5,1,2]=>[1,4,2,4,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[5,1,2,5,2,1]=>[5,1,6,1,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,5,1,2,2]=>[1,4,5,4,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,5,2,1,2]=>[5,1,2,2,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,5,2,2,1]=>[5,1,2,2,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,1,1,2,5]=>[2,6,1,2,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,1,1,5,2]=>[4,1,3,4,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,2,1,2,1,5]=>[4,1,3,5,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,2,1,2,5,1]=>[5,2,4,6,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,1,5,1,2]=>[5,2,4,2,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,5,2,1]=>[4,1,3,1,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[5,2,2,1,1,5]=>[4,1,4,3,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,2,2,1,5,1]=>[5,2,5,4,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,2,5,1,1]=>[1,5,1,4,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,2,5,1,1,2]=>[1,5,4,4,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,2,5,1,2,1]=>[5,2,1,1,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,5,2,1,1]=>[5,2,1,2,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,5,1,1,2,2]=>[1,1,4,1,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,5,1,2,1,2]=>[2,2,5,3,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,5,1,2,2,1]=>[2,2,5,3,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,5,2,1,1,2]=>[2,2,6,1,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,5,2,1,2,1]=>[2,2,6,1,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,5,2,2,1,1]=>[2,2,6,2,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,2,2,5,6]=>[1,1,2,1,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,2,2,6,5]=>[2,2,3,2,6,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,2,5,2,6]=>[1,1,2,4,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,2,5,6,2]=>[1,1,2,4,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,2,6,2,5]=>[1,1,2,5,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,2,6,5,2]=>[4,4,5,1,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,5,2,2,6]=>[4,4,1,1,4,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,5,2,6,2]=>[5,5,2,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,5,6,2,2]=>[1,1,5,2,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,6,2,2,5]=>[1,1,6,4,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,6,2,5,2]=>[5,5,3,1,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,6,5,2,2]=>[4,4,2,3,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,2,5,6]=>[2,3,1,3,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,1,2,6,5]=>[2,3,1,3,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,1,5,2,6]=>[4,5,3,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,2,1,5,6,2]=>[2,3,1,6,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,1,6,2,5]=>[5,6,4,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,1,6,5,2]=>[4,5,3,2,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,2,1,5,6]=>[2,3,2,1,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,2,1,6,5]=>[3,4,3,2,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,5,1,6]=>[1,2,1,4,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,2,5,6,1]=>[1,2,1,4,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,2,6,1,5]=>[1,2,1,5,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,2,6,5,1]=>[2,3,2,6,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,5,1,2,6]=>[1,2,4,4,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,2,5,1,6,2]=>[5,6,1,1,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,2,5,2,1,6]=>[5,6,1,2,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,2,6,1]=>[1,2,4,5,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,5,6,1,2]=>[1,2,4,2,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,5,6,2,1]=>[2,3,5,3,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,6,1,2,5]=>[1,2,5,3,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,6,1,5,2]=>[4,5,1,6,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,6,2,1,5]=>[5,6,2,1,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,2,5,1]=>[5,6,2,1,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,6,5,1,2]=>[2,3,6,1,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,5,2,1]=>[4,5,1,3,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,1,2,2,6]=>[1,5,4,2,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,1,2,6,2]=>[5,2,1,6,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,5,1,6,2,2]=>[5,2,1,3,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,2,1,2,6]=>[4,1,1,3,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,2,1,6,2]=>[5,2,2,4,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,2,2,1,6]=>[4,1,1,4,3,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,5,2,2,6,1]=>[4,1,1,4,1,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,5,2,6,1,2]=>[4,1,1,1,6,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,5,2,6,2,1]=>[5,2,2,2,1,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,6,1,2,2]=>[1,5,2,3,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,5,6,2,1,2]=>[2,6,3,5,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,6,2,2,1]=>[2,6,3,5,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,1,2,2,5]=>[1,6,3,2,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,1,2,5,2]=>[1,6,3,2,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,5,2,2]=>[4,2,6,1,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,6,2,1,2,5]=>[5,3,1,4,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,1,5,2]=>[5,3,1,4,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,2,2,1,5]=>[5,3,1,5,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,2,2,5,1]=>[5,3,1,5,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,6,2,5,1,2]=>[5,3,1,1,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,6,2,5,2,1]=>[5,3,1,1,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,6,5,1,2,2]=>[3,1,2,6,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,5,2,1,2]=>[4,2,3,1,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,5,2,2,1]=>[4,2,3,1,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,2,5,6]=>[2,1,2,3,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,1,1,2,6,5]=>[2,1,2,3,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,1,5,2,6]=>[4,3,4,1,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,1,1,5,6,2]=>[2,1,2,6,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,1,6,2,5]=>[5,4,5,3,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,1,6,5,2]=>[4,3,4,2,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,2,1,5,6]=>[2,1,3,1,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,1,2,1,6,5]=>[3,2,4,2,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,2,5,1,6]=>[5,4,6,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,2,5,6,1]=>[2,1,3,5,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,2,6,1,5]=>[4,3,5,1,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,2,6,5,1]=>[2,1,3,6,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,5,1,2,6]=>[5,4,2,1,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,5,1,6,2]=>[5,4,2,1,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,5,2,1,6]=>[4,3,1,1,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,5,2,6,1]=>[4,3,1,1,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,1,5,6,1,2]=>[2,1,6,3,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,5,6,2,1]=>[2,1,6,3,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,6,1,2,5]=>[3,2,1,5,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,1,5,2]=>[4,3,2,6,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,6,2,1,5]=>[5,4,3,1,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,6,2,5,1]=>[5,4,3,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,1,6,5,1,2]=>[3,2,1,2,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,5,2,1]=>[4,3,2,3,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,2,1,1,5,6]=>[2,2,1,2,6,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,2,1,1,6,5]=>[3,3,2,3,1,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,2,1,5,1,6]=>[5,5,4,2,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,5,6,1]=>[2,2,1,6,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,1,6,1,5]=>[4,4,3,2,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,2,1,6,5,1]=>[3,3,2,1,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,2,5,1,1,6]=>[1,1,4,4,1,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,2,5,1,6,1]=>[1,1,4,4,6,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,5,6,1,1]=>[1,1,4,2,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,6,1,1,5]=>[1,1,5,3,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,6,1,5,1]=>[1,1,5,3,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,6,5,1,1]=>[2,2,6,1,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,1,2,6]=>[1,4,4,1,2,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,5,1,1,6,2]=>[5,1,1,5,3,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,5,1,2,1,6]=>[5,1,1,6,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,5,1,2,6,1]=>[1,4,4,2,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,1,6,1,2]=>[1,4,4,6,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,5,1,6,2,1]=>[5,1,1,3,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,5,2,1,1,6]=>[5,1,2,4,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,2,1,6,1]=>[6,2,3,5,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,2,6,1,1]=>[1,4,5,5,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,5,6,1,1,2]=>[1,4,2,3,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,5,6,1,2,1]=>[2,5,3,4,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,5,6,2,1,1]=>[2,5,3,5,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,1,1,2,5]=>[1,5,3,1,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,1,1,5,2]=>[4,1,6,4,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,6,1,2,1,5]=>[4,1,6,5,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,6,1,2,5,1]=>[1,5,3,2,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,6,1,5,1,2]=>[1,5,3,5,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,6,1,5,2,1]=>[4,1,6,1,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,2,1,1,5]=>[5,2,1,4,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,6,2,1,5,1]=>[5,2,1,4,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,6,2,5,1,1]=>[5,2,1,1,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,6,5,1,1,2]=>[2,6,1,5,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,5,1,2,1]=>[2,6,1,5,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,5,2,1,1]=>[4,1,3,1,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,1,2,2,6]=>[1,4,1,2,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,1,1,2,6,2]=>[1,4,1,2,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,1,6,2,2]=>[1,4,1,6,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,1,2,1,2,6]=>[2,5,3,1,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,2,1,6,2]=>[5,1,6,4,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,2,2,1,6]=>[3,6,4,3,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,2,2,6,1]=>[1,4,2,1,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,2,6,1,2]=>[1,4,2,5,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,6,2,1]=>[5,1,6,2,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,6,1,2,2]=>[1,4,6,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,6,2,1,2]=>[5,1,3,1,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,6,2,2,1]=>[5,1,3,1,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,1,1,2,6]=>[4,1,3,4,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,2,1,1,6,2]=>[5,2,4,5,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,2,1,6]=>[4,1,3,5,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,2,1,2,6,1]=>[4,1,3,5,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,1,6,1,2]=>[4,1,3,2,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,6,2,1]=>[5,2,4,3,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,2,1,1,6]=>[4,1,4,3,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,2,2,1,6,1]=>[4,1,4,3,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,2,6,1,1]=>[1,5,1,5,3,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,2,6,1,1,2]=>[1,5,5,3,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,2,6,1,2,1]=>[4,1,1,6,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,6,2,1,1]=>[5,2,2,1,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,6,1,1,2,2]=>[1,2,3,1,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[5,6,1,2,1,2]=>[2,3,4,3,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[5,6,1,2,2,1]=>[2,3,4,3,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,6,2,1,1,2]=>[2,3,5,1,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,6,2,1,2,1]=>[2,3,5,1,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,6,2,2,1,1]=>[2,3,5,2,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,1,1,2,2,5]=>[1,3,1,2,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[6,1,1,2,5,2]=>[1,3,1,2,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,1,5,2,2]=>[1,3,1,5,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[6,1,2,1,2,5]=>[2,4,3,1,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,2,1,5,2]=>[4,6,5,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,2,2,1,5]=>[2,4,3,2,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,2,2,5,1]=>[1,3,2,1,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,2,5,1,2]=>[1,3,2,4,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,2,5,2,1]=>[2,4,3,5,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,5,1,2,2]=>[1,3,5,4,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,5,2,1,2]=>[4,6,1,1,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,5,2,2,1]=>[4,6,1,1,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,2,1,1,2,5]=>[2,5,1,2,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,2,1,1,5,2]=>[5,1,4,5,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,2,1,2,1,5]=>[2,5,1,3,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,1,2,5,1]=>[5,1,4,6,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,2,1,5,1,2]=>[5,1,4,2,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,1,5,2,1]=>[5,1,4,2,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,2,2,1,1,5]=>[2,5,2,1,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,2,2,1,5,1]=>[5,1,5,4,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,2,5,1,1]=>[1,4,1,4,4,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[6,2,5,1,1,2]=>[1,4,4,4,1,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,2,5,1,2,1]=>[5,1,1,1,6,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,2,5,2,1,1]=>[5,1,1,2,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,5,1,1,2,2]=>[2,1,5,2,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,5,1,2,1,2]=>[2,1,5,3,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,5,1,2,2,1]=>[2,1,5,3,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,5,2,1,1,2]=>[2,1,6,1,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,5,2,1,2,1]=>[2,1,6,1,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,5,2,2,1,1]=>[2,1,6,2,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,3,3,3]=>[1,1,2,2,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,3,2,3,3]=>[2,2,4,1,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,3,3,2,3]=>[2,2,4,2,1,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,3,3,3,2]=>[2,2,4,2,2,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,2,1,3,3,3]=>[2,3,1,4,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,1,3,3]=>[1,2,2,6,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,3,3,1,3]=>[1,2,2,1,6,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,3,3,3,1]=>[1,2,2,1,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,1,2,3,3]=>[1,3,6,2,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,1,3,2,3]=>[3,5,1,5,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,1,3,3,2]=>[3,5,1,5,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,1,3,3]=>[2,4,1,1,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,2,3,1,3]=>[3,5,2,4,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,2,3,3,1]=>[3,5,2,4,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,3,1,2,3]=>[1,3,1,6,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,3,1,3,2]=>[3,5,3,1,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,3,2,1,3]=>[2,4,2,1,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,3,2,3,1]=>[3,5,3,2,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,3,3,1,2]=>[1,3,1,1,6,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,3,3,2,1]=>[2,4,2,2,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,1,1,3,3,3]=>[2,1,2,4,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,3,1,3,3]=>[3,2,5,1,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,3,1,3]=>[3,2,5,3,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,3,3,1]=>[3,2,5,3,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,3,1,1,3,3]=>[1,2,6,1,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,1,3,1,3]=>[3,4,1,5,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,1,3,3,1]=>[3,4,1,5,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,3,1,1,3]=>[1,2,1,6,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,3,1,3,1]=>[3,4,3,1,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,3,3,1,1]=>[1,2,1,1,6,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,1,2,3,3]=>[1,6,1,2,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,1,1,3,2,3]=>[3,1,3,5,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,1,3,3,2]=>[3,1,3,5,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,2,1,3,3]=>[3,1,4,2,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,2,3,1,3]=>[3,1,4,4,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,2,3,3,1]=>[3,1,4,4,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,1,3,1,2,3]=>[3,1,5,1,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,3,1,3,2]=>[3,1,5,1,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,3,2,1,3]=>[3,1,5,2,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,3,2,3,1]=>[3,1,5,2,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,3,3,1,2]=>[3,1,5,3,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,3,3,2,1]=>[3,1,5,3,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,1,1,3,3]=>[2,1,1,2,4,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,2,1,3,1,3]=>[3,2,2,5,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,1,3,3,1]=>[3,2,2,5,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,3,1,1,3]=>[3,2,4,1,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,3,1,3,1]=>[3,2,4,1,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,3,3,1,1]=>[3,2,4,3,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,1,1,2,3]=>[1,1,6,1,2,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,3,1,1,3,2]=>[3,3,1,3,5,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,3,1,2,1,3]=>[3,3,1,4,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,3,1,2,3,1]=>[3,3,1,4,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,3,1,3,1,2]=>[3,3,1,5,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,3,1,3,2,1]=>[3,3,1,5,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,2,1,1,3]=>[2,2,1,1,2,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,3,2,1,3,1]=>[3,3,2,2,5,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,2,3,1,1]=>[3,3,2,4,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,3,1,1,2]=>[1,1,1,6,1,2]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,3,3,1,2,1]=>[3,3,3,1,4,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,3,2,1,1]=>[2,2,2,1,1,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,2,3,3,4]=>[1,1,2,2,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,3,4,3]=>[2,2,3,3,3,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,4,3,3]=>[2,2,3,4,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,3,2,3,4]=>[2,2,4,1,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,3,2,4,3]=>[2,2,4,1,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,3,3,2,4]=>[2,2,4,2,1,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,3,3,4,2]=>[1,1,3,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,3,4,2,3]=>[1,1,3,2,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,3,4,3,2]=>[2,2,4,3,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,4,2,3,3]=>[1,1,4,6,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,4,3,2,3]=>[2,2,5,1,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,4,3,3,2]=>[2,2,5,1,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,1,3,3,4]=>[2,3,1,4,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,3,4,3]=>[2,3,1,4,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,1,4,3,3]=>[2,3,1,5,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,3,1,3,4]=>[1,2,2,6,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,1,4,3]=>[3,4,4,1,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,3,3,1,4]=>[1,2,2,1,6,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,3,3,4,1]=>[1,2,2,1,2,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,3,4,1,3]=>[1,2,2,2,5,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,3,4,3,1]=>[3,4,4,4,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,4,1,3,3]=>[1,2,3,5,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,4,3,1,3]=>[3,4,5,2,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,3,3,1]=>[3,4,5,2,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,1,2,3,4]=>[1,3,6,2,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,3,1,2,4,3]=>[3,5,1,4,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,1,3,2,4]=>[6,1,4,1,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,1,3,4,2]=>[3,5,1,5,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,1,4,2,3]=>[3,5,1,6,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,4,3,2]=>[3,5,1,6,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,2,1,3,4]=>[2,4,1,1,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,2,1,4,3]=>[2,4,1,1,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,3,2,3,1,4]=>[3,5,2,4,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,3,4,1]=>[2,4,1,3,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,4,1,3]=>[6,1,5,1,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,2,4,3,1]=>[3,5,2,5,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,3,1,2,4]=>[1,3,1,6,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,3,1,4,2]=>[3,5,3,1,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,3,2,1,4]=>[2,4,2,1,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,3,2,4,1]=>[2,4,2,1,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,3,4,1,2]=>[1,3,1,2,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,3,4,2,1]=>[3,5,3,4,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,1,2,3]=>[1,3,2,5,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,3,4,1,3,2]=>[2,4,3,6,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,2,1,3]=>[3,5,4,1,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,2,3,1]=>[3,5,4,1,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,4,3,1,2]=>[3,5,4,2,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,3,2,1]=>[2,4,3,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,4,1,2,3,3]=>[1,4,5,2,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,1,3,2,3]=>[2,5,6,4,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,3,3,2]=>[2,5,6,4,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,2,1,3,3]=>[3,6,1,2,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,2,3,1,3]=>[3,6,1,4,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,3,3,1]=>[3,6,1,4,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,4,3,1,2,3]=>[3,6,2,1,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,3,1,3,2]=>[3,6,2,1,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,3,2,1,3]=>[2,5,1,1,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,3,2,3,1]=>[3,6,2,2,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,3,3,1,2]=>[3,6,2,3,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,3,3,2,1]=>[2,5,1,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,1,1,3,3,4]=>[2,1,2,4,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,1,3,4,3]=>[2,1,2,4,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,1,4,3,3]=>[2,1,2,5,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,3,1,3,4]=>[3,2,5,1,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,3,1,4,3]=>[3,2,5,1,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,3,3,1,4]=>[3,2,5,3,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,3,3,4,1]=>[2,1,4,2,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,3,4,1,3]=>[2,1,4,3,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,3,4,3,1]=>[3,2,5,4,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,4,1,3,3]=>[2,1,5,6,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,4,3,1,3]=>[3,2,6,2,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,3,3,1]=>[3,2,6,2,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,1,3,4]=>[1,2,6,1,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,1,1,4,3]=>[3,4,1,3,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,1,3,1,4]=>[3,4,1,5,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,3,4,1]=>[1,2,6,3,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,4,1,3]=>[1,2,6,4,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,4,3,1]=>[3,4,1,6,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,3,1,1,4]=>[1,2,1,6,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,3,3,1,4,1]=>[1,2,1,6,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,3,4,1,1]=>[1,2,1,2,5,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,1,1,3]=>[1,2,2,5,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,4,1,3,1]=>[1,2,2,5,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,4,3,1,1]=>[3,4,4,2,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,1,1,3,3]=>[1,3,5,1,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,1,3,1,3]=>[6,1,3,1,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,1,3,3,1]=>[1,3,5,3,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,3,1,1,3]=>[3,5,2,1,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,3,1,3,1]=>[3,5,2,1,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,3,3,1,1]=>[3,5,2,3,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,1,2,3,4]=>[1,6,1,2,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,1,1,2,4,3]=>[3,1,3,4,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,1,3,2,4]=>[3,1,3,5,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,1,3,4,2]=>[3,1,3,5,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,1,4,2,3]=>[3,1,3,6,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,4,3,2]=>[3,1,3,6,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,2,1,3,4]=>[3,1,4,2,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,1,4,3]=>[3,1,4,2,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,2,3,1,4]=>[3,1,4,4,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,2,3,4,1]=>[1,6,2,2,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,1,2,4,1,3]=>[1,6,2,3,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,2,4,3,1]=>[3,1,4,5,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,3,1,2,4]=>[3,1,5,1,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,3,1,4,2]=>[3,1,5,1,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,3,2,1,4]=>[3,1,5,2,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,3,2,4,1]=>[6,4,1,5,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,3,4,1,2]=>[1,6,3,2,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,3,4,2,1]=>[3,1,5,4,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,4,1,2,3]=>[1,6,4,5,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,4,1,3,2]=>[6,4,2,3,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,2,1,3]=>[3,1,6,1,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,2,3,1]=>[3,1,6,1,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,4,3,1,2]=>[3,1,6,2,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,4,3,2,1]=>[3,1,6,2,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,2,1,1,3,4]=>[2,1,1,2,4,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,1,4,3]=>[2,1,1,2,5,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,2,1,3,1,4]=>[3,2,2,5,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,1,3,4,1]=>[2,1,1,4,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,1,4,1,3]=>[2,1,1,5,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,4,3,1]=>[3,2,2,6,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,2,3,1,1,4]=>[3,2,4,1,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,3,1,4,1]=>[5,4,6,3,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,3,4,1,1]=>[2,1,3,3,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,4,1,1,3]=>[2,1,4,6,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,4,1,3,1]=>[6,5,1,3,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,4,3,1,1]=>[3,2,5,2,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,1,1,2,4]=>[1,1,6,1,2,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,3,1,1,4,2]=>[3,3,1,3,6,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,3,1,2,1,4]=>[3,3,1,4,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,3,1,2,4,1]=>[1,1,6,2,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,1,4,1,2]=>[1,1,6,4,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,1,4,2,1]=>[3,3,1,6,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,2,1,1,4]=>[2,2,1,1,2,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,3,2,1,4,1]=>[2,2,1,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,3,2,4,1,1]=>[2,2,1,4,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,4,1,1,2]=>[1,1,2,5,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,3,4,1,2,1]=>[2,2,3,6,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,3,4,2,1,1]=>[3,3,4,1,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,4,1,1,2,3]=>[1,2,5,1,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,4,1,1,3,2]=>[2,3,6,2,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,1,2,1,3]=>[2,3,6,3,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,1,2,3,1]=>[1,2,5,2,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,1,3,1,2]=>[1,2,5,3,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,3,2,1]=>[2,3,6,4,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,2,1,1,3]=>[3,4,1,2,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,2,1,3,1]=>[3,4,1,2,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,2,3,1,1]=>[3,4,1,4,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,4,3,1,1,2]=>[3,4,2,1,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,3,1,2,1]=>[3,4,2,1,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,4,3,2,1,1]=>[2,3,1,1,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,1,1,2,3,3]=>[1,5,1,2,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,1,1,3,2,3]=>[2,6,2,4,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,1,3,3,2]=>[2,6,2,4,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,1,2,1,3,3]=>[2,6,3,1,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,2,3,1,3]=>[1,5,2,2,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,3,3,1]=>[1,5,2,2,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,3,1,2,3]=>[1,5,3,6,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,3,1,3,2]=>[6,3,1,4,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,3,2,1,3]=>[2,6,4,1,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,3,2,3,1]=>[4,1,6,3,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,3,1,2]=>[1,5,3,1,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,3,3,2,1]=>[2,6,4,2,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,1,1,3,3]=>[3,1,2,3,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,2,1,3,1,3]=>[3,1,2,5,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,1,3,3,1]=>[3,1,2,5,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,3,1,1,3]=>[3,1,4,1,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,2,3,1,3,1]=>[3,1,4,1,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,2,3,3,1,1]=>[3,1,4,3,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,3,1,1,2,3]=>[3,2,1,3,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,1,1,3,2]=>[3,2,1,3,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,3,1,2,1,3]=>[3,2,1,4,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,1,2,3,1]=>[3,2,1,4,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,3,1,3,1,2]=>[3,2,1,5,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,3,2,1]=>[3,2,1,5,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,3,2,1,1,3]=>[2,1,1,1,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,3,2,1,3,1]=>[3,2,2,2,5,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,3,2,3,1,1]=>[3,2,2,4,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,1,1,2]=>[3,2,3,1,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,3,1,2,1]=>[3,2,3,1,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,2,1,1]=>[2,1,2,1,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,3,3,5]=>[1,1,2,2,1,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,2,3,5,3]=>[1,1,2,2,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,2,5,3,3]=>[1,1,2,4,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,3,2,3,5]=>[2,2,4,1,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,3,2,5,3]=>[3,3,5,2,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,3,3,2,5]=>[2,2,4,2,1,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,3,3,5,2]=>[1,1,3,1,3,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,3,5,2,3]=>[1,1,3,3,5,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,3,5,3,2]=>[3,3,5,5,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,5,2,3,3]=>[1,1,5,5,2,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,5,3,2,3]=>[4,4,1,2,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,5,3,3,2]=>[4,4,1,2,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,3,3,5]=>[2,3,1,4,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,1,3,5,3]=>[3,4,2,5,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,5,3,3]=>[4,5,3,1,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,1,3,5]=>[1,2,2,6,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,3,1,5,3]=>[4,5,5,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,3,3,1,5]=>[1,2,2,1,6,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,3,3,5,1]=>[1,2,2,1,3,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,5,1,3]=>[1,2,2,3,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,5,3,1]=>[3,4,4,5,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,5,1,3,3]=>[1,2,4,4,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,5,3,1,3]=>[3,4,6,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,5,3,3,1]=>[3,4,6,1,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,2,3,5]=>[1,3,6,2,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,3,1,2,5,3]=>[3,5,1,4,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,3,2,5]=>[6,1,4,1,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,3,5,2]=>[6,1,4,1,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,1,5,2,3]=>[4,6,2,1,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,5,3,2]=>[4,6,2,1,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,2,1,3,5]=>[2,4,1,1,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,3,2,1,5,3]=>[4,6,3,3,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,3,1,5]=>[4,6,3,5,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,3,5,1]=>[2,4,1,3,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,5,1,3]=>[6,1,5,2,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,2,5,3,1]=>[3,5,2,6,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,3,1,2,5]=>[1,3,1,6,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,3,1,5,2]=>[4,6,4,2,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,3,2,1,5]=>[2,4,2,1,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,3,2,5,1]=>[2,4,2,1,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,3,5,1,2]=>[1,3,1,3,4,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,3,5,2,1]=>[2,4,2,4,6,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,5,1,2,3]=>[1,3,3,4,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,5,1,3,2]=>[6,1,1,2,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,5,2,1,3]=>[6,1,1,3,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,5,2,3,1]=>[1,3,3,5,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,5,3,1,2]=>[3,5,5,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,5,3,2,1]=>[3,5,5,1,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,1,2,3,3]=>[1,5,4,2,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,1,3,2,3]=>[2,6,5,4,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,3,3,2]=>[2,6,5,4,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,2,1,3,3]=>[4,1,1,3,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,2,3,1,3]=>[4,1,1,5,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,2,3,3,1]=>[4,1,1,5,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,3,1,2,3]=>[4,1,2,2,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,3,1,3,2]=>[4,1,2,2,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,3,2,1,3]=>[4,1,2,3,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,3,2,3,1]=>[4,1,2,3,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,3,3,1,2]=>[4,1,2,4,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,3,3,2,1]=>[4,1,2,4,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,3,3,5]=>[2,1,2,4,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,1,3,5,3]=>[3,2,3,5,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,1,5,3,3]=>[4,3,4,1,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,1,3,5]=>[6,5,1,4,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,3,1,5,3]=>[4,3,6,2,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,3,3,1,5]=>[4,3,6,4,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,3,3,5,1]=>[2,1,4,2,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,3,5,1,3]=>[6,5,1,1,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,1,3,5,3,1]=>[3,2,5,5,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,1,5,1,3,3]=>[2,1,6,5,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,5,3,1,3]=>[4,3,1,2,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,5,3,3,1]=>[4,3,1,2,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,1,1,3,5]=>[1,2,6,1,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,1,1,5,3]=>[4,5,2,4,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,3,1,3,1,5]=>[4,5,2,6,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,3,5,1]=>[1,2,6,3,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,1,5,1,3]=>[1,2,6,5,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,5,3,1]=>[4,5,2,1,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,3,3,1,1,5]=>[1,2,1,6,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,3,3,1,5,1]=>[1,2,1,6,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,3,5,1,1]=>[1,2,1,3,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,5,1,1,3]=>[1,2,3,4,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,5,1,3,1]=>[1,2,3,4,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,5,3,1,1]=>[3,4,5,1,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,1,1,3,3]=>[1,4,4,1,3,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,5,1,3,1,3]=>[6,2,2,1,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,5,1,3,3,1]=>[1,4,4,3,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,3,1,1,3]=>[3,6,1,1,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,5,3,1,3,1]=>[3,6,1,1,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,5,3,3,1,1]=>[3,6,1,3,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,1,2,3,5]=>[1,6,1,2,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,1,2,5,3]=>[3,1,3,4,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,3,2,5]=>[3,1,3,5,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,1,3,5,2]=>[1,6,1,3,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,1,5,2,3]=>[4,2,4,1,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,1,5,3,2]=>[4,2,4,1,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,1,3,5]=>[3,1,4,2,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,2,1,5,3]=>[4,2,5,3,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,2,3,1,5]=>[4,2,5,5,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,1,2,3,5,1]=>[1,6,2,2,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,2,5,1,3]=>[1,6,2,4,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,2,5,3,1]=>[3,1,4,6,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,3,1,2,5]=>[3,1,5,1,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,3,1,5,2]=>[4,2,6,2,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,3,2,1,5]=>[4,2,6,3,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,3,2,5,1]=>[6,4,1,5,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,3,5,1,2]=>[1,6,3,3,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,3,5,2,1]=>[6,4,1,1,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,5,1,2,3]=>[1,6,5,4,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,5,1,3,2]=>[6,4,3,2,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,2,1,3]=>[4,2,1,1,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,5,2,3,1]=>[4,2,1,1,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,1,5,3,1,2]=>[4,2,1,2,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,5,3,2,1]=>[4,2,1,2,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,1,3,5]=>[2,1,1,2,4,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[3,2,1,1,5,3]=>[4,3,3,4,1,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,1,3,1,5]=>[4,3,3,6,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,1,3,5,1]=>[2,1,1,4,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,1,5,1,3]=>[2,1,1,6,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,5,3,1]=>[4,3,3,1,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,3,1,1,5]=>[4,3,5,2,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,3,1,5,1]=>[5,4,6,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,3,5,1,1]=>[2,1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,5,1,1,3]=>[2,1,5,5,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,2,5,1,3,1]=>[6,5,2,2,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,5,3,1,1]=>[3,2,6,1,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,1,1,2,5]=>[1,1,6,1,2,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,3,1,1,5,2]=>[4,4,2,4,1,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,3,1,2,1,5]=>[4,4,2,5,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,3,1,2,5,1]=>[1,1,6,2,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,3,1,5,1,2]=>[1,1,6,5,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,1,5,2,1]=>[4,4,2,1,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,2,1,1,5]=>[2,2,1,1,2,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,3,2,1,5,1]=>[2,2,1,1,6,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,3,2,5,1,1]=>[2,2,1,5,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,3,5,1,1,2]=>[1,1,3,4,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,5,1,2,1]=>[2,2,4,5,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,5,2,1,1]=>[2,2,4,6,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,5,1,1,2,3]=>[1,3,4,1,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,5,1,1,3,2]=>[2,4,5,2,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,5,1,2,1,3]=>[2,4,5,3,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,2,3,1]=>[1,3,4,2,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,1,3,1,2]=>[1,3,4,3,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,1,3,2,1]=>[2,4,5,4,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,5,2,1,1,3]=>[2,4,6,1,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,5,2,1,3,1]=>[6,1,3,5,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,2,3,1,1]=>[1,3,5,2,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,3,1,1,2]=>[3,5,1,1,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,5,3,1,2,1]=>[3,5,1,1,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,5,3,2,1,1]=>[3,5,1,2,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,1,2,3,3]=>[1,4,1,2,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,1,1,3,2,3]=>[2,5,2,4,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,1,3,3,2]=>[2,5,2,4,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,1,2,1,3,3]=>[2,5,3,1,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,3,1,3]=>[1,4,2,2,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,2,3,3,1]=>[1,4,2,2,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,3,1,2,3]=>[1,4,3,6,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,3,1,3,2]=>[6,2,1,4,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,3,2,1,3]=>[2,5,4,1,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,3,2,3,1]=>[3,6,5,2,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,3,1,2]=>[1,4,3,1,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,3,3,2,1]=>[2,5,4,2,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,1,1,3,3]=>[2,6,1,2,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,1,3,1,3]=>[6,3,5,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,1,3,3,1]=>[4,1,3,6,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,3,1,1,3]=>[1,5,2,6,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,3,1,3,1]=>[4,1,5,2,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,3,3,1,1]=>[1,5,2,1,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,3,1,1,2,3]=>[3,1,1,3,4,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,3,1,1,3,2]=>[3,1,1,3,5,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,3,1,2,1,3]=>[3,1,1,4,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,3,1,2,3,1]=>[3,1,1,4,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,3,1,3,1,2]=>[3,1,1,5,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,3,1,3,2,1]=>[3,1,1,5,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,3,2,1,1,3]=>[3,1,2,2,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,3,2,1,3,1]=>[3,1,2,2,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,3,2,3,1,1]=>[3,1,2,4,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,3,1,1,2]=>[3,1,3,1,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,3,3,1,2,1]=>[3,1,3,1,4,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,3,2,1,1]=>[3,1,3,2,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,3,3,6]=>[1,1,2,2,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,2,3,6,3]=>[1,1,2,2,4,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,2,6,3,3]=>[1,1,2,5,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,3,2,3,6]=>[2,2,4,1,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,3,2,6,3]=>[4,4,6,3,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,3,3,2,6]=>[2,2,4,2,1,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,3,3,6,2]=>[1,1,3,1,4,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,3,6,2,3]=>[1,1,3,4,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,3,6,3,2]=>[2,2,4,5,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,6,2,3,3]=>[1,1,6,4,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,6,3,2,3]=>[4,4,2,1,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,6,3,3,2]=>[4,4,2,1,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,3,3,6]=>[2,3,1,4,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,1,3,6,3]=>[2,3,1,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,6,3,3]=>[4,5,3,2,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,1,3,6]=>[1,2,2,6,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,3,1,6,3]=>[4,5,5,2,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,3,3,1,6]=>[3,4,4,3,1,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,2,3,3,6,1]=>[1,2,2,1,4,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,6,1,3]=>[1,2,2,4,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,6,3,1]=>[1,2,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,1,3,3]=>[1,2,5,3,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,6,3,1,3]=>[4,5,1,1,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,6,3,3,1]=>[4,5,1,1,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,1,2,3,6]=>[1,3,6,2,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,1,2,6,3]=>[4,6,2,5,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,3,2,6]=>[6,1,4,1,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,3,6,2]=>[6,1,4,1,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,1,6,2,3]=>[3,5,1,1,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,6,3,2]=>[4,6,2,2,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,2,1,3,6]=>[2,4,1,1,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,2,1,6,3]=>[4,6,3,3,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,3,1,6]=>[3,5,2,4,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,3,6,1]=>[2,4,1,3,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,6,1,3]=>[6,1,5,3,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,2,6,3,1]=>[4,6,3,1,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,3,1,2,6]=>[1,3,1,6,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,3,1,6,2]=>[3,5,3,1,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,3,2,1,6]=>[3,5,3,2,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,3,2,6,1]=>[2,4,2,1,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,3,6,1,2]=>[1,3,1,4,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,3,6,2,1]=>[2,4,2,5,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,6,1,2,3]=>[1,3,4,3,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,6,1,3,2]=>[6,1,2,1,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,6,2,1,3]=>[6,1,2,2,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,6,2,3,1]=>[1,3,4,4,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,6,3,1,2]=>[1,3,4,5,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,6,3,2,1]=>[2,4,5,6,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,1,2,3,3]=>[1,6,3,2,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,6,1,3,2,3]=>[3,1,5,5,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,1,3,3,2]=>[3,1,5,5,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,6,2,1,3,3]=>[3,1,6,2,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,2,3,1,3]=>[3,1,6,4,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,3,3,1]=>[3,1,6,4,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,6,3,1,2,3]=>[4,2,1,2,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,3,1,3,2]=>[4,2,1,2,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,3,2,1,3]=>[4,2,1,3,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,3,2,3,1]=>[4,2,1,3,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,3,3,1,2]=>[4,2,1,4,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,3,3,2,1]=>[4,2,1,4,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,3,3,6]=>[2,1,2,4,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,1,3,6,3]=>[2,1,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,1,6,3,3]=>[4,3,4,2,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,1,3,6]=>[6,5,1,4,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,3,1,6,3]=>[4,3,6,2,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,3,3,1,6]=>[3,2,5,3,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,3,3,6,1]=>[2,1,4,2,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,3,6,1,3]=>[6,5,1,2,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,1,3,6,3,1]=>[6,5,1,2,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,1,3,3]=>[3,2,1,5,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,6,3,1,3]=>[4,3,2,1,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,3,3,1]=>[4,3,2,1,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,1,1,3,6]=>[1,2,6,1,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,1,1,6,3]=>[4,5,2,4,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,3,1,3,1,6]=>[3,4,1,5,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,3,1,3,6,1]=>[1,2,6,3,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,1,6,1,3]=>[3,4,1,1,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,1,6,3,1]=>[4,5,2,2,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,3,3,1,1,6]=>[3,4,3,1,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,3,3,1,6,1]=>[3,4,3,1,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,3,6,1,1]=>[1,2,1,4,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,6,1,1,3]=>[1,2,4,3,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,6,1,3,1]=>[1,2,4,3,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,6,3,1,1]=>[1,2,4,5,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,1,1,3,3]=>[1,5,3,1,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,6,1,3,1,3]=>[6,3,1,1,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,1,3,3,1]=>[1,5,3,3,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,6,3,1,1,3]=>[4,1,1,2,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,3,1,3,1]=>[4,1,1,2,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,6,3,3,1,1]=>[4,1,1,4,2,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,1,2,3,6]=>[1,6,1,2,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,1,2,6,3]=>[4,2,4,5,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,1,3,2,6]=>[4,2,4,6,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,1,3,6,2]=>[1,6,1,3,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,1,6,2,3]=>[3,1,3,1,6,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,6,3,2]=>[4,2,4,2,1,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,1,3,6]=>[3,1,4,2,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,1,6,3]=>[4,2,5,3,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,2,3,1,6]=>[3,1,4,4,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,1,2,3,6,1]=>[1,6,2,2,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,2,6,1,3]=>[1,6,2,5,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,2,6,3,1]=>[4,2,5,1,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,1,3,1,2,6]=>[4,2,6,2,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,3,1,6,2]=>[3,1,5,1,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,3,2,1,6]=>[3,1,5,2,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,1,3,2,6,1]=>[6,4,1,5,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,3,6,1,2]=>[1,6,3,4,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,3,6,2,1]=>[6,4,1,2,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,6,1,2,3]=>[3,1,1,5,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,6,1,3,2]=>[3,1,1,5,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,6,2,1,3]=>[3,1,1,6,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,6,2,3,1]=>[3,1,1,6,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,6,3,1,2]=>[4,2,2,1,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,6,3,2,1]=>[4,2,2,1,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,1,3,6]=>[2,1,1,2,4,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,2,1,1,6,3]=>[4,3,3,4,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,1,3,1,6]=>[3,2,2,5,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,3,6,1]=>[2,1,1,4,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,1,6,1,3]=>[3,2,2,1,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,1,6,3,1]=>[4,3,3,2,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,3,1,1,6]=>[3,2,4,1,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,3,1,6,1]=>[3,2,4,1,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,3,6,1,1]=>[2,1,3,5,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,6,1,1,3]=>[2,1,6,4,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,6,1,3,1]=>[6,5,3,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,6,3,1,1]=>[4,3,1,1,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,1,1,2,6]=>[1,1,6,1,2,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,3,1,1,6,2]=>[3,3,1,3,1,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,3,1,2,1,6]=>[3,3,1,4,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,1,2,6,1]=>[1,1,6,2,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,1,6,1,2]=>[3,3,1,1,5,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,3,1,6,2,1]=>[3,3,1,1,6,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,2,1,1,6]=>[3,3,2,2,3,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,3,2,1,6,1]=>[3,3,2,2,1,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,2,6,1,1]=>[2,2,1,6,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,6,1,1,2]=>[1,1,4,3,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,6,1,2,1]=>[2,2,5,4,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,6,2,1,1]=>[2,2,5,5,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,6,1,1,2,3]=>[1,4,3,1,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,6,1,1,3,2]=>[2,5,4,2,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,6,1,2,1,3]=>[2,5,4,3,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,1,2,3,1]=>[1,4,3,2,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,6,1,3,1,2]=>[1,4,3,3,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,6,1,3,2,1]=>[2,5,4,4,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,6,2,1,1,3]=>[2,5,5,1,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,6,2,1,3,1]=>[6,2,2,5,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,2,3,1,1]=>[1,4,4,2,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,6,3,1,1,2]=>[1,4,5,6,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,3,1,2,1]=>[5,1,2,3,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,3,2,1,1]=>[2,5,6,1,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,1,1,2,3,3]=>[1,3,1,2,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[6,1,1,3,2,3]=>[2,4,2,4,1,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,1,3,3,2]=>[2,4,2,4,2,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[6,1,2,1,3,3]=>[2,4,3,1,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,2,3,1,3]=>[1,3,2,2,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,2,3,3,1]=>[1,3,2,2,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,1,3,1,2,3]=>[1,3,3,6,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,3,1,3,2]=>[6,1,1,4,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,1,3,2,1,3]=>[2,4,4,1,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,1,3,2,3,1]=>[3,5,5,2,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,1,3,3,1,2]=>[1,3,3,1,6,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,3,3,2,1]=>[2,4,4,2,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[6,2,1,1,3,3]=>[2,5,1,2,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,2,1,3,1,3]=>[6,2,5,1,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,1,3,3,1]=>[3,6,2,5,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,3,1,1,3]=>[1,4,2,6,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,2,3,1,3,1]=>[3,6,4,1,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,3,3,1,1]=>[1,4,2,1,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,3,1,1,2,3]=>[1,5,6,1,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,1,1,3,2]=>[4,1,2,4,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,3,1,2,1,3]=>[4,1,2,5,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,1,2,3,1]=>[4,1,2,5,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,3,1,3,1,2]=>[4,1,2,6,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,3,1,3,2,1]=>[4,1,2,6,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,3,2,1,1,3]=>[2,6,1,1,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,3,2,1,3,1]=>[4,1,3,3,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,3,2,3,1,1]=>[4,1,3,5,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,3,1,1,2]=>[1,5,1,6,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,3,3,1,2,1]=>[4,1,4,2,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,3,2,1,1]=>[2,6,2,1,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,2,3,4,4]=>[1,1,2,2,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,4,3,4]=>[2,2,3,4,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,4,4,3]=>[2,2,3,4,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,3,2,4,4]=>[2,2,4,1,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,3,4,2,4]=>[1,1,3,2,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,3,4,4,2]=>[1,1,3,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,4,2,3,4]=>[1,1,4,6,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,4,2,4,3]=>[3,3,6,1,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,4,3,2,4]=>[2,2,5,1,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,4,3,4,2]=>[3,3,6,2,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,4,4,2,3]=>[1,1,4,1,6,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,4,4,3,2]=>[2,2,5,2,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,1,3,4,4]=>[2,3,1,4,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,1,4,3,4]=>[2,3,1,5,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,1,4,4,3]=>[2,3,1,5,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,3,1,4,4]=>[1,2,2,6,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,3,4,1,4]=>[1,2,2,2,5,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,2,3,4,4,1]=>[1,2,2,2,1,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,2,4,1,3,4]=>[1,2,3,5,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,4,1,4,3]=>[2,3,4,6,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,3,1,4]=>[3,4,5,2,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,3,4,1]=>[2,3,4,1,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,4,4,1,3]=>[1,2,3,1,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,4,4,3,1]=>[3,4,5,3,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,1,2,4,4]=>[1,3,6,2,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,1,4,2,4]=>[6,1,4,2,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,1,4,4,2]=>[3,5,1,6,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,1,4,4]=>[2,4,1,1,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,2,4,1,4]=>[6,1,5,1,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,2,4,4,1]=>[2,4,1,4,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,4,1,2,4]=>[1,3,2,5,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,4,1,4,2]=>[1,3,2,5,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,2,1,4]=>[3,5,4,1,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,2,4,1]=>[1,3,2,6,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,4,4,1,2]=>[1,3,2,1,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,4,4,2,1]=>[3,5,4,3,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,2,3,4]=>[1,4,5,2,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,4,1,2,4,3]=>[2,5,6,3,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,3,2,4]=>[6,2,3,1,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,3,4,2]=>[1,4,5,3,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,4,2,3]=>[5,1,2,1,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,4,3,2]=>[5,1,2,1,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,2,1,3,4]=>[3,6,1,2,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,1,4,3]=>[5,1,3,4,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,2,3,1,4]=>[5,1,3,6,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,2,3,4,1]=>[1,4,6,2,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,2,4,1,3]=>[6,2,4,1,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,2,4,3,1]=>[3,6,1,5,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,3,1,2,4]=>[3,6,2,1,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,1,4,2]=>[5,1,4,3,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,3,2,1,4]=>[2,5,1,1,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,4,3,2,4,1]=>[2,5,1,1,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,3,4,1,2]=>[2,5,1,3,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,4,2,1]=>[3,6,2,4,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,4,1,2,3]=>[1,4,1,5,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,4,1,3,2]=>[2,5,2,6,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,4,2,1,3]=>[3,6,3,1,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,4,2,3,1]=>[3,6,3,1,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,4,4,3,1,2]=>[3,6,3,2,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,4,3,2,1]=>[2,5,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,1,1,3,4,4]=>[2,1,2,4,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,1,4,3,4]=>[2,1,2,5,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,1,4,4,3]=>[2,1,2,5,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,3,1,4,4]=>[3,2,5,1,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,3,4,1,4]=>[2,1,4,3,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,4,1]=>[2,1,4,3,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,1,3,4]=>[2,1,5,6,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,1,4,3]=>[5,4,1,2,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,4,3,1,4]=>[5,4,1,4,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,3,4,1]=>[2,1,5,1,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,4,1,3]=>[2,1,5,2,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,4,4,3,1]=>[3,2,6,3,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,1,4,4]=>[1,2,6,1,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,3,1,4,1,4]=>[5,6,3,1,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,1,4,4,1]=>[1,2,6,4,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,4,1,1,4]=>[1,2,2,5,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,3,4,1,4,1]=>[1,2,2,5,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,4,4,1,1]=>[1,2,2,1,5,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,4,1,1,3,4]=>[1,3,5,1,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,1,1,4,3]=>[2,4,6,2,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,4,1,3,1,4]=>[6,1,3,1,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,1,3,4,1]=>[1,3,5,3,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,1,4,1,3]=>[6,1,3,2,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,4,1,4,3,1]=>[6,1,3,2,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,1,1,4]=>[3,5,2,1,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,3,1,4,1]=>[6,1,5,4,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,4,1,1]=>[2,4,1,3,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,4,1,1,3]=>[1,3,1,5,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,4,1,3,1]=>[1,3,1,5,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,4,3,1,1]=>[3,5,3,2,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,1,2,4,4]=>[1,6,1,2,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,1,4,2,4]=>[3,1,3,6,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,1,4,4,2]=>[3,1,3,6,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,2,1,4,4]=>[3,1,4,2,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,2,4,1,4]=>[1,6,2,3,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,4,4,1]=>[1,6,2,3,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,1,2,4]=>[1,6,4,5,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,1,4,2]=>[5,3,1,2,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,4,2,1,4]=>[5,3,1,3,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,4,2,4,1]=>[6,4,2,4,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,4,4,1,2]=>[1,6,4,1,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,4,4,2,1]=>[3,1,6,3,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,2,1,1,4,4]=>[2,1,1,2,5,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,2,1,4,1,4]=>[5,4,4,1,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,1,4,4,1]=>[2,1,1,5,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,4,1,1,4]=>[2,1,4,6,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,4,1,4,1]=>[6,5,1,3,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,4,4,1,1]=>[2,1,4,2,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,4,1,1,2,4]=>[1,2,5,1,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,4,1,1,4,2]=>[1,2,5,1,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,1,2,1,4]=>[2,3,6,3,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,4,1,2,4,1]=>[1,2,5,2,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,4,1,4,1,2]=>[1,2,5,4,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,1,4,2,1]=>[5,6,2,1,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,1,1,4]=>[3,4,1,2,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,2,1,4,1]=>[5,6,3,4,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,4,1,1]=>[1,2,6,3,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,4,1,1,2]=>[1,2,1,5,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,4,4,1,2,1]=>[2,3,2,6,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,4,4,2,1,1]=>[3,4,3,1,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,1,2,3,4]=>[1,5,1,2,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,1,2,4,3]=>[2,6,2,3,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,1,3,2,4]=>[2,6,2,4,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,1,3,4,2]=>[1,5,1,3,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,1,4,2,3]=>[1,5,1,4,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,1,4,3,2]=>[2,6,2,5,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,2,1,3,4]=>[2,6,3,1,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,2,1,4,3]=>[2,6,3,1,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,2,3,1,4]=>[1,5,2,2,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,2,3,4,1]=>[1,5,2,2,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,1,2,4,1,3]=>[1,5,2,3,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,1,2,4,3,1]=>[4,1,5,6,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,1,2,4]=>[1,5,3,6,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,3,1,4,2]=>[6,3,1,4,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,3,2,1,4]=>[2,6,4,1,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,2,4,1]=>[6,3,1,5,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,3,4,1,2]=>[1,5,3,2,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,3,4,2,1]=>[4,1,6,5,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,1,2,3]=>[1,5,4,5,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,4,1,3,2]=>[6,3,2,3,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,4,2,1,3]=>[6,3,2,4,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,2,3,1]=>[5,2,1,3,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,4,3,1,2]=>[5,2,1,4,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,3,2,1]=>[2,6,5,1,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,2,1,1,3,4]=>[3,1,2,3,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,1,4,3]=>[3,1,2,3,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,2,1,3,1,4]=>[3,1,2,5,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,1,3,4,1]=>[4,2,3,6,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,4,1,3]=>[6,4,5,2,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,4,3,1]=>[3,1,2,6,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,3,1,1,4]=>[3,1,4,1,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,2,3,1,4,1]=>[5,3,6,3,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,3,4,1,1]=>[1,6,2,2,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,2,4,1,1,3]=>[1,6,3,5,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,4,1,3,1]=>[6,4,1,3,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,4,3,1,1]=>[3,1,5,2,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,1,1,2,4]=>[3,2,1,3,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,1,4,2]=>[3,2,1,3,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,1,2,1,4]=>[3,2,1,4,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,3,1,2,4,1]=>[4,3,2,5,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,4,1,2]=>[5,4,3,1,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,4,2,1]=>[3,2,1,6,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,3,2,1,1,4]=>[2,1,1,1,2,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,3,2,1,4,1]=>[2,1,1,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,3,2,4,1,1]=>[2,1,1,4,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,4,1,1,2]=>[2,1,3,6,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,3,4,1,2,1]=>[2,1,3,6,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,4,2,1,1]=>[3,2,4,1,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,1,1,2,3]=>[1,1,5,1,2,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,4,1,1,3,2]=>[2,2,6,2,4,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,4,1,2,1,3]=>[2,2,6,3,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,4,1,2,3,1]=>[1,1,5,2,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,4,1,3,1,2]=>[1,1,5,3,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,4,1,3,2,1]=>[2,2,6,4,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,4,2,1,1,3]=>[3,3,1,2,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,4,2,1,3,1]=>[3,3,1,2,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,2,3,1,1]=>[3,3,1,4,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,4,3,1,1,2]=>[3,3,2,1,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,3,1,2,1]=>[3,3,2,1,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,3,2,1,1]=>[2,2,1,1,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,2,3,4,5]=>[1,1,2,2,2,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,2,3,5,4]=>[2,2,3,3,4,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,4,3,5]=>[2,2,3,4,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,2,4,5,3]=>[1,1,2,3,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,2,5,3,4]=>[1,1,2,4,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,2,5,4,3]=>[2,2,3,5,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,3,2,4,5]=>[2,2,4,1,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,3,2,5,4]=>[2,2,4,1,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,3,4,2,5]=>[1,1,3,2,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,3,4,5,2]=>[1,1,3,2,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,3,5,2,4]=>[1,1,3,3,5,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,3,5,4,2]=>[3,3,5,5,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,4,2,3,5]=>[1,1,4,6,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,4,2,5,3]=>[5,5,1,3,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,4,3,2,5]=>[2,2,5,1,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,4,3,5,2]=>[2,2,5,1,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,4,5,2,3]=>[1,1,4,2,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,4,5,3,2]=>[3,3,6,4,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,5,2,3,4]=>[1,1,5,5,2,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,5,2,4,3]=>[4,4,1,1,6,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,5,3,2,4]=>[4,4,1,2,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,5,3,4,2]=>[4,4,1,2,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,5,4,2,3]=>[4,4,1,3,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,5,4,3,2]=>[2,2,6,1,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,2,1,3,4,5]=>[2,3,1,4,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,1,3,5,4]=>[2,3,1,4,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,1,4,3,5]=>[2,3,1,5,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,4,5,3]=>[3,4,2,6,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,1,5,3,4]=>[4,5,3,1,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,5,4,3]=>[2,3,1,6,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,3,1,4,5]=>[1,2,2,6,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,2,3,1,5,4]=>[4,5,5,2,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,4,1,5]=>[1,2,2,2,5,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,2,3,4,5,1]=>[1,2,2,2,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,2,3,5,1,4]=>[1,2,2,3,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,3,5,4,1]=>[2,3,3,4,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,4,1,3,5]=>[1,2,3,5,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,4,1,5,3]=>[4,5,6,1,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,4,3,1,5]=>[4,5,6,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,3,5,1]=>[2,3,4,1,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,5,1,3]=>[1,2,3,2,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,5,3,1]=>[3,4,5,4,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,5,1,3,4]=>[1,2,4,4,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,5,1,4,3]=>[5,6,1,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,5,3,1,4]=>[5,6,1,3,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,5,3,4,1]=>[1,2,4,6,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,5,4,1,3]=>[2,3,5,1,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,4,3,1]=>[3,4,6,2,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,1,2,4,5]=>[1,3,6,2,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,3,1,2,5,4]=>[3,5,1,4,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,4,2,5]=>[6,1,4,2,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,1,4,5,2]=>[1,3,6,4,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,2,4]=>[6,1,4,3,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,5,4,2]=>[4,6,2,1,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,2,1,4,5]=>[2,4,1,1,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,1,5,4]=>[2,4,1,1,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,2,4,1,5]=>[6,1,5,1,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,4,5,1]=>[2,4,1,4,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,5,1,4]=>[6,1,5,2,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,3,2,5,4,1]=>[2,4,1,5,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,4,1,2,5]=>[1,3,2,5,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,4,1,5,2]=>[4,6,5,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,4,2,1,5]=>[4,6,5,2,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,2,5,1]=>[1,3,2,6,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,5,1,2]=>[1,3,2,2,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,4,5,2,1]=>[2,4,3,3,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,5,1,2,4]=>[1,3,3,4,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,5,1,4,2]=>[6,1,1,2,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,5,2,1,4]=>[6,1,1,3,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,5,2,4,1]=>[6,1,1,3,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,5,4,1,2]=>[2,4,4,1,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,5,4,2,1]=>[3,5,5,2,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,1,2,3,5]=>[1,4,5,2,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,1,2,5,3]=>[5,1,2,6,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,3,2,5]=>[6,2,3,1,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,3,5,2]=>[6,2,3,1,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,1,5,2,3]=>[5,1,2,2,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,1,5,3,2]=>[5,1,2,2,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,2,1,3,5]=>[6,2,4,5,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,2,1,5,3]=>[5,1,3,4,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,2,3,1,5]=>[5,1,3,6,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,2,3,5,1]=>[1,4,6,2,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,5,1,3]=>[6,2,4,2,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,4,2,5,3,1]=>[5,1,3,1,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,4,3,1,2,5]=>[5,1,4,3,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,3,1,5,2]=>[5,1,4,3,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,3,2,1,5]=>[2,5,1,1,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,3,2,5,1]=>[5,1,4,4,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,3,5,1,2]=>[2,5,1,4,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,3,5,2,1]=>[2,5,1,4,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,5,1,2,3]=>[1,4,2,4,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,4,5,1,3,2]=>[2,5,3,5,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,5,2,1,3]=>[2,5,3,6,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,2,3,1]=>[1,4,2,5,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,5,3,1,2]=>[3,6,4,1,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,4,5,3,2,1]=>[3,6,4,1,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,2,3,4]=>[1,5,4,2,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,1,2,4,3]=>[2,6,5,3,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,3,2,4]=>[6,3,2,1,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,3,4,2]=>[1,5,4,3,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,4,2,3]=>[5,2,1,1,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,4,3,2]=>[5,2,1,1,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,2,1,3,4]=>[4,1,1,3,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,2,1,4,3]=>[5,2,2,4,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,2,3,1,4]=>[5,2,2,6,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,2,3,4,1]=>[4,1,1,5,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,5,2,4,1,3]=>[6,3,3,1,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,5,2,4,3,1]=>[4,1,1,6,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,3,1,2,4]=>[4,1,2,2,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,3,1,4,2]=>[5,2,3,3,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,5,3,2,1,4]=>[5,2,3,4,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,3,2,4,1]=>[4,1,2,3,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,3,4,1,2]=>[4,1,2,5,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,3,4,2,1]=>[4,1,2,5,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,1,2,3]=>[4,1,3,1,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,5,4,1,3,2]=>[4,1,3,1,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,4,2,1,3]=>[4,1,3,2,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,4,2,3,1]=>[4,1,3,2,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,3,1,2]=>[4,1,3,3,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,4,3,2,1]=>[2,6,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,1,1,3,4,5]=>[2,1,2,4,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,1,3,5,4]=>[2,1,2,4,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,1,4,3,5]=>[2,1,2,5,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,1,4,5,3]=>[3,2,3,6,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,1,5,3,4]=>[4,3,4,1,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,1,5,4,3]=>[2,1,2,6,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,1,3,1,4,5]=>[3,2,5,1,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,1,5,4]=>[4,3,6,2,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,3,4,1,5]=>[4,3,6,5,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,3,4,5,1]=>[2,1,4,3,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,5,1,4]=>[6,5,1,1,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,1,3,5,4,1]=>[2,1,4,4,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,4,1,3,5]=>[6,5,2,3,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,1,5,3]=>[5,4,1,2,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,4,3,1,5]=>[5,4,1,4,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,4,3,5,1]=>[2,1,5,1,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,4,5,1,3]=>[2,1,5,3,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,5,3,1]=>[3,2,6,4,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,5,1,3,4]=>[2,1,6,5,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,1,4,3]=>[5,4,2,1,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,5,3,1,4]=>[5,4,2,3,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,5,3,4,1]=>[4,3,1,2,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,5,4,1,3]=>[4,3,1,3,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,5,4,3,1]=>[4,3,1,3,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,3,1,1,4,5]=>[1,2,6,1,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,1,1,5,4]=>[4,5,2,4,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,4,1,5]=>[5,6,3,1,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,4,5,1]=>[1,2,6,4,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,3,1,5,1,4]=>[5,6,3,2,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,1,5,4,1]=>[4,5,2,1,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,4,1,1,5]=>[1,2,2,5,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,3,4,1,5,1]=>[1,2,2,5,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,4,5,1,1]=>[1,2,2,2,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,3,5,1,1,4]=>[1,2,3,4,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,5,1,4,1]=>[1,2,3,4,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,5,4,1,1]=>[2,3,4,1,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,1,1,3,5]=>[1,3,5,1,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,4,1,1,5,3]=>[4,6,1,4,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,1,3,1,5]=>[6,1,3,1,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,1,3,5,1]=>[6,1,3,1,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,4,1,5,1,3]=>[6,1,3,3,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,4,1,5,3,1]=>[4,6,1,1,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,3,1,1,5]=>[4,6,3,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,3,1,5,1]=>[6,1,5,4,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,5,1,1]=>[2,4,1,4,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,5,1,1,3]=>[1,3,2,4,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,4,5,1,3,1]=>[1,3,2,4,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,5,3,1,1]=>[3,5,4,1,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,1,1,3,4]=>[1,4,4,1,3,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,1,1,4,3]=>[5,1,1,5,1,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[2,5,1,3,1,4]=>[6,2,2,1,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,1,3,4,1]=>[1,4,4,3,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,1,4,1,3]=>[6,2,2,2,3,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,5,1,4,3,1]=>[5,1,1,1,4,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,5,3,1,1,4]=>[5,1,3,3,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,5,3,1,4,1]=>[5,1,3,3,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,3,4,1,1]=>[1,4,6,2,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,4,1,1,3]=>[2,5,1,6,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,4,1,3,1]=>[6,2,5,3,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,3,1,1]=>[3,6,2,2,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,1,2,4,5]=>[1,6,1,2,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,1,2,5,4]=>[3,1,3,4,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,1,4,2,5]=>[5,3,5,1,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,1,4,5,2]=>[1,6,1,4,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,5,2,4]=>[4,2,4,1,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,1,5,4,2]=>[4,2,4,1,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,1,4,5]=>[3,1,4,2,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,2,1,5,4]=>[4,2,5,3,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,2,4,1,5]=>[4,2,5,6,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,2,4,5,1]=>[1,6,2,3,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,2,5,1,4]=>[5,3,6,1,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,2,5,4,1]=>[5,3,6,1,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,1,2,5]=>[5,3,1,2,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,1,5,2]=>[5,3,1,2,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,1,4,2,1,5]=>[5,3,1,3,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,4,2,5,1]=>[5,3,1,3,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,1,4,5,1,2]=>[1,6,4,2,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,4,5,2,1]=>[5,3,1,6,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,2,4]=>[1,6,5,4,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,4,2]=>[5,3,2,1,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,5,2,1,4]=>[5,3,2,2,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,5,2,4,1]=>[4,2,1,1,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,5,4,1,2]=>[4,2,1,3,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,5,4,2,1]=>[4,2,1,3,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,1,4,5]=>[2,1,1,2,5,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,1,5,4]=>[2,1,1,2,6,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,2,1,4,1,5]=>[5,4,4,1,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,2,1,4,5,1]=>[2,1,1,5,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,1,5,1,4]=>[5,4,4,2,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,1,5,4,1]=>[4,3,3,1,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,2,4,1,1,5]=>[4,3,6,1,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,2,4,1,5,1]=>[6,5,1,3,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,4,5,1,1]=>[2,1,4,3,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,5,1,1,4]=>[5,4,1,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,2,5,1,4,1]=>[5,4,1,1,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,5,4,1,1]=>[2,1,5,1,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,4,1,1,2,5]=>[1,2,5,1,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,1,1,5,2]=>[4,5,1,4,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,4,1,2,1,5]=>[4,5,1,5,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,4,1,2,5,1]=>[1,2,5,2,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,4,1,5,1,2]=>[1,2,5,5,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,1,5,2,1]=>[4,5,1,1,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,4,2,1,1,5]=>[4,5,2,3,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,2,1,5,1]=>[5,6,3,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,5,1,1]=>[1,2,6,4,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,4,5,1,1,2]=>[1,2,2,4,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,4,5,1,2,1]=>[2,3,3,5,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,4,5,2,1,1]=>[2,3,3,6,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,5,1,1,2,4]=>[1,3,4,1,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,5,1,1,4,2]=>[1,3,4,1,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,1,2,1,4]=>[2,4,5,3,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,5,1,2,4,1]=>[1,3,4,2,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,1,4,1,2]=>[1,3,4,4,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,4,2,1]=>[6,1,2,2,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,2,1,1,4]=>[2,4,6,1,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,2,1,4,1]=>[6,1,3,5,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,2,4,1,1]=>[1,3,5,3,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,4,1,1,2]=>[2,4,1,6,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,4,1,2,1]=>[2,4,1,6,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,4,2,1,1]=>[3,5,2,1,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,1,2,3,5]=>[1,5,1,2,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,1,2,5,3]=>[1,5,1,2,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,1,3,2,5]=>[2,6,2,4,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,1,3,5,2]=>[1,5,1,3,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,1,5,2,3]=>[4,1,4,1,1,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,1,5,3,2]=>[4,1,4,1,2,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,1,2,1,3,5]=>[2,6,3,1,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,2,1,5,3]=>[4,1,5,3,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,2,3,1,5]=>[4,1,5,5,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,2,3,5,1]=>[1,5,2,2,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,2,5,1,3]=>[1,5,2,4,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,1,2,5,3,1]=>[5,2,6,1,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,3,1,2,5]=>[1,5,3,6,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,1,5,2]=>[4,1,6,2,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,1,3,2,1,5]=>[4,1,6,3,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,1,3,2,5,1]=>[6,3,1,5,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,3,5,1,2]=>[1,5,3,3,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,3,5,2,1]=>[6,3,1,1,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,5,1,2,3]=>[1,5,5,4,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,5,1,3,2]=>[6,3,3,2,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,5,2,1,3]=>[4,1,1,1,3,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,1,5,2,3,1]=>[4,1,1,1,5,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,5,3,1,2]=>[4,1,1,2,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,5,3,2,1]=>[4,1,1,2,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,2,1,1,3,5]=>[3,1,2,3,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,2,1,1,5,3]=>[4,2,3,4,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,1,3,1,5]=>[4,2,3,6,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,1,3,5,1]=>[6,4,5,1,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,2,1,5,1,3]=>[6,4,5,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,5,3,1]=>[4,2,3,1,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,2,3,1,1,5]=>[4,2,5,2,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,2,3,1,5,1]=>[5,3,6,3,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,3,5,1,1]=>[1,6,2,3,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,5,1,1,3]=>[1,6,4,4,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,5,1,3,1]=>[6,4,2,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,5,3,1,1]=>[3,1,6,1,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[4,3,1,1,2,5]=>[3,2,1,3,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,1,1,5,2]=>[4,3,2,4,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,3,1,2,1,5]=>[4,3,2,5,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,2,5,1]=>[5,4,3,6,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,3,1,5,1,2]=>[5,4,3,2,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,5,2,1]=>[4,3,2,1,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,3,2,1,1,5]=>[2,1,1,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[4,3,2,1,5,1]=>[2,1,1,1,6,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,3,2,5,1,1]=>[2,1,1,5,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,3,5,1,1,2]=>[2,1,4,5,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,5,1,2,1]=>[2,1,4,5,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,5,2,1,1]=>[2,1,4,6,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,5,1,1,2,3]=>[1,2,4,1,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[4,5,1,1,3,2]=>[2,3,5,2,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,1,2,1,3]=>[2,3,5,3,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,5,1,2,3,1]=>[1,2,4,2,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,5,1,3,1,2]=>[1,2,4,3,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,1,3,2,1]=>[2,3,5,4,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,5,2,1,1,3]=>[2,3,6,1,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,2,1,3,1]=>[4,5,1,3,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,3,1,1]=>[1,2,5,2,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,5,3,1,1,2]=>[3,4,1,1,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,5,3,1,2,1]=>[3,4,1,1,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,5,3,2,1,1]=>[3,4,1,2,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,1,2,3,4]=>[1,4,1,2,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[5,1,1,2,4,3]=>[2,5,2,3,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,1,3,2,4]=>[2,5,2,4,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,1,3,4,2]=>[1,4,1,3,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,1,4,2,3]=>[1,4,1,4,6,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,1,4,3,2]=>[2,5,2,5,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,1,2,1,3,4]=>[2,5,3,1,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,1,4,3]=>[2,5,3,1,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,1,2,3,1,4]=>[1,4,2,2,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,2,3,4,1]=>[1,4,2,2,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,1,2,4,1,3]=>[1,4,2,3,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,4,3,1]=>[3,6,4,5,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,1,2,4]=>[1,4,3,6,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,3,1,4,2]=>[6,2,1,4,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,3,2,1,4]=>[2,5,4,1,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,3,2,4,1]=>[6,2,1,5,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,1,3,4,1,2]=>[1,4,3,2,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,3,4,2,1]=>[3,6,5,4,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,4,1,2,3]=>[1,4,4,5,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,4,1,3,2]=>[6,2,2,3,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,4,2,1,3]=>[6,2,2,4,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,4,2,3,1]=>[5,1,1,3,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,1,4,3,1,2]=>[5,1,1,4,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,4,3,2,1]=>[2,5,5,1,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,2,1,1,3,4]=>[2,6,1,2,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,1,1,4,3]=>[2,6,1,2,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,1,3,1,4]=>[6,3,5,1,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,3,4,1]=>[4,1,3,6,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,1,4,1,3]=>[6,3,5,2,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,1,4,3,1]=>[5,2,4,1,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,3,1,1,4]=>[1,5,2,6,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,3,1,4,1]=>[5,2,6,3,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,3,4,1,1]=>[1,5,2,2,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,2,4,1,1,3]=>[1,5,3,5,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,4,1,3,1]=>[6,3,1,3,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,2,4,3,1,1]=>[4,1,6,3,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,1,1,2,4]=>[3,1,1,3,4,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,3,1,1,4,2]=>[3,1,1,3,6,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,1,2,1,4]=>[3,1,1,4,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,1,2,4,1]=>[4,2,2,5,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,1,4,1,2]=>[5,3,3,1,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,1,4,2,1]=>[3,1,1,6,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,3,2,1,1,4]=>[3,1,2,2,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,3,2,1,4,1]=>[5,3,4,4,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,2,4,1,1]=>[4,2,3,6,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,4,1,1,2]=>[1,6,2,5,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,3,4,1,2,1]=>[4,2,5,1,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,3,4,2,1,1]=>[3,1,4,1,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,1,1,2,3]=>[2,1,6,2,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,4,1,1,3,2]=>[2,1,6,2,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,4,1,2,1,3]=>[2,1,6,3,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,4,1,2,3,1]=>[4,3,1,5,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,1,3,1,2]=>[4,3,1,6,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,3,2,1]=>[2,1,6,4,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,4,2,1,1,3]=>[3,2,1,2,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,4,2,1,3,1]=>[3,2,1,2,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,4,2,3,1,1]=>[3,2,1,4,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,3,1,1,2]=>[3,2,2,1,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,3,1,2,1]=>[3,2,2,1,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,4,3,2,1,1]=>[2,1,1,1,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,2,3,4,6]=>[1,1,2,2,2,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,2,3,6,4]=>[1,1,2,2,4,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,2,4,3,6]=>[2,2,3,4,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,2,4,6,3]=>[1,1,2,3,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,2,6,3,4]=>[1,1,2,5,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,2,6,4,3]=>[4,4,5,1,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,3,2,4,6]=>[2,2,4,1,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,3,2,6,4]=>[4,4,6,3,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,3,4,2,6]=>[1,1,3,2,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,3,4,6,2]=>[1,1,3,2,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,3,6,2,4]=>[1,1,3,4,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,3,6,4,2]=>[3,3,5,6,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,4,2,3,6]=>[1,1,4,6,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,4,2,6,3]=>[5,5,1,3,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,4,3,2,6]=>[2,2,5,1,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,4,3,6,2]=>[5,5,1,4,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,4,6,2,3]=>[1,1,4,3,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,4,6,3,2]=>[2,2,5,4,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,6,2,3,4]=>[1,1,6,4,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,6,2,4,3]=>[3,3,1,6,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,6,3,2,4]=>[4,4,2,1,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,6,3,4,2]=>[4,4,2,1,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,6,4,2,3]=>[3,3,1,1,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,6,4,3,2]=>[3,3,1,1,2,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,1,3,4,6]=>[2,3,1,4,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,1,3,6,4]=>[3,4,2,5,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,4,3,6]=>[2,3,1,5,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,1,4,6,3]=>[2,3,1,5,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,6,3,4]=>[4,5,3,2,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,6,4,3]=>[3,4,2,1,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,1,4,6]=>[1,2,2,6,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,3,1,6,4]=>[3,4,4,1,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,2,3,4,1,6]=>[1,2,2,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,2,3,4,6,1]=>[1,2,2,2,3,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,6,1,4]=>[1,2,2,4,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,3,6,4,1]=>[1,2,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,4,1,3,6]=>[1,2,3,5,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,1,6,3]=>[4,5,6,1,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,4,3,1,6]=>[3,4,5,2,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,4,3,6,1]=>[2,3,4,1,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,6,1,3]=>[1,2,3,3,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,4,6,3,1]=>[1,2,3,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,1,3,4]=>[1,2,5,3,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,6,1,4,3]=>[2,3,6,4,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,6,3,1,4]=>[5,6,2,2,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,6,3,4,1]=>[4,5,1,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,2,6,4,1,3]=>[4,5,1,2,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,6,4,3,1]=>[4,5,1,2,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,1,2,4,6]=>[1,3,6,2,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,3,1,2,6,4]=>[4,6,2,5,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,1,4,2,6]=>[6,1,4,2,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,1,4,6,2]=>[6,1,4,2,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,1,6,2,4]=>[6,1,4,4,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,1,6,4,2]=>[3,5,1,1,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,3,2,1,4,6]=>[2,4,1,1,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,2,1,6,4]=>[3,5,2,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,2,4,1,6]=>[6,1,5,1,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,4,6,1]=>[6,1,5,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,3,2,6,1,4]=>[6,1,5,3,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,2,6,4,1]=>[4,6,3,1,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,4,1,2,6]=>[1,3,2,5,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,4,1,6,2]=>[1,3,2,5,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,2,1,6]=>[3,5,4,1,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,4,2,6,1]=>[1,3,2,6,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,4,6,1,2]=>[1,3,2,3,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,4,6,2,1]=>[2,4,3,4,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,6,1,2,4]=>[1,3,4,3,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,6,1,4,2]=>[6,1,2,1,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,6,2,1,4]=>[6,1,2,2,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,3,6,2,4,1]=>[6,1,2,2,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,6,4,1,2]=>[1,3,4,6,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,6,4,2,1]=>[3,5,6,1,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,2,3,6]=>[1,4,5,2,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,1,2,6,3]=>[5,1,2,6,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,1,3,2,6]=>[6,2,3,1,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,1,3,6,2]=>[6,2,3,1,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,1,6,2,3]=>[5,1,2,3,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,6,3,2]=>[5,1,2,3,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,2,1,3,6]=>[6,2,4,5,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,2,1,6,3]=>[5,1,3,4,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,2,3,1,6]=>[3,6,1,4,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,4,2,3,6,1]=>[1,4,6,2,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,6,1,3]=>[6,2,4,3,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,2,6,3,1]=>[5,1,3,2,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,4,3,1,2,6]=>[5,1,4,3,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,1,6,2]=>[5,1,4,3,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,3,2,1,6]=>[3,6,2,2,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,3,2,6,1]=>[2,5,1,1,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,3,6,1,2]=>[2,5,1,5,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,3,6,2,1]=>[5,1,4,1,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,6,1,2,3]=>[1,4,3,3,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,4,6,1,3,2]=>[6,2,1,1,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,6,2,1,3]=>[6,2,1,2,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,6,2,3,1]=>[1,4,3,4,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,6,3,1,2]=>[1,4,3,5,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,6,3,2,1]=>[2,5,4,6,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,1,2,3,4]=>[1,6,3,2,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,6,1,2,4,3]=>[3,1,5,4,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,1,3,2,4]=>[6,4,1,1,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,6,1,3,4,2]=>[3,1,5,5,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,1,4,2,3]=>[3,1,5,6,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,4,3,2]=>[3,1,5,6,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,2,1,3,4]=>[3,1,6,2,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,1,4,3]=>[5,3,1,4,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,6,2,3,1,4]=>[5,3,1,6,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,2,3,4,1]=>[1,6,4,2,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,2,4,1,3]=>[6,4,2,1,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,2,4,3,1]=>[3,1,6,5,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,3,1,2,4]=>[4,2,1,2,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,3,1,4,2]=>[5,3,2,3,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,6,3,2,1,4]=>[5,3,2,4,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,3,2,4,1]=>[4,2,1,3,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,3,4,1,2]=>[4,2,1,5,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,6,3,4,2,1]=>[4,2,1,5,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,4,1,2,3]=>[4,2,2,1,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,4,1,3,2]=>[4,2,2,1,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,4,2,1,3]=>[3,1,1,1,2,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,6,4,2,3,1]=>[3,1,1,1,4,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,6,4,3,1,2]=>[3,1,1,2,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,6,4,3,2,1]=>[3,1,1,2,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,3,4,6]=>[2,1,2,4,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,1,3,6,4]=>[3,2,3,5,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,4,3,6]=>[2,1,2,5,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,1,1,4,6,3]=>[2,1,2,5,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,1,6,3,4]=>[4,3,4,2,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,1,6,4,3]=>[3,2,3,1,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,1,4,6]=>[6,5,1,4,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,3,1,6,4]=>[3,2,5,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,3,4,1,6]=>[4,3,6,5,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,6,1]=>[2,1,4,3,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,6,1,4]=>[6,5,1,2,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,1,3,6,4,1]=>[6,5,1,2,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,1,3,6]=>[6,5,2,3,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,1,6,3]=>[5,4,1,2,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,4,3,1,6]=>[3,2,6,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,4,3,6,1]=>[2,1,5,1,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,4,6,1,3]=>[6,5,2,1,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,1,4,6,3,1]=>[6,5,2,1,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,1,3,4]=>[3,2,1,5,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,6,1,4,3]=>[3,2,1,5,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,6,3,1,4]=>[5,4,3,2,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,3,4,1]=>[4,3,2,1,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,6,4,1,3]=>[4,3,2,2,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,4,3,1]=>[3,2,1,1,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[2,3,1,1,4,6]=>[1,2,6,1,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,1,1,6,4]=>[3,4,1,3,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[2,3,1,4,1,6]=>[5,6,3,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,3,1,4,6,1]=>[1,2,6,4,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,1,6,1,4]=>[3,4,1,1,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,6,4,1]=>[4,5,2,2,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,3,4,1,1,6]=>[1,2,2,5,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,4,1,6,1]=>[1,2,2,5,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,4,6,1,1]=>[1,2,2,3,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,6,1,1,4]=>[1,2,4,3,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,6,1,4,1]=>[1,2,4,3,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,6,4,1,1]=>[1,2,4,6,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,1,1,3,6]=>[1,3,5,1,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,1,1,6,3]=>[4,6,1,4,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,1,3,1,6]=>[6,1,3,1,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,4,1,3,6,1]=>[6,1,3,1,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,4,1,6,1,3]=>[6,1,3,4,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,1,6,3,1]=>[4,6,1,2,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,3,1,1,6]=>[3,5,2,1,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,3,1,6,1]=>[3,5,2,1,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,3,6,1,1]=>[2,4,1,5,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,6,1,1,3]=>[1,3,3,3,1,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[2,4,6,1,3,1]=>[6,1,1,1,1,4]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[2,4,6,3,1,1]=>[1,3,3,5,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,6,1,1,3,4]=>[1,5,3,1,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,1,1,4,3]=>[2,6,4,2,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,1,3,1,4]=>[6,3,1,1,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,1,3,4,1]=>[1,5,3,3,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,6,1,4,1,3]=>[6,3,1,2,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,6,1,4,3,1]=>[6,3,1,2,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,3,1,1,4]=>[5,2,2,3,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,3,1,4,1]=>[5,2,2,3,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,6,3,4,1,1]=>[4,1,1,5,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,6,4,1,1,3]=>[4,1,2,1,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,4,1,3,1]=>[4,1,2,1,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,6,4,3,1,1]=>[4,1,2,3,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,1,2,4,6]=>[1,6,1,2,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,1,2,6,4]=>[4,2,4,5,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,1,4,2,6]=>[5,3,5,1,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,1,4,6,2]=>[1,6,1,4,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,1,6,2,4]=>[3,1,3,1,6,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,1,6,4,2]=>[3,1,3,1,1,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[3,1,2,1,4,6]=>[3,1,4,2,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,1,6,4]=>[3,1,4,2,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,2,4,1,6]=>[4,2,5,6,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,2,4,6,1]=>[1,6,2,3,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,2,6,1,4]=>[1,6,2,5,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,6,4,1]=>[4,2,5,1,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,1,4,1,2,6]=>[5,3,1,2,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,4,1,6,2]=>[5,3,1,2,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,4,2,1,6]=>[3,1,6,1,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,4,2,6,1]=>[6,4,2,4,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,4,6,1,2]=>[1,6,4,3,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,4,6,2,1]=>[6,4,2,1,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,6,1,2,4]=>[3,1,1,5,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,6,1,4,2]=>[3,1,1,5,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,6,2,1,4]=>[5,3,3,1,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,6,2,4,1]=>[6,4,4,2,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,6,4,1,2]=>[4,2,2,2,1,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,6,4,2,1]=>[3,1,1,1,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[3,2,1,1,4,6]=>[2,1,1,2,5,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,2,1,1,6,4]=>[3,2,2,3,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,1,4,1,6]=>[5,4,4,1,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,1,4,6,1]=>[2,1,1,5,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,1,6,1,4]=>[3,2,2,1,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,1,6,4,1]=>[4,3,3,2,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,4,1,1,6]=>[4,3,6,1,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,4,1,6,1]=>[6,5,1,3,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,4,6,1,1]=>[2,1,4,4,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,2,6,1,1,4]=>[2,1,6,4,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,6,1,4,1]=>[6,5,3,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,6,4,1,1]=>[4,3,1,2,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,1,2,6]=>[1,2,5,1,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[3,4,1,1,6,2]=>[1,2,5,1,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,1,2,1,6]=>[4,5,1,5,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,1,2,6,1]=>[1,2,5,2,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,4,1,6,1,2]=>[1,2,5,6,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,6,2,1]=>[5,6,2,3,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,1,1,6]=>[3,4,1,2,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,4,2,1,6,1]=>[3,4,1,2,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,2,6,1,1]=>[1,2,6,5,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,6,1,1,2]=>[1,2,3,3,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,4,6,1,2,1]=>[2,3,4,4,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,6,2,1,1]=>[2,3,4,5,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,6,1,1,2,4]=>[1,4,3,1,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,6,1,1,4,2]=>[1,4,3,1,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,6,1,2,1,4]=>[2,5,4,3,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,6,1,2,4,1]=>[1,4,3,2,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,6,1,4,1,2]=>[1,4,3,4,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,1,4,2,1]=>[6,2,1,2,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,2,1,1,4]=>[5,1,1,4,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,6,2,1,4,1]=>[5,1,1,4,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,6,2,4,1,1]=>[1,4,4,3,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,4,1,1,2]=>[1,4,6,5,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,4,1,2,1]=>[5,1,3,2,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,4,2,1,1]=>[3,6,1,1,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,1,2,3,6]=>[1,5,1,2,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,1,2,6,3]=>[4,1,4,5,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,1,3,2,6]=>[4,1,4,6,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,1,1,3,6,2]=>[1,5,1,3,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,1,6,2,3]=>[1,5,1,6,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,1,6,3,2]=>[4,1,4,2,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,1,2,1,3,6]=>[2,6,3,1,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,1,6,3]=>[4,1,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,2,3,1,6]=>[4,1,5,5,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,2,3,6,1]=>[1,5,2,2,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,2,6,1,3]=>[1,5,2,5,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,1,2,6,3,1]=>[4,1,5,1,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,3,1,2,6]=>[4,1,6,2,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,1,6,2]=>[6,3,1,4,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,3,2,1,6]=>[4,1,6,3,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,3,2,6,1]=>[6,3,1,5,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,3,6,1,2]=>[1,5,3,4,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,3,6,2,1]=>[6,3,1,2,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,6,1,2,3]=>[1,5,6,3,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,6,1,3,2]=>[6,3,4,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,6,2,1,3]=>[6,3,4,2,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,2,3,1]=>[5,2,3,1,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,6,3,1,2]=>[4,1,2,1,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,6,3,2,1]=>[4,1,2,1,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,2,1,1,3,6]=>[3,1,2,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,1,1,6,3]=>[4,2,3,4,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,1,3,1,6]=>[3,1,2,5,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,2,1,3,6,1]=>[6,4,5,1,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,2,1,6,1,3]=>[3,1,2,1,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,1,6,3,1]=>[4,2,3,2,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,2,3,1,1,6]=>[3,1,4,1,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[4,2,3,1,6,1]=>[3,1,4,1,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,2,3,6,1,1]=>[1,6,2,4,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,6,1,1,3]=>[1,6,5,3,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,6,1,3,1]=>[6,4,3,1,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,6,3,1,1]=>[4,2,1,1,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,3,1,1,2,6]=>[4,3,2,4,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,1,1,6,2]=>[3,2,1,3,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,1,2,1,6]=>[3,2,1,4,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,3,1,2,6,1]=>[4,3,2,5,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,6,1,2]=>[3,2,1,1,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,6,2,1]=>[3,2,1,1,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,3,2,1,1,6]=>[3,2,2,2,3,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[4,3,2,1,6,1]=>[3,2,2,2,1,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,3,2,6,1,1]=>[2,1,1,6,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,6,1,1,2]=>[2,1,5,4,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,6,1,2,1]=>[2,1,5,4,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,6,2,1,1]=>[2,1,5,5,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,6,1,1,2,3]=>[1,3,3,1,2,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,6,1,1,3,2]=>[2,4,4,2,4,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,6,1,2,1,3]=>[2,4,4,3,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,6,1,2,3,1]=>[1,3,3,2,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,6,1,3,1,2]=>[1,3,3,3,6,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,6,1,3,2,1]=>[2,4,4,4,1,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,6,2,1,1,3]=>[2,4,5,1,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,6,2,1,3,1]=>[6,1,2,5,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,6,2,3,1,1]=>[1,3,4,2,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,6,3,1,1,2]=>[1,3,5,6,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,6,3,1,2,1]=>[4,6,1,2,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,3,2,1,1]=>[2,4,6,1,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,1,1,2,3,4]=>[1,3,1,2,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[6,1,1,2,4,3]=>[2,4,2,3,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,1,3,2,4]=>[2,4,2,4,1,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[6,1,1,3,4,2]=>[1,3,1,3,2,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,1,4,2,3]=>[1,3,1,4,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,1,4,3,2]=>[2,4,2,5,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,1,2,1,3,4]=>[2,4,3,1,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,2,1,4,3]=>[2,4,3,1,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,2,3,1,4]=>[1,3,2,2,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,2,3,4,1]=>[1,3,2,2,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,1,2,4,1,3]=>[1,3,2,3,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[6,1,2,4,3,1]=>[3,5,4,5,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,1,3,1,2,4]=>[1,3,3,6,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[6,1,3,1,4,2]=>[6,1,1,4,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,1,3,2,1,4]=>[2,4,4,1,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[6,1,3,2,4,1]=>[6,1,1,5,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,3,4,1,2]=>[1,3,3,2,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,1,3,4,2,1]=>[3,5,5,4,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,1,4,1,2,3]=>[1,3,4,5,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,4,1,3,2]=>[6,1,2,3,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,1,4,2,1,3]=>[6,1,2,4,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,1,4,2,3,1]=>[3,5,6,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,4,3,1,2]=>[3,5,6,2,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,3,2,1]=>[2,4,5,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,2,1,1,3,4]=>[2,5,1,2,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,1,1,4,3]=>[2,5,1,2,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,2,1,3,1,4]=>[6,2,5,1,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,2,1,3,4,1]=>[2,5,1,4,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,1,4,1,3]=>[6,2,5,2,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,2,1,4,3,1]=>[5,1,4,1,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,2,3,1,1,4]=>[1,4,2,6,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,2,3,1,4,1]=>[5,1,6,3,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,3,4,1,1]=>[1,4,2,2,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,4,1,1,3]=>[1,4,3,5,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,2,4,1,3,1]=>[6,2,1,3,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,2,4,3,1,1]=>[3,6,5,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,1,2,4]=>[1,5,6,1,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,1,1,4,2]=>[5,2,3,5,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,3,1,2,1,4]=>[5,2,3,6,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,1,2,4,1]=>[4,1,2,5,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,1,4,1,2]=>[5,2,3,1,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,1,4,2,1]=>[5,2,3,1,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,3,2,1,1,4]=>[2,6,1,1,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,2,1,4,1]=>[5,2,4,4,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,3,2,4,1,1]=>[4,1,3,6,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,3,4,1,1,2]=>[1,5,2,5,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,3,4,1,2,1]=>[4,1,5,1,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,3,4,2,1,1]=>[4,1,5,2,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,1,1,2,3]=>[1,6,5,1,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,4,1,1,3,2]=>[4,2,1,4,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,1,2,1,3]=>[4,2,1,5,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,1,2,3,1]=>[4,2,1,5,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,4,1,3,1,2]=>[4,2,1,6,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,4,1,3,2,1]=>[4,2,1,6,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,4,2,1,1,3]=>[3,1,1,2,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,4,2,1,3,1]=>[3,1,1,2,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[6,4,2,3,1,1]=>[3,1,1,4,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[6,4,3,1,1,2]=>[3,1,2,1,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,3,1,2,1]=>[3,1,2,1,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,3,2,1,1]=>[3,1,2,2,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,3,5,5]=>[1,1,2,2,3,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,2,5,3,5]=>[1,1,2,4,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,2,5,5,3]=>[1,1,2,4,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,3,2,5,5]=>[2,2,4,1,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,3,5,2,5]=>[1,1,3,3,5,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,5,5,2]=>[1,1,3,3,1,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,5,2,3,5]=>[1,1,5,5,2,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,5,2,5,3]=>[5,5,2,2,1,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,5,3,2,5]=>[5,5,2,3,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,5,3,5,2]=>[4,4,1,2,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,5,5,2,3]=>[1,1,5,1,5,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,5,5,3,2]=>[4,4,1,4,2,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,3,5,5]=>[2,3,1,4,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,1,5,3,5]=>[4,5,3,1,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,5,5,3]=>[4,5,3,1,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,1,5,5]=>[1,2,2,6,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,3,5,1,5]=>[1,2,2,3,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,5,5,1]=>[1,2,2,3,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,5,1,3,5]=>[1,2,4,4,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,5,1,5,3]=>[5,6,1,1,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,5,3,1,5]=>[5,6,1,3,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,5,3,5,1]=>[1,2,4,6,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,5,1,3]=>[1,2,4,1,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,5,5,3,1]=>[3,4,6,3,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,2,5,5]=>[1,3,6,2,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,5,2,5]=>[6,1,4,3,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,1,5,5,2]=>[4,6,2,1,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,2,1,5,5]=>[2,4,1,1,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,2,5,1,5]=>[6,1,5,2,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,2,5,5,1]=>[2,4,1,5,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,5,1,2,5]=>[1,3,3,4,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,5,1,5,2]=>[6,1,1,2,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,5,2,1,5]=>[6,1,1,3,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,5,2,5,1]=>[6,1,1,3,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,5,5,1,2]=>[1,3,3,1,4,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,5,5,2,1]=>[2,4,4,2,6,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,1,2,3,5]=>[1,5,4,2,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,1,2,5,3]=>[5,2,1,6,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,3,2,5]=>[6,3,2,1,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,3,5,2]=>[6,3,2,1,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,5,1,5,2,3]=>[5,2,1,2,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,5,1,5,3,2]=>[5,2,1,2,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,2,1,3,5]=>[6,3,3,5,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,5,2,1,5,3]=>[4,1,1,3,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,5,2,3,1,5]=>[4,1,1,5,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,2,3,5,1]=>[1,5,5,2,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,2,5,1,3]=>[6,3,3,2,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,5,2,5,3,1]=>[5,2,2,1,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,3,1,2,5]=>[5,2,3,3,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,3,1,5,2]=>[4,1,2,2,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,5,3,2,1,5]=>[4,1,2,3,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,5,3,2,5,1]=>[5,2,3,4,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,3,5,1,2]=>[1,5,6,3,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,3,5,2,1]=>[4,1,2,6,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,5,1,2,3]=>[1,5,1,4,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,5,1,3,2]=>[2,6,2,5,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,5,2,1,3]=>[4,1,4,1,3,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,5,2,3,1]=>[4,1,4,1,5,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,5,3,1,2]=>[4,1,4,2,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,5,3,2,1]=>[4,1,4,2,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,3,5,5]=>[2,1,2,4,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,1,5,3,5]=>[4,3,4,1,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,1,5,5,3]=>[4,3,4,1,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,1,5,5]=>[4,3,6,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,3,5,1,5]=>[6,5,1,1,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,5,5,1]=>[2,1,4,4,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,5,1,3,5]=>[6,5,3,2,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,5,1,5,3]=>[5,4,2,1,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,5,3,1,5]=>[4,3,1,2,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,5,3,5,1]=>[6,5,3,4,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,5,1,3]=>[2,1,6,2,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,5,5,3,1]=>[4,3,1,4,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,1,1,5,5]=>[1,2,6,1,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,3,1,5,1,5]=>[5,6,3,2,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,5,5,1]=>[1,2,6,5,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,5,1,1,5]=>[1,2,3,4,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,5,1,5,1]=>[1,2,3,4,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,5,5,1,1]=>[1,2,3,1,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,5,1,1,3,5]=>[1,4,4,1,3,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,5,1,1,5,3]=>[5,1,1,5,2,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,5,1,3,1,5]=>[6,2,2,1,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,3,5,1]=>[6,2,2,1,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,5,1,5,1,3]=>[6,2,2,3,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,5,1,5,3,1]=>[5,1,1,2,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,3,1,1,5]=>[5,1,3,3,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,5,3,1,5,1]=>[5,1,3,3,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,3,5,1,1]=>[1,4,6,3,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,5,1,1,3]=>[1,4,1,4,1,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,5,5,1,3,1]=>[1,4,1,4,3,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,5,3,1,1]=>[3,6,3,1,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,1,2,5,5]=>[1,6,1,2,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,1,5,2,5]=>[5,3,5,2,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,1,5,5,2]=>[4,2,4,1,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,2,1,5,5]=>[4,2,5,3,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,5,1,5]=>[5,3,6,1,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,2,5,5,1]=>[1,6,2,4,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,5,1,2,5]=>[5,3,2,1,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,5,1,5,2]=>[5,3,2,1,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,1,5,2,1,5]=>[4,2,1,1,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,5,2,5,1]=>[5,3,2,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,1,5,5,1,2]=>[1,6,5,1,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,5,2,1]=>[4,2,1,4,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,1,1,5,5]=>[2,1,1,2,6,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,2,1,5,1,5]=>[5,4,4,2,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,2,1,5,5,1]=>[2,1,1,6,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,5,1,1,5]=>[5,4,1,1,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,2,5,1,5,1]=>[5,4,1,1,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,5,5,1,1]=>[2,1,5,2,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,5,1,1,2,5]=>[1,3,4,1,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,5,1,1,5,2]=>[1,3,4,1,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,5,1,2,1,5]=>[2,4,5,3,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,1,2,5,1]=>[1,3,4,2,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,5,1,5,1,2]=>[1,3,4,5,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,5,2,1]=>[6,1,2,3,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,2,1,1,5]=>[4,6,1,3,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,2,1,5,1]=>[6,1,3,5,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,2,5,1,1]=>[1,3,5,4,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,5,1,1,2]=>[1,3,1,4,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,5,5,1,2,1]=>[2,4,2,5,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,5,2,1,1]=>[2,4,2,6,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,1,2,3,5]=>[1,4,1,2,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,1,1,2,5,3]=>[1,4,1,2,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,1,3,2,5]=>[2,5,2,4,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,1,3,5,2]=>[1,4,1,3,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,1,1,5,2,3]=>[1,4,1,5,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,1,5,3,2]=>[5,1,5,2,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,2,1,3,5]=>[2,5,3,1,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,2,1,5,3]=>[5,1,6,4,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,2,3,1,5]=>[1,4,2,2,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,2,3,5,1]=>[1,4,2,2,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,1,2,5,1,3]=>[1,4,2,4,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,1,2,5,3,1]=>[5,1,6,1,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,1,3,1,2,5]=>[1,4,3,6,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,3,1,5,2]=>[6,2,1,4,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,3,2,1,5]=>[2,5,4,1,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,3,2,5,1]=>[6,2,1,5,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,3,5,1,2]=>[1,4,3,3,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,1,3,5,2,1]=>[6,2,1,1,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,1,5,1,2,3]=>[1,4,5,4,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,5,1,3,2]=>[6,2,3,2,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,5,2,1,3]=>[6,2,3,3,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,5,2,3,1]=>[5,1,2,2,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,5,3,1,2]=>[5,1,2,3,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,5,3,2,1]=>[5,1,2,3,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,1,1,3,5]=>[2,6,1,2,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,2,1,1,5,3]=>[4,1,3,4,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,2,1,3,1,5]=>[4,1,3,6,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,1,3,5,1]=>[6,3,5,1,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,1,5,1,3]=>[6,3,5,3,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,1,5,3,1]=>[4,1,3,1,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,2,3,1,1,5]=>[4,1,5,2,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,2,3,1,5,1]=>[5,2,6,3,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,3,5,1,1]=>[1,5,2,3,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,5,1,1,3]=>[1,5,4,4,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,2,5,1,3,1]=>[6,3,2,2,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,5,3,1,1]=>[5,2,1,3,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,1,2,5]=>[3,1,1,3,4,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,1,1,5,2]=>[4,2,2,4,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[5,3,1,2,1,5]=>[4,2,2,5,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,3,1,2,5,1]=>[5,3,3,6,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,3,1,5,1,2]=>[5,3,3,2,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,1,5,2,1]=>[4,2,2,1,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,3,2,1,1,5]=>[4,2,3,3,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,3,2,1,5,1]=>[5,3,4,4,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,2,5,1,1]=>[5,3,4,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,5,1,1,2]=>[1,6,3,4,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,5,1,2,1]=>[3,1,5,6,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,5,2,1,1]=>[4,2,6,1,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,5,1,1,2,3]=>[1,1,4,1,2,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,5,1,1,3,2]=>[2,2,5,2,4,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,5,1,2,1,3]=>[2,2,5,3,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,5,1,2,3,1]=>[1,1,4,2,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,5,1,3,1,2]=>[1,1,4,3,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,5,1,3,2,1]=>[2,2,5,4,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,5,2,1,1,3]=>[2,2,6,1,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,5,2,1,3,1]=>[4,4,1,3,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,5,2,3,1,1]=>[1,1,5,2,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,5,3,1,1,2]=>[3,3,1,1,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,5,3,1,2,1]=>[3,3,1,1,4,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,5,3,2,1,1]=>[3,3,1,2,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,3,5,6]=>[1,1,2,2,3,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,2,3,6,5]=>[2,2,3,3,5,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,2,5,3,6]=>[1,1,2,4,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,2,5,6,3]=>[1,1,2,4,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,2,6,3,5]=>[1,1,2,5,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,2,6,5,3]=>[4,4,5,1,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,3,2,5,6]=>[2,2,4,1,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,3,2,6,5]=>[2,2,4,1,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,3,5,2,6]=>[1,1,3,3,5,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,3,5,6,2]=>[1,1,3,3,2,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,3,6,2,5]=>[1,1,3,4,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,3,6,5,2]=>[2,2,4,5,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,5,2,3,6]=>[1,1,5,5,2,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,5,2,6,3]=>[4,4,1,1,1,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,5,3,2,6]=>[4,4,1,2,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,5,3,6,2]=>[5,5,2,3,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,5,6,2,3]=>[1,1,5,2,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,5,6,3,2]=>[4,4,1,5,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,6,2,3,5]=>[1,1,6,4,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,6,2,5,3]=>[5,5,3,1,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,6,3,2,5]=>[5,5,3,2,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,6,3,5,2]=>[4,4,2,1,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,6,5,2,3]=>[4,4,2,3,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,6,5,3,2]=>[3,3,1,2,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,1,3,5,6]=>[2,3,1,4,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,1,3,6,5]=>[2,3,1,4,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,5,3,6]=>[5,6,4,2,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,5,6,3]=>[4,5,3,1,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,1,6,3,5]=>[4,5,3,2,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,6,5,3]=>[3,4,2,1,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,1,5,6]=>[1,2,2,6,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,2,3,1,6,5]=>[3,4,4,1,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,3,5,1,6]=>[1,2,2,3,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,3,5,6,1]=>[1,2,2,3,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,6,1,5]=>[1,2,2,4,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,6,5,1]=>[2,3,3,5,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,5,1,3,6]=>[1,2,4,4,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,5,1,6,3]=>[5,6,1,1,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,5,3,1,6]=>[3,4,6,1,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,2,5,3,6,1]=>[1,2,4,6,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,6,1,3]=>[1,2,4,2,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,5,6,3,1]=>[1,2,4,2,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,1,3,5]=>[1,2,5,3,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,6,1,5,3]=>[4,5,1,6,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,6,3,1,5]=>[4,5,1,1,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,6,3,5,1]=>[1,2,5,5,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,6,5,1,3]=>[2,3,6,1,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,6,5,3,1]=>[4,5,1,3,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,1,2,5,6]=>[1,3,6,2,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,1,2,6,5]=>[4,6,2,5,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,2,6]=>[4,6,2,1,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,1,5,6,2]=>[1,3,6,5,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,6,2,5]=>[6,1,4,4,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,1,6,5,2]=>[4,6,2,2,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,2,1,5,6]=>[2,4,1,1,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,2,1,6,5]=>[3,5,2,2,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,3,2,5,1,6]=>[6,1,5,2,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,2,5,6,1]=>[2,4,1,5,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,6,1,5]=>[6,1,5,3,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,6,5,1]=>[2,4,1,6,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,5,1,2,6]=>[1,3,3,4,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,5,1,6,2]=>[6,1,1,2,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,5,2,1,6]=>[6,1,1,3,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,5,2,6,1]=>[6,1,1,3,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,5,6,1,2]=>[1,3,3,2,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,3,5,6,2,1]=>[2,4,4,3,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,6,1,2,5]=>[1,3,4,3,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,6,1,5,2]=>[6,1,2,1,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,6,2,1,5]=>[6,1,2,2,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,6,2,5,1]=>[6,1,2,2,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,3,6,5,1,2]=>[2,4,5,1,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,6,5,2,1]=>[2,4,5,1,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,1,2,3,6]=>[1,5,4,2,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,1,2,6,3]=>[5,2,1,6,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,5,1,3,2,6]=>[6,3,2,1,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,1,3,6,2]=>[6,3,2,1,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,5,1,6,2,3]=>[5,2,1,3,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,6,3,2]=>[5,2,1,3,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,2,1,3,6]=>[6,3,3,5,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,2,1,6,3]=>[4,1,1,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,5,2,3,1,6]=>[4,1,1,5,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,2,3,6,1]=>[1,5,5,2,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,2,6,1,3]=>[6,3,3,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,5,2,6,3,1]=>[4,1,1,1,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,3,1,2,6]=>[4,1,2,2,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,3,1,6,2]=>[5,2,3,3,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,5,3,2,1,6]=>[4,1,2,3,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,5,3,2,6,1]=>[4,1,2,3,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,3,6,1,2]=>[1,5,6,4,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,3,6,2,1]=>[5,2,3,1,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,6,1,2,3]=>[1,5,2,3,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,5,6,1,3,2]=>[2,6,3,4,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,6,2,1,3]=>[2,6,3,5,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,6,2,3,1]=>[1,5,2,4,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,6,3,1,2]=>[4,1,5,1,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,6,3,2,1]=>[4,1,5,1,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,6,1,2,3,5]=>[1,6,3,2,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,6,1,2,5,3]=>[3,1,5,4,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,3,2,5]=>[6,4,1,1,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,1,3,5,2]=>[6,4,1,1,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,6,1,5,2,3]=>[4,2,6,1,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,1,5,3,2]=>[4,2,6,1,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,2,1,3,5]=>[6,4,2,5,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,2,1,5,3]=>[5,3,1,4,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,2,3,1,5]=>[5,3,1,6,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,2,3,5,1]=>[1,6,4,2,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,2,5,1,3]=>[6,4,2,2,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,6,2,5,3,1]=>[5,3,1,1,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,6,3,1,2,5]=>[5,3,2,3,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,3,1,5,2]=>[4,2,1,2,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,6,3,2,1,5]=>[4,2,1,3,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,6,3,2,5,1]=>[5,3,2,4,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,6,3,5,1,2]=>[1,6,5,3,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,3,5,2,1]=>[4,2,1,6,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,5,1,2,3]=>[3,1,2,6,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,5,1,3,2]=>[3,1,2,6,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,5,2,1,3]=>[4,2,3,1,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,5,2,3,1]=>[4,2,3,1,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,5,3,1,2]=>[3,1,2,1,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,6,5,3,2,1]=>[3,1,2,1,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,3,5,6]=>[2,1,2,4,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,1,3,6,5]=>[2,1,2,4,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,1,5,3,6]=>[5,4,5,2,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,1,5,6,3]=>[4,3,4,1,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,1,6,3,5]=>[4,3,4,2,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,1,6,5,3]=>[3,2,3,1,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,1,5,6]=>[4,3,6,2,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,1,6,5]=>[3,2,5,1,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,3,5,1,6]=>[6,5,1,1,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,3,5,6,1]=>[2,1,4,4,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,6,1,5]=>[6,5,1,2,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,6,5,1]=>[2,1,4,5,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,5,1,3,6]=>[6,5,3,2,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,1,6,3]=>[5,4,2,1,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,5,3,1,6]=>[4,3,1,2,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,5,3,6,1]=>[6,5,3,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,6,1,3]=>[2,1,6,3,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,5,6,3,1]=>[4,3,1,5,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,6,1,3,5]=>[6,5,4,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,6,1,5,3]=>[4,3,2,6,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,3,1,5]=>[4,3,2,1,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,6,3,5,1]=>[6,5,4,3,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,5,1,3]=>[3,2,1,2,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,6,5,3,1]=>[3,2,1,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[2,3,1,1,5,6]=>[1,2,6,1,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,1,1,6,5]=>[3,4,1,3,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,1,5,1,6]=>[5,6,3,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,3,1,5,6,1]=>[1,2,6,5,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,6,1,5]=>[4,5,2,2,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,6,5,1]=>[3,4,1,1,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,5,1,1,6]=>[1,2,3,4,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,5,1,6,1]=>[1,2,3,4,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,5,6,1,1]=>[1,2,3,2,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,6,1,1,5]=>[1,2,4,3,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,6,1,5,1]=>[1,2,4,3,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,6,5,1,1]=>[2,3,5,1,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,5,1,1,3,6]=>[1,4,4,1,3,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,5,1,1,6,3]=>[5,1,1,5,3,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,5,1,3,1,6]=>[6,2,2,1,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,5,1,3,6,1]=>[6,2,2,1,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,5,1,6,1,3]=>[6,2,2,4,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,5,1,6,3,1]=>[5,1,1,3,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,3,1,1,6]=>[3,6,1,1,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,5,3,1,6,1]=>[3,6,1,1,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,5,3,6,1,1]=>[1,4,6,4,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,6,1,1,3]=>[1,4,2,3,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,5,6,1,3,1]=>[1,4,2,3,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,5,6,3,1,1]=>[1,4,2,5,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,1,1,3,5]=>[1,5,3,1,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,6,1,1,5,3]=>[4,1,6,4,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,1,3,1,5]=>[6,3,1,1,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,6,1,3,5,1]=>[6,3,1,1,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,6,1,5,1,3]=>[6,3,1,3,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,6,1,5,3,1]=>[4,1,6,1,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,6,3,1,1,5]=>[4,1,1,2,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,6,3,1,5,1]=>[5,2,2,3,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,6,3,5,1,1]=>[1,5,5,3,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,5,1,1,3]=>[2,6,1,5,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,5,1,3,1]=>[6,3,5,2,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,5,3,1,1]=>[4,1,3,2,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,1,2,5,6]=>[1,6,1,2,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,1,2,6,5]=>[4,2,4,5,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,1,5,2,6]=>[4,2,4,1,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[3,1,1,5,6,2]=>[1,6,1,5,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,1,6,2,5]=>[5,3,5,3,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,1,6,5,2]=>[4,2,4,2,3,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,1,5,6]=>[4,2,5,3,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,2,1,6,5]=>[3,1,4,2,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,1,2,5,1,6]=>[5,3,6,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,2,5,6,1]=>[1,6,2,4,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,2,6,1,5]=>[4,2,5,1,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,2,6,5,1]=>[5,3,6,2,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,2,6]=>[5,3,2,1,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,5,1,6,2]=>[5,3,2,1,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,5,2,1,6]=>[4,2,1,1,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,1,5,2,6,1]=>[4,2,1,1,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,5,6,1,2]=>[1,6,5,2,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,5,6,2,1]=>[5,3,2,6,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,6,1,2,5]=>[3,1,1,5,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,6,1,5,2]=>[4,2,2,6,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,6,2,1,5]=>[5,3,3,1,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,6,2,5,1]=>[5,3,3,1,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,1,6,5,1,2]=>[3,1,1,2,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,6,5,2,1]=>[4,2,2,3,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,2,1,1,5,6]=>[2,1,1,2,6,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,2,1,1,6,5]=>[3,2,2,3,1,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[3,2,1,5,1,6]=>[5,4,4,2,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,1,5,6,1]=>[2,1,1,6,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,1,6,1,5]=>[4,3,3,2,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,1,6,5,1]=>[3,2,2,1,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,2,5,1,1,6]=>[5,4,1,1,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,2,5,1,6,1]=>[6,5,2,2,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,5,6,1,1]=>[2,1,5,3,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,6,1,1,5]=>[4,3,1,6,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,2,6,1,5,1]=>[6,5,3,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,6,5,1,1]=>[2,1,6,1,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,5,1,1,2,6]=>[1,3,4,1,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,5,1,1,6,2]=>[1,3,4,1,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,1,2,1,6]=>[3,5,6,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,1,2,6,1]=>[1,3,4,2,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,1,6,1,2]=>[1,3,4,6,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,1,6,2,1]=>[6,1,2,4,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,2,1,1,6]=>[4,6,1,3,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,2,1,6,1]=>[6,1,3,5,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,2,6,1,1]=>[1,3,5,5,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,6,1,1,2]=>[1,3,2,3,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,5,6,1,2,1]=>[2,4,3,4,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,5,6,2,1,1]=>[2,4,3,5,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,6,1,1,2,5]=>[1,4,3,1,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,6,1,1,5,2]=>[1,4,3,1,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,6,1,2,1,5]=>[2,5,4,3,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,1,2,5,1]=>[1,4,3,2,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,6,1,5,1,2]=>[1,4,3,5,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,1,5,2,1]=>[6,2,1,3,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,6,2,1,1,5]=>[5,1,1,4,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,6,2,1,5,1]=>[5,1,1,4,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,6,2,5,1,1]=>[5,1,1,1,1,5]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[3,6,5,1,1,2]=>[2,5,1,5,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,6,5,1,2,1]=>[2,5,1,5,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,6,5,2,1,1]=>[2,5,1,6,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,1,1,2,3,6]=>[1,4,1,2,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[5,1,1,2,6,3]=>[1,4,1,2,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,1,3,2,6]=>[2,5,2,4,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,1,3,6,2]=>[1,4,1,3,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,1,1,6,2,3]=>[1,4,1,6,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,1,6,3,2]=>[5,1,5,3,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,2,1,3,6]=>[2,5,3,1,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,2,1,6,3]=>[5,1,6,4,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,2,3,1,6]=>[3,6,4,4,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,2,3,6,1]=>[1,4,2,2,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,1,2,6,1,3]=>[1,4,2,5,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,6,3,1]=>[5,1,6,2,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,3,1,2,6]=>[1,4,3,6,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,1,6,2]=>[6,2,1,4,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,3,2,1,6]=>[3,6,5,2,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,3,2,6,1]=>[6,2,1,5,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,1,3,6,1,2]=>[1,4,3,4,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,1,3,6,2,1]=>[6,2,1,2,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,6,1,2,3]=>[1,4,6,3,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,6,1,3,2]=>[6,2,4,1,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,6,2,1,3]=>[6,2,4,2,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,6,2,3,1]=>[5,1,3,1,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,1,6,3,1,2]=>[5,1,3,2,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,6,3,2,1]=>[5,1,3,2,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,1,1,3,6]=>[2,6,1,2,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,1,6,3]=>[4,1,3,4,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,2,1,3,1,6]=>[4,1,3,6,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,1,3,6,1]=>[6,3,5,1,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,1,6,1,3]=>[6,3,5,4,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,1,6,3,1]=>[4,1,3,2,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,2,3,1,1,6]=>[4,1,5,2,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,2,3,1,6,1]=>[4,1,5,2,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,3,6,1,1]=>[1,5,2,4,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,6,1,1,3]=>[1,5,5,3,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,6,1,3,1]=>[6,3,3,1,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,2,6,3,1,1]=>[4,1,1,1,2,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,3,1,1,2,6]=>[4,2,2,4,5,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,3,1,1,6,2]=>[3,1,1,3,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,1,2,1,6]=>[3,1,1,4,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,3,1,2,6,1]=>[4,2,2,5,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,1,6,1,2]=>[3,1,1,1,5,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,3,1,6,2,1]=>[3,1,1,1,6,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,3,2,1,1,6]=>[3,1,2,2,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,3,2,1,6,1]=>[3,1,2,2,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,3,2,6,1,1]=>[4,2,3,1,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,6,1,1,2]=>[1,6,4,3,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,6,1,2,1]=>[3,1,6,5,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,6,2,1,1]=>[5,3,1,1,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,6,1,1,2,3]=>[1,2,3,1,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[5,6,1,1,3,2]=>[2,3,4,2,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,6,1,2,1,3]=>[2,3,4,3,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,6,1,2,3,1]=>[1,2,3,2,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,6,1,3,1,2]=>[1,2,3,3,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,6,1,3,2,1]=>[2,3,4,4,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,6,2,1,1,3]=>[2,3,5,1,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,6,2,1,3,1]=>[3,4,6,2,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,2,3,1,1]=>[1,2,4,2,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,6,3,1,1,2]=>[1,2,5,6,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,6,3,1,2,1]=>[4,5,1,2,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,6,3,2,1,1]=>[2,3,6,1,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,1,1,2,3,5]=>[1,3,1,2,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[6,1,1,2,5,3]=>[1,3,1,2,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,1,3,2,5]=>[2,4,2,4,1,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,1,1,3,5,2]=>[1,3,1,3,3,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[6,1,1,5,2,3]=>[1,3,1,5,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,1,1,5,3,2]=>[4,6,4,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,1,2,1,3,5]=>[2,4,3,1,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,1,2,1,5,3]=>[4,6,5,3,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,2,3,1,5]=>[1,3,2,2,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,1,2,3,5,1]=>[1,3,2,2,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,2,5,1,3]=>[1,3,2,4,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,2,5,3,1]=>[3,5,4,6,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,3,1,2,5]=>[1,3,3,6,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,1,3,1,5,2]=>[6,1,1,4,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,3,2,1,5]=>[2,4,4,1,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,1,3,2,5,1]=>[6,1,1,5,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,1,3,5,1,2]=>[1,3,3,3,4,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[6,1,3,5,2,1]=>[6,1,1,1,3,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,5,1,2,3]=>[1,3,5,4,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,5,1,3,2]=>[6,1,3,2,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,1,5,2,1,3]=>[6,1,3,3,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,1,5,2,3,1]=>[4,6,1,1,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,1,5,3,1,2]=>[4,6,1,2,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,1,5,3,2,1]=>[4,6,1,2,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,2,1,1,3,5]=>[2,5,1,2,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,2,1,1,5,3]=>[5,1,4,5,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,2,1,3,1,5]=>[6,2,5,1,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,1,3,5,1]=>[6,2,5,1,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,2,1,5,1,3]=>[6,2,5,3,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,2,1,5,3,1]=>[5,1,4,2,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,2,3,1,1,5]=>[1,4,2,6,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,3,1,5,1]=>[5,1,6,3,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,3,5,1,1]=>[1,4,2,3,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,2,5,1,1,3]=>[1,4,4,4,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[6,2,5,1,3,1]=>[6,2,2,2,1,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[6,2,5,3,1,1]=>[5,1,1,3,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[6,3,1,1,2,5]=>[1,5,6,1,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,1,1,5,2]=>[4,1,2,4,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[6,3,1,2,1,5]=>[4,1,2,5,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,3,1,2,5,1]=>[5,2,3,6,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,1,5,1,2]=>[5,2,3,2,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,1,5,2,1]=>[4,1,2,1,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[6,3,2,1,1,5]=>[4,1,3,3,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[6,3,2,1,5,1]=>[5,2,4,4,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,3,2,5,1,1]=>[5,2,4,1,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,3,5,1,1,2]=>[1,5,3,4,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,3,5,1,2,1]=>[2,6,4,5,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,5,2,1,1]=>[4,1,6,1,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,5,1,1,2,3]=>[2,1,5,2,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,5,1,1,3,2]=>[2,1,5,2,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,5,1,2,1,3]=>[2,1,5,3,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,5,1,2,3,1]=>[3,2,6,4,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,5,1,3,1,2]=>[3,2,6,5,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,1,3,2,1]=>[2,1,5,4,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,5,2,1,1,3]=>[2,1,6,1,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,5,2,1,3,1]=>[4,3,1,3,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,2,3,1,1]=>[4,3,1,5,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,3,1,1,2]=>[3,2,1,1,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,5,3,1,2,1]=>[3,2,1,1,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,5,3,2,1,1]=>[3,2,1,2,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,2,4,4,4]=>[1,1,2,3,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,4,2,4,4]=>[1,1,4,6,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,4,4,2,4]=>[1,1,4,1,6,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,4,4,4,2]=>[1,1,4,1,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,2,1,4,4,4]=>[2,3,1,5,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,4,1,4,4]=>[1,2,3,5,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,4,4,1,4]=>[1,2,3,1,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,4,4,4,1]=>[1,2,3,1,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,2,4,4]=>[1,4,5,2,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,4,2,4]=>[6,2,3,2,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,1,4,4,2]=>[5,1,2,1,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,2,1,4,4]=>[5,1,3,4,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,2,4,1,4]=>[6,2,4,1,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,2,4,4,1]=>[1,4,6,3,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,4,1,2,4]=>[1,4,1,5,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,4,1,4,2]=>[5,1,5,2,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,4,2,1,4]=>[5,1,5,3,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,4,2,4,1]=>[1,4,1,6,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,4,4,1,2]=>[1,4,1,1,5,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,4,4,2,1]=>[3,6,3,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,1,1,4,4,4]=>[2,1,2,5,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,1,4,1,4,4]=>[5,4,1,2,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,4,4,1,4]=>[5,4,1,5,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,4,4,4,1]=>[2,1,5,2,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,4,1,1,4,4]=>[1,3,5,1,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,4,1,4,1,4]=>[6,1,3,2,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,4,1,4,4,1]=>[1,3,5,4,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,4,1,1,4]=>[1,3,1,5,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,4,4,1,4,1]=>[1,3,1,5,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,4,4,1,1]=>[1,3,1,1,5,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,1,2,4,4]=>[1,5,1,2,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,4,2,4]=>[1,5,1,4,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,1,4,4,2]=>[1,5,1,4,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,2,1,4,4]=>[2,6,3,1,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,4,1,4]=>[1,5,2,3,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,2,4,4,1]=>[1,5,2,3,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,4,1,2,4]=>[1,5,4,5,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,4,1,4,2]=>[5,2,1,2,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,4,2,1,4]=>[5,2,1,3,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,4,2,4,1]=>[6,3,2,4,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,4,4,1,2]=>[1,5,4,1,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,4,4,2,1]=>[5,2,1,5,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,1,4,4]=>[3,1,2,3,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,2,1,4,1,4]=>[5,3,4,1,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,4,4,1]=>[5,3,4,1,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,4,1,1,4]=>[1,6,3,5,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,4,1,4,1]=>[6,4,1,3,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,4,4,1,1]=>[1,6,3,1,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,1,1,2,4]=>[1,1,5,1,2,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,4,1,1,4,2]=>[1,1,5,1,4,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,4,1,2,1,4]=>[2,2,6,3,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,4,1,2,4,1]=>[1,1,5,2,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,4,1,4,1,2]=>[1,1,5,4,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,4,1,4,2,1]=>[5,5,2,1,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2,1,1,4]=>[3,3,1,2,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,4,2,1,4,1]=>[5,5,3,4,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2,4,1,1]=>[1,1,6,3,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,4,1,1,2]=>[1,1,1,5,1,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,4,4,1,2,1]=>[2,2,2,6,3,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,4,4,2,1,1]=>[3,3,3,1,2,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,2,4,4,5]=>[1,1,2,3,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,2,4,5,4]=>[2,2,3,4,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,2,5,4,4]=>[2,2,3,5,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,4,2,4,5]=>[1,1,4,6,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,4,2,5,4]=>[5,5,1,3,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,4,4,2,5]=>[1,1,4,1,6,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,4,4,5,2]=>[1,1,4,1,2,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,4,5,2,4]=>[1,1,4,2,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,4,5,4,2]=>[3,3,6,4,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,5,2,4,4]=>[1,1,5,5,3,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,5,4,2,4]=>[4,4,1,3,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,5,4,4,2]=>[4,4,1,3,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,4,4,5]=>[2,3,1,5,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,1,4,5,4]=>[2,3,1,5,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,1,5,4,4]=>[2,3,1,6,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,1,4,5]=>[1,2,3,5,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,4,1,5,4]=>[4,5,6,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,4,4,1,5]=>[1,2,3,1,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,4,4,5,1]=>[1,2,3,1,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,4,5,1,4]=>[1,2,3,2,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,4,5,4,1]=>[2,3,4,3,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,5,1,4,4]=>[1,2,4,4,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,2,5,4,1,4]=>[5,6,1,4,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,5,4,4,1]=>[2,3,5,1,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,2,4,5]=>[1,4,5,2,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,1,2,5,4]=>[5,1,2,6,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,1,4,2,5]=>[5,1,2,1,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,4,5,2]=>[5,1,2,1,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,1,5,2,4]=>[6,2,3,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,4,1,5,4,2]=>[5,1,2,2,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,2,1,4,5]=>[5,1,3,4,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,1,5,4]=>[5,1,3,4,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,4,2,4,1,5]=>[6,2,4,1,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,4,5,1]=>[1,4,6,3,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,5,1,4]=>[5,1,3,1,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,4,2,5,4,1]=>[5,1,3,1,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,4,1,2,5]=>[1,4,1,5,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,4,1,5,2]=>[5,1,5,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,4,4,2,1,5]=>[5,1,5,3,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,4,2,5,1]=>[5,1,5,3,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,4,4,5,1,2]=>[1,4,1,2,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,4,4,5,2,1]=>[2,5,2,3,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,5,1,2,4]=>[1,4,2,4,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,4,5,1,4,2]=>[5,1,6,1,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,5,2,1,4]=>[5,1,6,2,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,5,2,4,1]=>[1,4,2,5,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,5,4,1,2]=>[2,5,3,1,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,5,4,2,1]=>[3,6,4,2,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,2,4,4]=>[1,5,4,2,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,4,2,4]=>[6,3,2,2,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,4,4,2]=>[5,2,1,1,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,2,1,4,4]=>[5,2,2,4,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,2,4,1,4]=>[6,3,3,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,5,2,4,4,1]=>[4,1,1,6,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,5,4,1,2,4]=>[4,1,3,1,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,4,1,4,2]=>[5,2,4,2,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,2,1,4]=>[5,2,4,3,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,4,2,4,1]=>[4,1,3,2,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,4,4,1,2]=>[4,1,3,4,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,4,4,2,1]=>[4,1,3,4,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,4,4,5]=>[2,1,2,5,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,4,5,4]=>[2,1,2,5,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,1,5,4,4]=>[2,1,2,6,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,4,1,4,5]=>[5,4,1,2,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,1,5,4]=>[5,4,1,2,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,4,4,1,5]=>[5,4,1,5,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,4,4,5,1]=>[2,1,5,2,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,4,5,1,4]=>[5,4,1,6,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,4,5,4,1]=>[2,1,5,3,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,5,1,4,4]=>[5,4,2,1,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,5,4,1,4]=>[5,4,2,4,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,5,4,4,1]=>[4,3,1,3,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,1,1,4,5]=>[1,3,5,1,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,4,1,1,5,4]=>[4,6,1,4,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,4,1,4,1,5]=>[6,1,3,2,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,4,1,4,5,1]=>[1,3,5,4,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,1,5,1,4]=>[6,1,3,3,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,4,1,5,4,1]=>[4,6,1,1,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,4,1,1,5]=>[1,3,1,5,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,4,4,1,5,1]=>[1,3,1,5,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,4,5,1,1]=>[1,3,1,2,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,4,5,1,1,4]=>[1,3,2,4,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,4,5,1,4,1]=>[1,3,2,4,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,5,4,1,1]=>[2,4,3,1,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,1,4,4]=>[1,4,4,1,4,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[2,5,1,4,1,4]=>[5,1,1,1,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[2,5,1,4,4,1]=>[5,1,1,1,5,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,4,1,1,4]=>[5,1,4,2,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,4,1,4,1]=>[5,1,4,2,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,4,4,1,1]=>[2,5,1,2,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,1,2,4,5]=>[1,5,1,2,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,1,2,5,4]=>[2,6,2,3,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,1,4,2,5]=>[5,2,5,1,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,1,4,5,2]=>[1,5,1,4,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,1,5,2,4]=>[4,1,4,1,1,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,1,1,5,4,2]=>[4,1,4,1,3,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,1,2,1,4,5]=>[2,6,3,1,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,2,1,5,4]=>[4,1,5,3,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,2,4,1,5]=>[4,1,5,6,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,2,4,5,1]=>[1,5,2,3,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,2,5,1,4]=>[5,2,6,1,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,1,2,5,4,1]=>[5,2,6,1,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,4,1,2,5]=>[5,2,1,2,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,4,1,5,2]=>[5,2,1,2,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,1,4,2,1,5]=>[5,2,1,3,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,4,2,5,1]=>[5,2,1,3,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,4,5,1,2]=>[1,5,4,2,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,1,4,5,2,1]=>[5,2,1,6,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,5,1,2,4]=>[1,5,5,4,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,5,1,4,2]=>[5,2,2,1,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,5,2,1,4]=>[5,2,2,2,4,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,1,5,2,4,1]=>[4,1,1,1,6,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,1,5,4,1,2]=>[4,1,1,3,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,5,4,2,1]=>[4,1,1,3,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,2,1,1,4,5]=>[3,1,2,3,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,1,1,5,4]=>[4,2,3,4,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,2,1,4,1,5]=>[5,3,4,1,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,4,5,1]=>[5,3,4,1,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,1,5,1,4]=>[5,3,4,2,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,5,4,1]=>[4,2,3,1,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,2,4,1,1,5]=>[4,2,6,1,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,4,1,5,1]=>[6,4,1,3,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,4,5,1,1]=>[1,6,3,2,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,5,1,1,4]=>[5,3,1,1,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[4,2,5,1,4,1]=>[5,3,1,1,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,2,5,4,1,1]=>[5,3,1,4,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,1,1,2,5]=>[1,1,5,1,2,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,4,1,1,5,2]=>[4,4,1,4,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,4,1,2,1,5]=>[4,4,1,5,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,4,1,2,5,1]=>[1,1,5,2,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,4,1,5,1,2]=>[1,1,5,5,4,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,4,1,5,2,1]=>[4,4,1,1,1,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[4,4,2,1,1,5]=>[4,4,2,3,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,4,2,1,5,1]=>[5,5,3,4,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2,5,1,1]=>[1,1,6,4,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,4,5,1,1,2]=>[1,1,2,4,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,4,5,1,2,1]=>[2,2,3,5,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,4,5,2,1,1]=>[2,2,3,6,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,5,1,1,2,4]=>[1,2,4,1,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,5,1,1,4,2]=>[1,2,4,1,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,5,1,2,1,4]=>[2,3,5,3,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,5,1,2,4,1]=>[1,2,4,2,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,1,4,1,2]=>[1,2,4,4,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,5,1,4,2,1]=>[5,6,1,1,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,5,2,1,1,4]=>[2,3,6,1,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,5,2,1,4,1]=>[5,6,2,4,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,5,2,4,1,1]=>[1,2,5,3,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,5,4,1,1,2]=>[2,3,1,6,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,5,4,1,2,1]=>[2,3,1,6,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,5,4,2,1,1]=>[3,4,2,1,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,1,2,4,4]=>[1,4,1,2,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,1,4,2,4]=>[1,4,1,4,6,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,1,4,4,2]=>[1,4,1,4,1,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,1,2,1,4,4]=>[2,5,3,1,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,1,2,4,1,4]=>[1,4,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,2,4,4,1]=>[1,4,2,3,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,4,1,2,4]=>[1,4,4,5,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,4,1,4,2]=>[5,1,1,2,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[5,1,4,2,1,4]=>[5,1,1,3,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,1,4,2,4,1]=>[6,2,2,4,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,4,4,1,2]=>[1,4,4,1,5,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,4,4,2,1]=>[5,1,1,5,3,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,1,1,4,4]=>[2,6,1,2,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,2,1,4,1,4]=>[5,2,4,1,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,1,4,4,1]=>[5,2,4,1,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,4,1,1,4]=>[1,5,3,5,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,4,1,4,1]=>[6,3,1,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,2,4,4,1,1]=>[1,5,3,1,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,4,1,1,2,4]=>[2,1,6,2,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,4,1,1,4,2]=>[5,4,2,5,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,1,2,1,4]=>[2,1,6,3,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,4,1,2,4,1]=>[4,3,1,5,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,1,4,1,2]=>[5,4,2,1,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,1,4,2,1]=>[5,4,2,1,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,2,1,1,4]=>[3,2,1,2,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,4,2,1,4,1]=>[5,4,3,4,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,2,4,1,1]=>[4,3,2,6,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,4,1,1,2]=>[2,1,2,6,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,4,4,1,2,1]=>[2,1,2,6,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,4,2,1,1]=>[3,2,3,1,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,4,4,6]=>[1,1,2,3,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,2,4,6,4]=>[1,1,2,3,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,2,6,4,4]=>[1,1,2,5,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,4,2,4,6]=>[1,1,4,6,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,4,2,6,4]=>[5,5,1,3,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,4,4,2,6]=>[1,1,4,1,6,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,4,4,6,2]=>[1,1,4,1,3,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,4,6,2,4]=>[1,1,4,3,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,4,6,4,2]=>[3,3,6,5,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,6,2,4,4]=>[1,1,6,4,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,6,4,2,4]=>[3,3,1,1,1,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,6,4,4,2]=>[3,3,1,1,3,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,2,1,4,4,6]=>[2,3,1,5,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,1,4,6,4]=>[3,4,2,6,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,1,6,4,4]=>[3,4,2,1,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,4,1,4,6]=>[1,2,3,5,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,4,1,6,4]=>[4,5,6,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,4,4,1,6]=>[1,2,3,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,4,4,6,1]=>[1,2,3,1,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,4,6,1,4]=>[1,2,3,3,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,4,6,4,1]=>[1,2,3,3,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,1,4,4]=>[1,2,5,3,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,6,4,1,4]=>[5,6,2,3,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,6,4,4,1]=>[4,5,1,2,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,1,2,4,6]=>[1,4,5,2,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,2,6,4]=>[5,1,2,6,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,4,2,6]=>[5,1,2,1,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,1,4,6,2]=>[6,2,3,2,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,1,6,2,4]=>[6,2,3,4,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,1,6,4,2]=>[5,1,2,3,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,4,2,1,4,6]=>[6,2,4,5,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,2,1,6,4]=>[3,6,1,2,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,2,4,1,6]=>[6,2,4,1,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,4,6,1]=>[6,2,4,1,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,2,6,1,4]=>[6,2,4,3,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,2,6,4,1]=>[5,1,3,2,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,4,4,1,2,6]=>[1,4,1,5,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,4,1,6,2]=>[5,1,5,2,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,4,2,1,6]=>[3,6,3,1,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,4,2,6,1]=>[1,4,1,6,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,4,6,1,2]=>[1,4,1,3,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,4,4,6,2,1]=>[2,5,2,4,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,6,1,2,4]=>[1,4,3,3,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,4,6,1,4,2]=>[6,2,1,1,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,4,6,2,1,4]=>[6,2,1,2,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,6,2,4,1]=>[6,2,1,2,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,6,4,1,2]=>[1,4,3,6,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,6,4,2,1]=>[3,6,5,1,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,1,2,4,4]=>[1,6,3,2,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,6,1,4,2,4]=>[6,4,1,2,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,6,1,4,4,2]=>[3,1,5,6,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,2,1,4,4]=>[5,3,1,4,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,2,4,1,4]=>[6,4,2,1,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,2,4,4,1]=>[1,6,4,3,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,4,1,2,4]=>[4,2,2,1,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,4,1,4,2]=>[5,3,3,2,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,6,4,2,1,4]=>[3,1,1,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,6,4,2,4,1]=>[4,2,2,2,6,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,6,4,4,1,2]=>[4,2,2,4,1,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,4,4,2,1]=>[3,1,1,3,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,1,1,4,4,6]=>[2,1,2,5,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,1,4,6,4]=>[3,2,3,6,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,1,6,4,4]=>[3,2,3,1,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,1,4,1,4,6]=>[6,5,2,3,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,1,6,4]=>[5,4,1,2,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,4,1,6]=>[5,4,1,5,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,4,6,1]=>[2,1,5,2,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,4,6,1,4]=>[6,5,2,1,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,1,4,6,4,1]=>[6,5,2,1,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,1,4,4]=>[3,2,1,5,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,6,4,1,4]=>[5,4,3,3,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,4,4,1]=>[4,3,2,2,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,4,1,1,4,6]=>[1,3,5,1,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,1,1,6,4]=>[4,6,1,4,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,4,1,4,1,6]=>[6,1,3,2,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,1,4,6,1]=>[6,1,3,2,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,4,1,6,1,4]=>[6,1,3,4,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,1,6,4,1]=>[4,6,1,2,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,4,1,1,6]=>[1,3,1,5,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,4,4,1,6,1]=>[1,3,1,5,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,4,6,1,1]=>[1,3,1,3,3,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[2,4,6,1,1,4]=>[1,3,3,3,1,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,4,6,1,4,1]=>[6,1,1,1,2,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,4,6,4,1,1]=>[1,3,3,6,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,6,1,1,4,4]=>[1,5,3,1,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,6,1,4,1,4]=>[6,3,1,2,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,6,1,4,4,1]=>[1,5,3,4,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,4,1,1,4]=>[5,2,3,2,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,4,1,4,1]=>[5,2,3,2,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,6,4,4,1,1]=>[4,1,2,4,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,1,1,2,4,6]=>[1,5,1,2,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,1,1,2,6,4]=>[4,1,4,5,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,1,4,2,6]=>[5,2,5,1,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,1,4,6,2]=>[1,5,1,4,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,1,6,2,4]=>[1,5,1,6,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,1,6,4,2]=>[4,1,4,2,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[4,1,2,1,4,6]=>[2,6,3,1,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,1,6,4]=>[4,1,5,3,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,2,4,1,6]=>[4,1,5,6,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,2,4,6,1]=>[1,5,2,3,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,2,6,1,4]=>[1,5,2,5,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,2,6,4,1]=>[4,1,5,1,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,4,1,2,6]=>[5,2,1,2,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,4,1,6,2]=>[5,2,1,2,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,4,2,1,6]=>[5,2,1,3,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,4,2,6,1]=>[6,3,2,4,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,4,6,1,2]=>[1,5,4,3,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,4,6,2,1]=>[6,3,2,1,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,6,1,2,4]=>[1,5,6,3,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,6,1,4,2]=>[6,3,4,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,6,2,1,4]=>[5,2,3,1,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,6,2,4,1]=>[6,3,4,2,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,6,4,1,2]=>[4,1,2,2,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,6,4,2,1]=>[4,1,2,2,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,2,1,1,4,6]=>[3,1,2,3,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,1,1,6,4]=>[3,1,2,3,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,2,1,4,1,6]=>[5,3,4,1,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,4,6,1]=>[6,4,5,2,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,2,1,6,1,4]=>[3,1,2,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,1,6,4,1]=>[4,2,3,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,2,4,1,1,6]=>[4,2,6,1,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,4,1,6,1]=>[6,4,1,3,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,4,6,1,1]=>[1,6,3,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[4,2,6,1,1,4]=>[1,6,5,3,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,6,1,4,1]=>[6,4,3,1,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,6,4,1,1]=>[4,2,1,2,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,4,1,1,2,6]=>[1,1,5,1,2,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[4,4,1,1,6,2]=>[1,1,5,1,6,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,4,1,2,1,6]=>[4,4,1,5,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,4,1,2,6,1]=>[1,1,5,2,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,4,1,6,1,2]=>[1,1,5,6,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,4,1,6,2,1]=>[5,5,2,3,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,2,1,1,6]=>[3,3,1,2,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,4,2,1,6,1]=>[3,3,1,2,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,2,6,1,1]=>[1,1,6,5,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,6,1,1,2]=>[1,1,3,3,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,4,6,1,2,1]=>[2,2,4,4,3,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,4,6,2,1,1]=>[2,2,4,5,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,6,1,1,2,4]=>[1,3,3,1,2,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,6,1,1,4,2]=>[1,3,3,1,4,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,6,1,2,1,4]=>[2,4,4,3,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,6,1,2,4,1]=>[1,3,3,2,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,6,1,4,1,2]=>[1,3,3,4,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,6,1,4,2,1]=>[6,1,1,2,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,6,2,1,1,4]=>[2,4,5,1,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,6,2,1,4,1]=>[6,1,2,5,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,6,2,4,1,1]=>[1,3,4,3,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,6,4,1,1,2]=>[1,3,6,5,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,6,4,1,2,1]=>[4,6,2,1,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,4,2,1,1]=>[3,5,1,1,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,1,2,4,4]=>[1,3,1,2,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,1,4,2,4]=>[1,3,1,4,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,1,4,4,2]=>[1,3,1,4,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[6,1,2,1,4,4]=>[2,4,3,1,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,2,4,1,4]=>[1,3,2,3,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,2,4,4,1]=>[1,3,2,3,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,4,1,2,4]=>[1,3,4,5,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,4,1,4,2]=>[6,1,2,3,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,4,2,1,4]=>[6,1,2,4,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,1,4,2,4,1]=>[6,1,2,4,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,4,4,1,2]=>[1,3,4,1,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,4,4,2,1]=>[3,5,6,3,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,1,1,4,4]=>[2,5,1,2,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,2,1,4,1,4]=>[5,1,4,1,2,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,2,1,4,4,1]=>[5,1,4,1,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,4,1,1,4]=>[1,4,3,5,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,2,4,1,4,1]=>[6,2,1,3,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,2,4,4,1,1]=>[1,4,3,1,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,4,1,1,2,4]=>[1,6,5,1,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,4,1,1,4,2]=>[5,3,2,5,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,4,1,2,1,4]=>[5,3,2,6,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,1,2,4,1]=>[4,2,1,5,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,4,1,4,1,2]=>[5,3,2,1,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,4,1,4,2,1]=>[5,3,2,1,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,4,2,1,1,4]=>[3,1,1,2,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,4,2,1,4,1]=>[5,3,3,4,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,4,2,4,1,1]=>[4,2,2,6,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,4,4,1,1,2]=>[1,6,1,5,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,4,4,1,2,1]=>[4,2,4,1,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,4,2,1,1]=>[3,1,3,1,2,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,2,4,5,5]=>[1,1,2,3,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,2,5,4,5]=>[2,2,3,5,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,2,5,5,4]=>[2,2,3,5,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,4,2,5,5]=>[1,1,4,6,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,4,5,2,5]=>[1,1,4,2,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,4,5,5,2]=>[1,1,4,2,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,5,2,4,5]=>[1,1,5,5,3,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,5,2,5,4]=>[5,5,2,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,5,4,2,5]=>[5,5,2,4,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,5,4,5,2]=>[4,4,1,3,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,5,5,2,4]=>[1,1,5,1,5,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,5,5,4,2]=>[4,4,1,4,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,1,4,5,5]=>[2,3,1,5,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,1,5,4,5]=>[2,3,1,6,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,1,5,5,4]=>[2,3,1,6,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,1,5,5]=>[1,2,3,5,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,4,5,1,5]=>[1,2,3,2,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,4,5,5,1]=>[1,2,3,2,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,5,1,4,5]=>[1,2,4,4,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,2,5,1,5,4]=>[5,6,1,1,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,5,4,1,5]=>[5,6,1,4,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,5,4,5,1]=>[2,3,5,1,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,2,5,5,1,4]=>[1,2,4,1,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,2,5,5,4,1]=>[2,3,5,2,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,2,5,5]=>[1,4,5,2,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,1,5,2,5]=>[5,1,2,2,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,4,1,5,5,2]=>[5,1,2,2,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,4,2,1,5,5]=>[5,1,3,4,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,2,5,1,5]=>[5,1,3,1,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,2,5,5,1]=>[5,1,3,1,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,4,5,1,2,5]=>[1,4,2,4,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,4,5,1,5,2]=>[5,1,6,1,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,5,2,1,5]=>[5,1,6,2,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,5,2,5,1]=>[5,1,6,2,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,5,5,1,2]=>[1,4,2,1,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,4,5,5,2,1]=>[2,5,3,2,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,2,4,5]=>[1,5,4,2,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,1,2,5,4]=>[5,2,1,6,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,1,4,2,5]=>[5,2,1,1,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,5,1,4,5,2]=>[5,2,1,1,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,5,1,5,2,4]=>[6,3,2,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,5,1,5,4,2]=>[5,2,1,2,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,2,1,4,5]=>[5,2,2,4,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,2,1,5,4]=>[4,1,1,3,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,5,2,4,1,5]=>[4,1,1,6,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,5,2,4,5,1]=>[1,5,5,3,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,2,5,1,4]=>[5,2,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,5,2,5,4,1]=>[5,2,2,1,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,4,1,2,5]=>[5,2,4,2,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,4,1,5,2]=>[4,1,3,1,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,4,2,1,5]=>[4,1,3,2,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,5,4,2,5,1]=>[5,2,4,3,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,4,5,1,2]=>[2,6,1,3,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,4,5,2,1]=>[4,1,3,5,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,5,1,2,4]=>[1,5,1,4,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,5,1,4,2]=>[5,2,5,1,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,5,2,1,4]=>[5,2,5,2,4,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,5,2,4,1]=>[4,1,4,1,6,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,5,5,4,1,2]=>[4,1,4,3,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,5,4,2,1]=>[4,1,4,3,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,1,1,4,5,5]=>[2,1,2,5,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,1,5,4,5]=>[2,1,2,6,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,1,5,5,4]=>[2,1,2,6,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,1,4,1,5,5]=>[5,4,1,2,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,4,5,1,5]=>[5,4,1,6,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,5,5,1]=>[2,1,5,3,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,5,1,4,5]=>[5,4,2,1,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,5,1,5,4]=>[5,4,2,1,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,5,4,1,5]=>[4,3,1,3,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[2,1,5,4,5,1]=>[2,1,6,1,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,5,5,1,4]=>[5,4,2,5,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,5,5,4,1]=>[4,3,1,4,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,1,1,5,5]=>[1,3,5,1,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,4,1,5,1,5]=>[6,1,3,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,4,1,5,5,1]=>[1,3,5,5,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,5,1,1,5]=>[1,3,2,4,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,4,5,1,5,1]=>[1,3,2,4,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,5,5,1,1]=>[1,3,2,1,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,5,1,1,4,5]=>[1,4,4,1,4,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,5,1,1,5,4]=>[5,1,1,5,2,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,1,4,1,5]=>[5,1,1,1,2,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,5,1,4,5,1]=>[5,1,1,1,6,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[2,5,1,5,1,4]=>[5,1,1,2,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[2,5,1,5,4,1]=>[5,1,1,2,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,4,1,1,5]=>[5,1,4,2,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,4,1,5,1]=>[5,1,4,2,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,4,5,1,1]=>[2,5,1,3,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,5,5,1,1,4]=>[1,4,1,4,1,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[2,5,5,1,4,1]=>[5,1,5,1,1,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,5,4,1,1]=>[2,5,2,1,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,1,2,5,5]=>[1,5,1,2,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,1,5,2,5]=>[5,2,5,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,1,1,5,5,2]=>[4,1,4,1,4,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,1,2,1,5,5]=>[4,1,5,3,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,2,5,1,5]=>[5,2,6,1,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,2,5,5,1]=>[1,5,2,4,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,5,1,2,5]=>[5,2,2,1,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,5,1,5,2]=>[5,2,2,1,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,1,5,2,1,5]=>[4,1,1,1,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,1,5,2,5,1]=>[5,2,2,2,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,5,5,1,2]=>[1,5,5,1,4,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,5,5,2,1]=>[4,1,1,4,1,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[4,2,1,1,5,5]=>[4,2,3,4,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,1,5,1,5]=>[5,3,4,2,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,5,5,1]=>[5,3,4,2,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,5,1,1,5]=>[5,3,1,1,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,5,1,5,1]=>[5,3,1,1,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,2,5,5,1,1]=>[1,6,4,1,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,5,1,1,2,5]=>[1,2,4,1,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,5,1,1,5,2]=>[1,2,4,1,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,5,1,2,1,5]=>[2,3,5,3,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,5,1,2,5,1]=>[1,2,4,2,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,5,1,5,1,2]=>[1,2,4,5,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,5,1,5,2,1]=>[5,6,1,2,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,5,2,1,1,5]=>[4,5,1,3,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,5,2,1,5,1]=>[5,6,2,4,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,5,2,5,1,1]=>[1,2,5,4,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,5,5,1,1,2]=>[1,2,1,4,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,5,5,1,2,1]=>[2,3,2,5,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,5,5,2,1,1]=>[2,3,2,6,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,1,2,4,5]=>[1,4,1,2,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,1,1,2,5,4]=>[2,5,2,3,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,1,1,4,2,5]=>[5,1,5,1,3,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,1,1,4,5,2]=>[1,4,1,4,2,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,1,5,2,4]=>[1,4,1,5,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,1,1,5,4,2]=>[5,1,5,2,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,2,1,4,5]=>[2,5,3,1,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,1,2,1,5,4]=>[2,5,3,1,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,1,2,4,1,5]=>[1,4,2,3,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,2,4,5,1]=>[1,4,2,3,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,1,2,5,1,4]=>[5,1,6,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[5,1,2,5,4,1]=>[5,1,6,1,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,4,1,2,5]=>[5,1,1,2,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,1,4,1,5,2]=>[5,1,1,2,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[5,1,4,2,1,5]=>[5,1,1,3,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,4,2,5,1]=>[5,1,1,3,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[5,1,4,5,1,2]=>[1,4,4,2,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[5,1,4,5,2,1]=>[5,1,1,6,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,5,1,2,4]=>[1,4,5,4,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,5,1,4,2]=>[5,1,2,1,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[5,1,5,2,1,4]=>[5,1,2,2,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,1,5,2,4,1]=>[6,2,3,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,1,5,4,1,2]=>[5,1,2,4,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,5,4,2,1]=>[5,1,2,4,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,1,1,4,5]=>[2,6,1,2,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,1,1,5,4]=>[4,1,3,4,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,2,1,4,1,5]=>[5,2,4,1,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,2,1,4,5,1]=>[5,2,4,1,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,1,5,1,4]=>[5,2,4,2,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,1,5,4,1]=>[4,1,3,1,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[5,2,4,1,1,5]=>[4,1,6,1,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,2,4,1,5,1]=>[6,3,1,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,2,4,5,1,1]=>[1,5,3,2,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,5,1,1,4]=>[5,2,1,1,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,2,5,1,4,1]=>[5,2,1,1,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[5,2,5,4,1,1]=>[5,2,1,4,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,4,1,1,2,5]=>[2,1,6,2,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,4,1,1,5,2]=>[4,3,1,4,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,4,1,2,1,5]=>[4,3,1,5,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,4,1,2,5,1]=>[5,4,2,6,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,4,1,5,1,2]=>[5,4,2,2,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,1,5,2,1]=>[4,3,1,1,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[5,4,2,1,1,5]=>[4,3,2,3,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,4,2,1,5,1]=>[5,4,3,4,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,2,5,1,1]=>[5,4,3,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,4,5,1,1,2]=>[2,1,3,5,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,4,5,1,2,1]=>[2,1,3,5,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,4,5,2,1,1]=>[2,1,3,6,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,5,1,1,2,4]=>[1,1,4,1,2,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,5,1,1,4,2]=>[1,1,4,1,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,5,1,2,1,4]=>[2,2,5,3,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,5,1,2,4,1]=>[1,1,4,2,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,5,1,4,1,2]=>[1,1,4,4,5,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,5,1,4,2,1]=>[5,5,1,1,3,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,5,2,1,1,4]=>[2,2,6,1,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,5,2,1,4,1]=>[5,5,2,4,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,5,2,4,1,1]=>[1,1,5,3,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,5,4,1,1,2]=>[2,2,1,6,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,5,4,1,2,1]=>[2,2,1,6,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,5,4,2,1,1]=>[3,3,2,1,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,2,4,5,6]=>[1,1,2,3,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,2,4,6,5]=>[2,2,3,4,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,2,5,4,6]=>[2,2,3,5,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,2,5,6,4]=>[1,1,2,4,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,2,6,4,5]=>[1,1,2,5,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,2,6,5,4]=>[2,2,3,6,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,4,2,5,6]=>[1,1,4,6,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,4,2,6,5]=>[5,5,1,3,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,4,5,2,6]=>[1,1,4,2,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,4,5,6,2]=>[1,1,4,2,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,4,6,2,5]=>[1,1,4,3,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,4,6,5,2]=>[2,2,5,4,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,5,2,4,6]=>[1,1,5,5,3,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,5,2,6,4]=>[4,4,1,1,1,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,5,4,2,6]=>[4,4,1,3,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,5,4,6,2]=>[2,2,6,1,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,5,6,2,4]=>[1,1,5,2,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,5,6,4,2]=>[4,4,1,5,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,6,2,4,5]=>[1,1,6,4,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,6,2,5,4]=>[5,5,3,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,6,4,2,5]=>[3,3,1,1,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,6,4,5,2]=>[4,4,2,2,5,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,6,5,2,4]=>[4,4,2,3,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,6,5,4,2]=>[3,3,1,2,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,2,1,4,5,6]=>[2,3,1,5,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,1,4,6,5]=>[2,3,1,5,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,1,5,4,6]=>[2,3,1,6,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,1,5,6,4]=>[4,5,3,1,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,1,6,4,5]=>[3,4,2,1,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,1,6,5,4]=>[3,4,2,1,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,4,1,5,6]=>[1,2,3,5,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,1,6,5]=>[4,5,6,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,5,1,6]=>[1,2,3,2,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,4,5,6,1]=>[1,2,3,2,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,4,6,1,5]=>[1,2,3,3,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,4,6,5,1]=>[2,3,4,4,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,5,1,4,6]=>[1,2,4,4,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,2,5,1,6,4]=>[5,6,1,1,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,5,4,1,6]=>[5,6,1,4,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,4,6,1]=>[2,3,5,1,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,5,6,1,4]=>[1,2,4,2,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,5,6,4,1]=>[1,2,4,2,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,1,4,5]=>[1,2,5,3,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,6,1,5,4]=>[4,5,1,6,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,6,4,1,5]=>[4,5,1,2,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,6,4,5,1]=>[1,2,5,6,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,5,1,4]=>[5,6,2,4,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,6,5,4,1]=>[4,5,1,3,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,1,2,5,6]=>[1,4,5,2,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,1,2,6,5]=>[5,1,2,6,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,1,5,2,6]=>[5,1,2,2,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,4,1,5,6,2]=>[5,1,2,2,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,1,6,2,5]=>[5,1,2,3,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,6,5,2]=>[5,1,2,3,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,2,1,5,6]=>[5,1,3,4,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,1,6,5]=>[3,6,1,2,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,2,5,1,6]=>[5,1,3,1,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,4,2,5,6,1]=>[1,4,6,4,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,6,1,5]=>[6,2,4,3,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,6,5,1]=>[5,1,3,2,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,5,1,2,6]=>[1,4,2,4,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,5,1,6,2]=>[5,1,6,1,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,5,2,1,6]=>[5,1,6,2,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,2,6,1]=>[1,4,2,5,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,5,6,1,2]=>[1,4,2,2,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,4,5,6,2,1]=>[2,5,3,3,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,6,1,2,5]=>[1,4,3,3,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,4,6,1,5,2]=>[6,2,1,1,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,6,2,1,5]=>[6,2,1,2,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,6,2,5,1]=>[6,2,1,2,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,4,6,5,1,2]=>[2,5,4,1,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,6,5,2,1]=>[2,5,4,1,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,1,2,4,6]=>[1,5,4,2,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,1,2,6,4]=>[5,2,1,6,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,4,2,6]=>[5,2,1,1,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,5,1,4,6,2]=>[6,3,2,2,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,5,1,6,2,4]=>[6,3,2,4,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,6,4,2]=>[5,2,1,3,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,5,2,1,4,6]=>[6,3,3,5,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,2,1,6,4]=>[4,1,1,3,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,5,2,4,1,6]=>[4,1,1,6,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,5,2,4,6,1]=>[6,3,3,1,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,5,2,6,1,4]=>[6,3,3,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,5,2,6,4,1]=>[4,1,1,1,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,5,4,1,2,6]=>[4,1,3,1,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,4,1,6,2]=>[5,2,4,2,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,2,1,6]=>[4,1,3,2,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,5,4,2,6,1]=>[4,1,3,2,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,4,6,1,2]=>[2,6,1,4,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,4,6,2,1]=>[2,6,1,4,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,6,1,2,4]=>[1,5,2,3,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,6,1,4,2]=>[1,5,2,3,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,6,2,1,4]=>[5,2,6,1,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,6,2,4,1]=>[1,5,2,4,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,6,4,1,2]=>[4,1,5,2,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,6,4,2,1]=>[4,1,5,2,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,1,2,4,5]=>[1,6,3,2,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,6,1,2,5,4]=>[3,1,5,4,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,4,2,5]=>[6,4,1,2,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,1,4,5,2]=>[1,6,3,4,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,5,2,4]=>[6,4,1,3,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,6,1,5,4,2]=>[4,2,6,1,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,2,1,4,5]=>[5,3,1,4,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,1,5,4]=>[5,3,1,4,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,2,4,1,5]=>[6,4,2,1,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,2,4,5,1]=>[1,6,4,3,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,2,5,1,4]=>[5,3,1,1,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,6,2,5,4,1]=>[5,3,1,1,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,6,4,1,2,5]=>[5,3,3,2,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,4,1,5,2]=>[4,2,2,1,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,6,4,2,1,5]=>[4,2,2,2,3,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,6,4,2,5,1]=>[5,3,3,3,1,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,6,4,5,1,2]=>[3,1,1,4,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,6,4,5,2,1]=>[4,2,2,5,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,5,1,2,4]=>[3,1,2,6,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,5,1,4,2]=>[5,3,4,1,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,6,5,2,1,4]=>[5,3,4,2,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,5,2,4,1]=>[4,2,3,1,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,5,4,1,2]=>[4,2,3,3,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,5,4,2,1]=>[3,1,2,2,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,1,1,4,5,6]=>[2,1,2,5,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,1,1,4,6,5]=>[2,1,2,5,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,1,5,4,6]=>[2,1,2,6,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,1,1,5,6,4]=>[4,3,4,1,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,1,6,4,5]=>[3,2,3,1,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,1,6,5,4]=>[3,2,3,1,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,4,1,5,6]=>[5,4,1,2,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,4,1,6,5]=>[5,4,1,2,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,4,5,1,6]=>[5,4,1,6,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,4,5,6,1]=>[2,1,5,3,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,6,1,5]=>[6,5,2,1,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,6,5,1]=>[2,1,5,4,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,1,5,1,4,6]=>[6,5,3,2,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,1,6,4]=>[5,4,2,1,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,5,4,1,6]=>[4,3,1,3,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,5,4,6,1]=>[2,1,6,1,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,1,5,6,1,4]=>[2,1,6,3,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,6,4,1]=>[4,3,1,5,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,6,1,4,5]=>[3,2,1,5,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,1,5,4]=>[4,3,2,6,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,6,4,1,5]=>[4,3,2,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,6,4,5,1]=>[3,2,1,1,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,6,5,1,4]=>[5,4,3,4,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,6,5,4,1]=>[4,3,2,3,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,4,1,1,5,6]=>[1,3,5,1,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,1,1,6,5]=>[4,6,1,4,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,1,5,1,6]=>[6,1,3,3,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,1,5,6,1]=>[1,3,5,5,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,1,6,1,5]=>[6,1,3,4,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,1,6,5,1]=>[6,1,3,4,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,5,1,1,6]=>[1,3,2,4,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,5,1,6,1]=>[1,3,2,4,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,5,6,1,1]=>[1,3,2,2,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,4,6,1,1,5]=>[1,3,3,3,1,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,4,6,1,5,1]=>[6,1,1,1,3,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,4,6,5,1,1]=>[2,4,4,1,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,5,1,1,4,6]=>[1,4,4,1,4,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,5,1,1,6,4]=>[5,1,1,5,3,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,5,1,4,1,6]=>[5,1,1,1,2,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,5,1,4,6,1]=>[6,2,2,2,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,5,1,6,1,4]=>[6,2,2,4,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,1,6,4,1]=>[5,1,1,3,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,4,1,1,6]=>[5,1,4,2,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,4,1,6,1]=>[6,2,5,3,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,6,1,1]=>[2,5,1,4,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,5,6,1,1,4]=>[1,4,2,3,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,6,1,4,1]=>[1,4,2,3,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,6,4,1,1]=>[1,4,2,6,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,1,1,4,5]=>[1,5,3,1,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,1,1,5,4]=>[4,1,6,4,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,6,1,4,1,5]=>[6,3,1,2,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,6,1,4,5,1]=>[1,5,3,4,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,6,1,5,1,4]=>[6,3,1,3,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,6,1,5,4,1]=>[4,1,6,1,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,4,1,1,5]=>[4,1,2,1,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,6,4,1,5,1]=>[5,2,3,2,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,6,4,5,1,1]=>[1,5,6,2,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,5,1,1,4]=>[5,2,4,1,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,6,5,1,4,1]=>[5,2,4,1,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,6,5,4,1,1]=>[4,1,3,3,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,1,1,2,5,6]=>[1,5,1,2,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,1,2,6,5]=>[4,1,4,5,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,1,5,2,6]=>[4,1,4,1,1,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,1,5,6,2]=>[1,5,1,5,2,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,1,6,2,5]=>[5,2,5,3,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,1,6,5,2]=>[4,1,4,2,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,1,2,1,5,6]=>[4,1,5,3,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,2,1,6,5]=>[4,1,5,3,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,2,5,1,6]=>[5,2,6,1,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,2,5,6,1]=>[1,5,2,4,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,2,6,1,5]=>[4,1,5,1,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,2,6,5,1]=>[5,2,6,2,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,5,1,2,6]=>[5,2,2,1,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,5,1,6,2]=>[5,2,2,1,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,5,2,1,6]=>[4,1,1,1,3,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,1,5,2,6,1]=>[4,1,1,1,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,1,5,6,1,2]=>[1,5,5,2,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,5,6,2,1]=>[5,2,2,6,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,6,1,2,5]=>[1,5,6,3,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,1,5,2]=>[4,1,2,6,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,1,6,2,1,5]=>[5,2,3,1,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,6,2,5,1]=>[5,2,3,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,6,5,1,2]=>[5,2,3,4,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,5,2,1]=>[4,1,2,3,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,2,1,1,5,6]=>[4,2,3,4,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,1,1,6,5]=>[3,1,2,3,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,2,1,5,1,6]=>[5,3,4,2,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,5,6,1]=>[4,2,3,1,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,6,1,5]=>[4,2,3,2,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,1,6,5,1]=>[3,1,2,1,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,2,5,1,1,6]=>[5,3,1,1,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,2,5,1,6,1]=>[6,4,2,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,5,6,1,1]=>[1,6,4,2,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,6,1,1,5]=>[4,2,1,6,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,6,1,5,1]=>[6,4,3,1,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,6,5,1,1]=>[5,3,2,4,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,5,1,1,2,6]=>[1,2,4,1,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,5,1,1,6,2]=>[1,2,4,1,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,5,1,2,1,6]=>[3,4,6,4,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,5,1,2,6,1]=>[1,2,4,2,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,1,6,1,2]=>[1,2,4,6,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,1,6,2,1]=>[5,6,1,3,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,5,2,1,1,6]=>[4,5,1,3,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,5,2,1,6,1]=>[4,5,1,3,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,6,1,1]=>[1,2,5,5,3,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,5,6,1,1,2]=>[1,2,2,3,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[4,5,6,1,2,1]=>[2,3,3,4,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,5,6,2,1,1]=>[2,3,3,5,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,6,1,1,2,5]=>[1,3,3,1,2,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,6,1,1,5,2]=>[1,3,3,1,5,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,6,1,2,1,5]=>[2,4,4,3,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,6,1,2,5,1]=>[1,3,3,2,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,6,1,5,1,2]=>[1,3,3,5,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,6,1,5,2,1]=>[6,1,1,3,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,6,2,1,1,5]=>[2,4,5,1,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,6,2,1,5,1]=>[6,1,2,5,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,6,2,5,1,1]=>[1,3,4,4,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,6,5,1,1,2]=>[2,4,1,5,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,6,5,1,2,1]=>[2,4,1,5,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,6,5,2,1,1]=>[2,4,1,6,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,1,2,4,6]=>[1,4,1,2,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,1,1,2,6,4]=>[1,4,1,2,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,1,4,2,6]=>[5,1,5,1,3,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,1,1,4,6,2]=>[1,4,1,4,3,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,1,1,6,2,4]=>[1,4,1,6,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,1,6,4,2]=>[3,6,3,1,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,1,2,1,4,6]=>[2,5,3,1,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,2,1,6,4]=>[3,6,4,2,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,2,4,1,6]=>[1,4,2,3,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,2,4,6,1]=>[1,4,2,3,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[5,1,2,6,1,4]=>[1,4,2,5,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,2,6,4,1]=>[5,1,6,2,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,4,1,2,6]=>[5,1,1,2,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,1,4,1,6,2]=>[5,1,1,2,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[5,1,4,2,1,6]=>[5,1,1,3,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,1,4,2,6,1]=>[6,2,2,4,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,4,6,1,2]=>[1,4,4,3,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,1,4,6,2,1]=>[6,2,2,1,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,6,1,2,4]=>[1,4,6,3,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,6,1,4,2]=>[6,2,4,1,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,6,2,1,4]=>[5,1,3,1,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,1,6,2,4,1]=>[6,2,4,2,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,6,4,1,2]=>[5,1,3,3,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,6,4,2,1]=>[3,6,1,1,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,2,1,1,4,6]=>[2,6,1,2,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,1,6,4]=>[4,1,3,4,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,2,1,4,1,6]=>[5,2,4,1,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,2,1,4,6,1]=>[6,3,5,2,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,1,6,1,4]=>[6,3,5,4,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,6,4,1]=>[4,1,3,2,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,2,4,1,1,6]=>[4,1,6,1,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,2,4,1,6,1]=>[6,3,1,3,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,2,4,6,1,1]=>[1,5,3,3,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,2,6,1,1,4]=>[1,5,5,3,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,6,1,4,1]=>[6,3,3,1,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,2,6,4,1,1]=>[4,1,1,2,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,4,1,1,2,6]=>[4,3,1,4,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,4,1,1,6,2]=>[5,4,2,5,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,1,2,1,6]=>[4,3,1,5,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,4,1,2,6,1]=>[4,3,1,5,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,1,6,1,2]=>[4,3,1,2,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,6,2,1]=>[5,4,2,3,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,2,1,1,6]=>[3,2,1,2,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,4,2,1,6,1]=>[3,2,1,2,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,4,2,6,1,1]=>[4,3,2,1,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,6,1,1,2]=>[2,1,4,4,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,4,6,1,2,1]=>[2,1,4,4,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,4,6,2,1,1]=>[2,1,4,5,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,6,1,1,2,4]=>[1,2,3,1,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,6,1,1,4,2]=>[1,2,3,1,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,6,1,2,1,4]=>[2,3,4,3,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,6,1,2,4,1]=>[1,2,3,2,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,6,1,4,1,2]=>[1,2,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,6,1,4,2,1]=>[3,4,5,6,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,2,1,1,4]=>[2,3,5,1,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,6,2,1,4,1]=>[5,6,1,4,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,6,2,4,1,1]=>[1,2,4,3,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,6,4,1,1,2]=>[1,2,6,5,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,6,4,1,2,1]=>[4,5,2,1,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,6,4,2,1,1]=>[3,4,1,1,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,1,1,2,4,5]=>[1,3,1,2,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[6,1,1,2,5,4]=>[2,4,2,3,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,1,4,2,5]=>[1,3,1,4,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,1,1,4,5,2]=>[1,3,1,4,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,1,5,2,4]=>[1,3,1,5,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[6,1,1,5,4,2]=>[4,6,4,1,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,1,2,1,4,5]=>[2,4,3,1,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,2,1,5,4]=>[2,4,3,1,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,2,4,1,5]=>[1,3,2,3,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,1,2,4,5,1]=>[1,3,2,3,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,2,5,1,4]=>[1,3,2,4,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,1,2,5,4,1]=>[2,4,3,5,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,1,2,5]=>[1,3,4,5,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,1,4,1,5,2]=>[6,1,2,3,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[6,1,4,2,1,5]=>[6,1,2,4,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,2,5,1]=>[6,1,2,4,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[6,1,4,5,1,2]=>[1,3,4,2,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,4,5,2,1]=>[2,4,5,3,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,5,1,2,4]=>[1,3,5,4,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,5,1,4,2]=>[6,1,3,2,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,5,2,1,4]=>[6,1,3,3,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,1,5,2,4,1]=>[6,1,3,3,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[6,1,5,4,1,2]=>[4,6,1,3,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,5,4,2,1]=>[4,6,1,3,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,2,1,1,4,5]=>[2,5,1,2,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,2,1,1,5,4]=>[2,5,1,2,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,2,1,4,1,5]=>[5,1,4,1,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,1,4,5,1]=>[5,1,4,1,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,2,1,5,1,4]=>[5,1,4,2,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,2,1,5,4,1]=>[5,1,4,2,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,2,4,1,1,5]=>[1,4,3,5,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,2,4,1,5,1]=>[6,2,1,3,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,2,4,5,1,1]=>[1,4,3,2,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,2,5,1,1,4]=>[5,1,1,1,5,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[6,2,5,1,4,1]=>[5,1,1,1,1,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[6,2,5,4,1,1]=>[5,1,1,4,2,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,4,1,1,2,5]=>[1,6,5,1,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,4,1,1,5,2]=>[4,2,1,4,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[6,4,1,2,1,5]=>[4,2,1,5,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,4,1,2,5,1]=>[5,3,2,6,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,4,1,5,1,2]=>[5,3,2,2,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,4,1,5,2,1]=>[4,2,1,1,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[6,4,2,1,1,5]=>[4,2,2,3,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,4,2,1,5,1]=>[5,3,3,4,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,4,2,5,1,1]=>[5,3,3,1,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[6,4,5,1,1,2]=>[1,6,2,4,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,4,5,1,2,1]=>[3,1,4,6,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,5,2,1,1]=>[4,2,5,1,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,1,1,2,4]=>[2,1,5,2,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,5,1,1,4,2]=>[5,4,1,5,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,5,1,2,1,4]=>[2,1,5,3,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,5,1,2,4,1]=>[2,1,5,3,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,1,4,1,2]=>[5,4,1,1,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,5,1,4,2,1]=>[5,4,1,1,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,5,2,1,1,4]=>[2,1,6,1,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,5,2,1,4,1]=>[5,4,2,4,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,5,2,4,1,1]=>[4,3,1,6,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,5,4,1,1,2]=>[2,1,1,6,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,5,4,1,2,1]=>[2,1,1,6,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,5,4,2,1,1]=>[3,2,2,1,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,3,3,3,3]=>[1,1,3,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,3,1,3,3,3]=>[1,3,6,3,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,3,1,3,3]=>[1,3,1,6,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,3,3,1,3]=>[1,3,1,1,6,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,3,3,3,3,1]=>[1,3,1,1,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,1,3,3,3]=>[1,6,1,3,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,3,1,3,3]=>[3,1,5,1,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,3,3,1,3]=>[3,1,5,3,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,3,3,3,1]=>[3,1,5,3,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,1,1,3,3]=>[1,1,6,1,3,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,3,1,3,1,3]=>[3,3,1,5,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,3,1,3,3,1]=>[3,3,1,5,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,3,1,1,3]=>[1,1,1,6,1,3]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,3,3,1,3,1]=>[3,3,3,1,5,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,3,3,1,1]=>[1,1,1,1,6,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,3,3,3,4]=>[1,1,3,1,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,3,4,3]=>[2,2,4,2,3,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,3,4,3,3]=>[2,2,4,3,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,4,3,3,3]=>[2,2,5,1,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,3,1,3,3,4]=>[1,3,6,3,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,1,3,4,3]=>[3,5,1,5,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,1,4,3,3]=>[3,5,1,6,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,3,1,3,4]=>[1,3,1,6,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,3,1,4,3]=>[3,5,3,1,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,3,3,1,4]=>[1,3,1,1,6,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,3,3,4,1]=>[1,3,1,1,2,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,3,4,1,3]=>[1,3,1,2,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,3,4,3,1]=>[3,5,3,4,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,1,3,3]=>[1,3,2,5,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,4,3,1,3]=>[3,5,4,2,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,3,3,1]=>[3,5,4,2,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,3,3,3]=>[1,4,5,3,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,3,1,3,3]=>[3,6,2,1,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,3,1,3]=>[3,6,2,3,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,3,3,1]=>[3,6,2,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,1,3,3,4]=>[1,6,1,3,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,1,3,4,3]=>[3,1,3,5,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,1,4,3,3]=>[3,1,3,6,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,3,1,3,4]=>[3,1,5,1,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,3,1,4,3]=>[3,1,5,1,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,3,3,1,4]=>[3,1,5,3,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,3,3,4,1]=>[1,6,3,1,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,3,4,1,3]=>[1,6,3,2,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,3,4,3,1]=>[3,1,5,4,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,4,1,3,3]=>[1,6,4,5,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,3,1,3]=>[3,1,6,2,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,3,3,1]=>[3,1,6,2,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,1,1,3,4]=>[1,1,6,1,3,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,3,1,1,4,3]=>[3,3,1,3,6,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,3,1,3,1,4]=>[3,3,1,5,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,3,1,3,4,1]=>[1,1,6,3,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,1,4,1,3]=>[1,1,6,4,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,3,1,4,3,1]=>[3,3,1,6,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,3,1,1,4]=>[1,1,1,6,1,4]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[3,3,3,1,4,1]=>[1,1,1,6,4,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,3,4,1,1]=>[1,1,1,2,5,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[3,3,4,1,1,3]=>[1,1,2,5,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,3,4,1,3,1]=>[1,1,2,5,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,4,3,1,1]=>[3,3,4,2,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,4,1,1,3,3]=>[1,2,5,1,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,4,1,3,1,3]=>[1,2,5,3,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,4,1,3,3,1]=>[1,2,5,3,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,3,1,1,3]=>[3,4,2,1,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,3,1,3,1]=>[3,4,2,1,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,3,3,1,1]=>[3,4,2,3,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,1,3,3,3]=>[1,5,1,3,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,1,3,1,3,3]=>[1,5,3,6,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,3,3,1,3]=>[1,5,3,1,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,3,3,3,1]=>[1,5,3,1,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,3,1,1,3,3]=>[3,2,1,3,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,3,1,3,1,3]=>[3,2,1,5,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,3,1,3,3,1]=>[3,2,1,5,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,3,1,1,3]=>[3,2,3,1,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,3,3,1,3,1]=>[3,2,3,1,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,3,3,1,1]=>[3,2,3,3,1,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,3,3,3,5]=>[1,1,3,1,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,3,3,5,3]=>[1,1,3,1,3,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,3,5,3,3]=>[1,1,3,3,6,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,5,3,3,3]=>[1,1,5,6,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,3,1,3,3,5]=>[1,3,6,3,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,3,1,3,5,3]=>[6,1,4,1,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,3,1,5,3,3]=>[4,6,2,1,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,3,1,3,5]=>[1,3,1,6,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,3,3,1,5,3]=>[4,6,4,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,3,3,1,5]=>[1,3,1,1,6,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,3,3,5,1]=>[1,3,1,1,3,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,3,5,1,3]=>[1,3,1,3,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,3,5,3,1]=>[3,5,3,5,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,5,1,3,3]=>[1,3,3,4,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,5,3,1,3]=>[6,1,1,4,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,3,5,3,3,1]=>[3,5,5,1,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,5,1,3,3,3]=>[1,5,4,3,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,3,1,3,3]=>[4,1,2,2,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,3,3,1,3]=>[4,1,2,4,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,3,3,3,1]=>[4,1,2,4,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,3,3,5]=>[1,6,1,3,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[3,1,1,3,5,3]=>[3,1,3,5,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,1,5,3,3]=>[4,2,4,1,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,3,1,3,5]=>[6,4,1,4,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[3,1,3,1,5,3]=>[4,2,6,2,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,3,3,1,5]=>[4,2,6,4,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,3,3,5,1]=>[1,6,3,1,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,3,5,1,3]=>[6,4,1,1,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,3,5,3,1]=>[3,1,5,5,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,1,5,1,3,3]=>[1,6,5,4,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,5,3,1,3]=>[4,2,1,2,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,5,3,3,1]=>[4,2,1,2,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,1,1,3,5]=>[1,1,6,1,3,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[3,3,1,1,5,3]=>[4,4,2,4,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,3,1,3,1,5]=>[4,4,2,6,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,3,1,3,5,1]=>[1,1,6,3,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,1,5,1,3]=>[1,1,6,5,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,3,1,5,3,1]=>[4,4,2,1,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,3,1,1,5]=>[1,1,1,6,1,5]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[3,3,3,1,5,1]=>[1,1,1,6,5,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,3,5,1,1]=>[1,1,1,3,4,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[3,3,5,1,1,3]=>[1,1,3,4,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,3,5,1,3,1]=>[1,1,3,4,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,5,3,1,1]=>[3,3,5,1,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,5,1,1,3,3]=>[1,3,4,1,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,5,1,3,1,3]=>[6,1,2,1,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,5,1,3,3,1]=>[1,3,4,3,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,3,1,1,3]=>[3,5,1,1,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,3,1,3,1]=>[3,5,1,1,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,5,3,3,1,1]=>[3,5,1,3,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,1,1,3,3,3]=>[1,4,1,3,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,1,3,1,3,3]=>[1,4,3,6,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,3,3,1,3]=>[1,4,3,1,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,3,3,3,1]=>[1,4,3,1,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,1,1,3,3]=>[3,1,1,3,5,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,3,1,3,1,3]=>[3,1,1,5,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,3,1,3,3,1]=>[3,1,1,5,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,3,3,1,1,3]=>[3,1,3,1,3,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,3,3,1,3,1]=>[3,1,3,1,5,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,3,3,3,1,1]=>[3,1,3,3,1,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,3,3,3,6]=>[1,1,3,1,1,4]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,3,3,6,3]=>[1,1,3,1,4,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,3,6,3,3]=>[1,1,3,4,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,6,3,3,3]=>[1,1,6,5,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,3,1,3,3,6]=>[1,3,6,3,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,3,6,3]=>[6,1,4,1,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,6,3,3]=>[4,6,2,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,3,1,3,6]=>[1,3,1,6,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,3,1,6,3]=>[4,6,4,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,3,3,1,6]=>[3,5,3,3,1,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,3,3,3,6,1]=>[1,3,1,1,4,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,3,6,1,3]=>[1,3,1,4,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,3,6,3,1]=>[1,3,1,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,6,1,3,3]=>[1,3,4,3,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,6,3,1,3]=>[6,1,2,3,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,6,3,3,1]=>[1,3,4,5,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,3,3,3]=>[1,6,3,3,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,6,3,1,3,3]=>[4,2,1,2,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,3,3,1,3]=>[4,2,1,4,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,3,3,3,1]=>[4,2,1,4,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,3,3,6]=>[1,6,1,3,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,1,3,6,3]=>[1,6,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,1,6,3,3]=>[4,2,4,2,1,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,3,1,3,6]=>[6,4,1,4,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,3,1,6,3]=>[4,2,6,2,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,3,3,1,6]=>[3,1,5,3,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,1,3,3,6,1]=>[1,6,3,1,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,3,6,1,3]=>[6,4,1,2,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,3,6,3,1]=>[6,4,1,2,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,6,1,3,3]=>[3,1,1,5,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,6,3,1,3]=>[4,2,2,1,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,6,3,3,1]=>[4,2,2,1,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,1,1,3,6]=>[1,1,6,1,3,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,3,1,1,6,3]=>[4,4,2,4,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,3,1,3,1,6]=>[3,3,1,5,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,3,1,3,6,1]=>[1,1,6,3,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,1,6,1,3]=>[3,3,1,1,5,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,3,1,6,3,1]=>[4,4,2,2,1,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,3,1,1,6]=>[3,3,3,1,3,1]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[3,3,3,1,6,1]=>[3,3,3,1,1,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,3,3,6,1,1]=>[1,1,1,4,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[3,3,6,1,1,3]=>[1,1,4,3,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,3,6,1,3,1]=>[1,1,4,3,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,6,3,1,1]=>[1,1,4,5,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,6,1,1,3,3]=>[1,4,3,1,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,6,1,3,1,3]=>[6,2,1,1,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,6,1,3,3,1]=>[1,4,3,3,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,6,3,1,1,3]=>[1,4,5,6,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,6,3,1,3,1]=>[6,2,3,4,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,6,3,3,1,1]=>[1,4,5,1,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,1,1,3,3,3]=>[1,3,1,3,1,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[6,1,3,1,3,3]=>[1,3,3,6,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[6,1,3,3,1,3]=>[1,3,3,1,6,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[6,1,3,3,3,1]=>[1,3,3,1,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[6,3,1,1,3,3]=>[1,5,6,1,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,3,1,3,1,3]=>[6,3,4,1,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,3,1,3,3,1]=>[4,1,2,6,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,3,3,1,1,3]=>[1,5,1,6,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,3,3,1,3,1]=>[4,1,4,2,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,3,3,3,1,1]=>[1,5,1,1,6,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,3,3,4,4]=>[1,1,3,1,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,3,4,3,4]=>[2,2,4,3,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,3,4,4,3]=>[2,2,4,3,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,4,3,3,4]=>[2,2,5,1,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,4,3,4,3]=>[2,2,5,1,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,4,4,3,3]=>[2,2,5,2,1,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,3,1,3,4,4]=>[1,3,6,3,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,1,4,3,4]=>[3,5,1,6,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,4,4,3]=>[3,5,1,6,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,3,1,4,4]=>[1,3,1,6,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,3,4,1,4]=>[1,3,1,2,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,3,4,4,1]=>[1,3,1,2,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,4,1,3,4]=>[1,3,2,5,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,4,1,4,3]=>[2,4,3,6,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,3,1,4]=>[3,5,4,2,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,3,4,1]=>[2,4,3,1,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,4,4,1,3]=>[1,3,2,1,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,4,4,3,1]=>[3,5,4,3,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,3,3,4]=>[1,4,5,3,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,3,4,3]=>[2,5,6,4,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,1,4,3,3]=>[5,1,2,1,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,3,1,3,4]=>[3,6,2,1,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,1,4,3]=>[5,1,4,3,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,3,3,1,4]=>[5,1,4,5,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,3,3,4,1]=>[2,5,1,2,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,3,4,1,3]=>[2,5,1,3,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,4,3,1]=>[3,6,2,4,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,4,1,3,3]=>[1,4,1,5,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,4,3,1,3]=>[3,6,3,2,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,4,3,3,1]=>[3,6,3,2,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,1,3,4,4]=>[1,6,1,3,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,1,4,3,4]=>[3,1,3,6,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,1,4,4,3]=>[3,1,3,6,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,3,1,4,4]=>[3,1,5,1,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,3,4,1,4]=>[1,6,3,2,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,3,4,4,1]=>[1,6,3,2,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,1,3,4]=>[1,6,4,5,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,1,4,3]=>[5,3,1,2,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,4,3,1,4]=>[5,3,1,4,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,4,3,4,1]=>[5,3,1,4,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,4,1,3]=>[1,6,4,1,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,4,3,1]=>[3,1,6,3,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,1,1,4,4]=>[1,1,6,1,4,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[3,3,1,4,1,4]=>[5,5,3,1,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,3,1,4,4,1]=>[1,1,6,4,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,4,1,1,4]=>[1,1,2,5,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,3,4,1,4,1]=>[1,1,2,5,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,3,4,4,1,1]=>[1,1,2,1,5,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[3,4,1,1,3,4]=>[1,2,5,1,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,4,1,1,4,3]=>[2,3,6,2,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,3,1,4]=>[1,2,5,3,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,1,3,4,1]=>[1,2,5,3,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,4,1,4,1,3]=>[1,2,5,4,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,1,4,3,1]=>[5,6,2,1,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,3,1,1,4]=>[3,4,2,1,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,3,1,4,1]=>[5,6,4,3,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,3,4,1,1]=>[2,3,1,3,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,4,4,1,1,3]=>[1,2,1,5,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,4,4,1,3,1]=>[1,2,1,5,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,4,3,1,1]=>[3,4,3,2,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,1,3,3,4]=>[1,5,1,3,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,3,4,3]=>[2,6,2,4,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,1,4,3,3]=>[2,6,2,5,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,3,1,3,4]=>[1,5,3,6,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,3,1,4,3]=>[6,3,1,4,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,3,1,4]=>[1,5,3,1,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,3,3,4,1]=>[1,5,3,1,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,3,4,1,3]=>[1,5,3,2,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,1,3,4,3,1]=>[4,1,6,5,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,1,3,3]=>[1,5,4,5,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,4,3,1,3]=>[6,3,2,5,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,3,3,1]=>[5,2,1,4,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,3,4]=>[3,2,1,3,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,1,4,3]=>[3,2,1,3,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,3,1,3,1,4]=>[3,2,1,5,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,3,1,3,4,1]=>[4,3,2,6,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,4,1,3]=>[6,5,4,2,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,4,3,1]=>[3,2,1,6,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,3,3,1,1,4]=>[3,2,3,1,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,3,3,1,4,1]=>[5,4,5,3,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,4,1,1]=>[2,1,2,3,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,3,4,1,1,3]=>[2,1,3,6,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,3,4,1,3,1]=>[4,3,5,1,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,4,3,1,1]=>[3,2,4,2,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,1,1,3,3]=>[1,1,5,1,3,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,4,1,3,1,3]=>[1,1,5,3,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,4,1,3,3,1]=>[1,1,5,3,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,3,1,1,3]=>[3,3,2,1,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,4,3,1,3,1]=>[3,3,2,1,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,3,3,1,1]=>[3,3,2,3,1,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,3,3,4,5]=>[1,1,3,1,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,3,3,5,4]=>[2,2,4,2,4,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,3,4,3,5]=>[2,2,4,3,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,3,4,5,3]=>[1,1,3,2,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,3,5,3,4]=>[1,1,3,3,6,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,3,5,4,3]=>[2,2,4,4,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,4,3,3,5]=>[2,2,5,1,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,4,3,5,3]=>[3,3,6,2,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,4,5,3,3]=>[1,1,4,2,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,5,3,3,4]=>[1,1,5,6,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,5,3,4,3]=>[4,4,1,2,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,5,4,3,3]=>[2,2,6,1,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,3,1,3,4,5]=>[1,3,6,3,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,3,1,3,5,4]=>[6,1,4,1,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,1,4,3,5]=>[6,1,4,2,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,4,5,3]=>[3,5,1,6,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,5,3,4]=>[4,6,2,1,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,1,5,4,3]=>[4,6,2,1,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,3,1,4,5]=>[1,3,1,6,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,3,1,5,4]=>[4,6,4,2,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,3,4,1,5]=>[1,3,1,2,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,3,4,5,1]=>[1,3,1,2,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,3,5,1,4]=>[1,3,1,3,4,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,3,5,4,1]=>[2,4,2,4,1,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,4,1,3,5]=>[1,3,2,5,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,3,4,1,5,3]=>[4,6,5,1,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,4,3,1,5]=>[4,6,5,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,3,5,1]=>[2,4,3,1,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,5,1,3]=>[1,3,2,2,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,4,5,3,1]=>[3,5,4,4,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,5,1,3,4]=>[1,3,3,4,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,5,1,4,3]=>[6,1,1,2,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,5,3,1,4]=>[6,1,1,4,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,5,3,4,1]=>[1,3,3,6,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,5,4,1,3]=>[6,1,1,5,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,5,4,3,1]=>[3,5,5,2,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,1,3,3,5]=>[1,4,5,3,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,1,3,5,3]=>[6,2,3,1,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,1,5,3,3]=>[5,1,2,2,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,3,1,3,5]=>[6,2,5,4,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,3,1,5,3]=>[5,1,4,3,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,3,3,1,5]=>[5,1,4,5,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,3,3,5,1]=>[2,5,1,2,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,3,5,1,3]=>[6,2,5,1,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,3,5,3,1]=>[3,6,2,5,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,5,1,3,3]=>[1,4,2,4,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,5,3,1,3]=>[3,6,4,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,5,3,3,1]=>[3,6,4,1,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,1,3,3,4]=>[1,5,4,3,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,3,4,3]=>[2,6,5,4,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,1,4,3,3]=>[5,2,1,1,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,3,1,3,4]=>[4,1,2,2,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,3,1,4,3]=>[5,2,3,3,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,3,3,1,4]=>[5,2,3,5,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,3,3,4,1]=>[4,1,2,4,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,3,4,1,3]=>[4,1,2,5,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,3,4,3,1]=>[4,1,2,5,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,1,3,3]=>[4,1,3,1,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,4,3,1,3]=>[4,1,3,3,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,4,3,3,1]=>[4,1,3,3,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,1,3,4,5]=>[1,6,1,3,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,1,3,5,4]=>[3,1,3,5,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,1,4,3,5]=>[3,1,3,6,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,1,4,5,3]=>[3,1,3,6,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,1,5,3,4]=>[4,2,4,1,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,1,5,4,3]=>[4,2,4,1,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,3,1,4,5]=>[3,1,5,1,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,3,1,5,4]=>[4,2,6,2,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,3,4,1,5]=>[4,2,6,5,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,3,4,5,1]=>[1,6,3,2,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,3,5,1,4]=>[6,4,1,1,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,3,5,4,1]=>[6,4,1,1,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,1,3,5]=>[6,4,2,3,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,4,1,5,3]=>[5,3,1,2,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,1,4,3,1,5]=>[5,3,1,4,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,4,3,5,1]=>[6,4,2,5,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,4,5,1,3]=>[1,6,4,2,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,4,5,3,1]=>[3,1,6,4,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,5,1,3,4]=>[1,6,5,4,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,4,3]=>[5,3,2,1,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,5,3,1,4]=>[5,3,2,3,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,5,3,4,1]=>[4,2,1,2,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,1,5,4,1,3]=>[4,2,1,3,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,5,4,3,1]=>[4,2,1,3,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,3,1,1,4,5]=>[1,1,6,1,4,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,3,1,1,5,4]=>[4,4,2,4,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,3,1,4,1,5]=>[5,5,3,1,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,3,1,4,5,1]=>[1,1,6,4,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,3,1,5,1,4]=>[5,5,3,2,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,3,1,5,4,1]=>[4,4,2,1,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,4,1,1,5]=>[1,1,2,5,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[3,3,4,1,5,1]=>[1,1,2,5,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,3,4,5,1,1]=>[1,1,2,2,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,3,5,1,1,4]=>[1,1,3,4,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,3,5,1,4,1]=>[1,1,3,4,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,3,5,4,1,1]=>[2,2,4,1,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,4,1,1,3,5]=>[1,2,5,1,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,4,1,1,5,3]=>[4,5,1,4,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,4,1,3,1,5]=>[4,5,1,6,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,1,3,5,1]=>[1,2,5,3,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,1,5,1,3]=>[1,2,5,5,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,1,5,3,1]=>[4,5,1,1,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,3,1,1,5]=>[4,5,3,2,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,3,1,5,1]=>[5,6,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,3,5,1,1]=>[2,3,1,4,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,4,5,1,1,3]=>[1,2,2,4,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,4,5,1,3,1]=>[1,2,2,4,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,5,3,1,1]=>[3,4,4,1,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,5,1,1,3,4]=>[1,3,4,1,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,5,1,1,4,3]=>[2,4,5,2,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,5,1,3,1,4]=>[6,1,2,1,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,5,1,3,4,1]=>[1,3,4,3,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,1,4,1,3]=>[6,1,2,2,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,5,1,4,3,1]=>[6,1,2,2,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,3,1,1,4]=>[3,5,1,1,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,5,3,1,4,1]=>[6,1,4,4,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,3,4,1,1]=>[1,3,6,2,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,4,1,1,3]=>[2,4,1,6,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,5,4,1,3,1]=>[6,1,5,3,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,4,3,1,1]=>[3,5,2,2,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,1,3,3,5]=>[1,5,1,3,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[4,1,1,3,5,3]=>[1,5,1,3,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,1,5,3,3]=>[4,1,4,1,2,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,1,3,1,3,5]=>[6,3,1,4,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,1,3,1,5,3]=>[4,1,6,2,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,1,3,3,1,5]=>[4,1,6,4,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,3,3,5,1]=>[1,5,3,1,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,3,5,1,3]=>[6,3,1,1,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,1,3,5,3,1]=>[6,3,1,1,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,1,5,1,3,3]=>[1,5,5,4,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,5,3,1,3]=>[4,1,1,2,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,1,5,3,3,1]=>[4,1,1,2,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,3,1,1,3,5]=>[3,2,1,3,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,3,1,1,5,3]=>[4,3,2,4,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,1,3,1,5]=>[4,3,2,6,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,3,1,3,5,1]=>[6,5,4,1,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,1,5,1,3]=>[6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,5,3,1]=>[4,3,2,1,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,3,1,1,5]=>[4,3,4,2,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,3,1,5,1]=>[5,4,5,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,3,5,1,1]=>[2,1,2,4,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,3,5,1,1,3]=>[2,1,4,5,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,3,5,1,3,1]=>[6,5,1,2,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,5,3,1,1]=>[3,2,5,1,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,5,1,1,3,3]=>[1,2,4,1,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,5,1,3,1,3]=>[1,2,4,3,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,5,1,3,3,1]=>[1,2,4,3,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,3,1,1,3]=>[3,4,1,1,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,5,3,1,3,1]=>[3,4,1,1,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,5,3,3,1,1]=>[3,4,1,3,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,1,1,3,3,4]=>[1,4,1,3,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,1,3,4,3]=>[2,5,2,4,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,1,4,3,3]=>[2,5,2,5,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[5,1,3,1,3,4]=>[1,4,3,6,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,3,1,4,3]=>[6,2,1,4,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,3,3,1,4]=>[1,4,3,1,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,3,3,4,1]=>[1,4,3,1,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,3,4,1,3]=>[1,4,3,2,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,3,4,3,1]=>[3,6,5,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,4,1,3,3]=>[1,4,4,5,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,4,3,1,3]=>[6,2,2,5,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,4,3,3,1]=>[5,1,1,4,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,1,1,3,4]=>[3,1,1,3,5,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,3,1,1,4,3]=>[3,1,1,3,6,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,3,1,3,1,4]=>[3,1,1,5,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[5,3,1,3,4,1]=>[4,2,2,6,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,1,4,1,3]=>[6,4,4,2,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,1,4,3,1]=>[3,1,1,6,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,3,3,1,1,4]=>[3,1,3,1,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[5,3,3,1,4,1]=>[5,3,5,3,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,3,4,1,1]=>[1,6,1,2,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,3,4,1,1,3]=>[1,6,2,5,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,3,4,1,3,1]=>[4,2,5,1,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,4,3,1,1]=>[3,1,4,2,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,1,1,3,3]=>[2,1,6,2,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,4,1,3,1,3]=>[6,5,3,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,1,3,3,1]=>[4,3,1,6,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,3,1,1,3]=>[3,2,2,1,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,4,3,1,3,1]=>[3,2,2,1,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,4,3,3,1,1]=>[3,2,2,3,1,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,3,3,4,6]=>[1,1,3,1,2,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,3,3,6,4]=>[1,1,3,1,4,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,3,4,3,6]=>[2,2,4,3,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,3,4,6,3]=>[1,1,3,2,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,3,6,3,4]=>[1,1,3,4,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,3,6,4,3]=>[3,3,5,6,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,4,3,3,6]=>[2,2,5,1,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,4,3,6,3]=>[5,5,1,4,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,4,6,3,3]=>[1,1,4,3,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,6,3,3,4]=>[1,1,6,5,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,6,3,4,3]=>[4,4,2,1,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,6,4,3,3]=>[3,3,1,1,2,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,1,3,4,6]=>[1,3,6,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,3,1,3,6,4]=>[6,1,4,1,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,1,4,3,6]=>[6,1,4,2,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,1,4,6,3]=>[6,1,4,2,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,6,3,4]=>[4,6,2,2,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,1,6,4,3]=>[3,5,1,1,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,3,1,4,6]=>[1,3,1,6,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,3,1,6,4]=>[3,5,3,1,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,3,4,1,6]=>[1,3,1,2,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,3,4,6,1]=>[1,3,1,2,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,3,6,1,4]=>[1,3,1,4,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,3,6,4,1]=>[1,3,1,4,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,4,1,3,6]=>[1,3,2,5,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,1,6,3]=>[4,6,5,1,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,4,3,1,6]=>[3,5,4,2,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,4,3,6,1]=>[2,4,3,1,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,6,1,3]=>[1,3,2,3,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,3,4,6,3,1]=>[1,3,2,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,6,1,3,4]=>[1,3,4,3,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,6,1,4,3]=>[6,1,2,1,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,6,3,1,4]=>[6,1,2,3,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,6,3,4,1]=>[1,3,4,5,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,6,4,1,3]=>[6,1,2,4,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,6,4,3,1]=>[3,5,6,1,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,3,3,6]=>[1,4,5,3,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,1,3,6,3]=>[6,2,3,1,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,4,1,6,3,3]=>[5,1,2,3,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,3,1,3,6]=>[6,2,5,4,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,3,1,6,3]=>[5,1,4,3,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,3,3,1,6]=>[3,6,2,3,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,3,3,6,1]=>[2,5,1,2,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,3,6,1,3]=>[6,2,5,2,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,3,6,3,1]=>[5,1,4,1,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,6,1,3,3]=>[1,4,3,3,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,4,6,3,1,3]=>[6,2,1,3,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,6,3,3,1]=>[1,4,3,5,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,3,3,4]=>[1,6,3,3,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,6,1,3,4,3]=>[3,1,5,5,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,1,4,3,3]=>[3,1,5,6,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,3,1,3,4]=>[4,2,1,2,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,3,1,4,3]=>[5,3,2,3,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,3,3,1,4]=>[5,3,2,5,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,6,3,3,4,1]=>[4,2,1,4,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,6,3,4,1,3]=>[4,2,1,5,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,3,4,3,1]=>[4,2,1,5,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,4,1,3,3]=>[4,2,2,1,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,4,3,1,3]=>[3,1,1,2,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,6,4,3,3,1]=>[3,1,1,2,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,1,1,3,4,6]=>[1,6,1,3,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,1,3,6,4]=>[3,1,3,5,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,1,4,3,6]=>[5,3,5,1,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,1,4,6,3]=>[1,6,1,4,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,1,6,3,4]=>[4,2,4,2,1,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,1,6,4,3]=>[3,1,3,1,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,1,3,1,4,6]=>[6,4,1,4,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,3,1,6,4]=>[3,1,5,1,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[3,1,3,4,1,6]=>[4,2,6,5,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,3,4,6,1]=>[1,6,3,2,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,3,6,1,4]=>[6,4,1,2,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,3,6,4,1]=>[6,4,1,2,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,4,1,3,6]=>[6,4,2,3,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,4,1,6,3]=>[5,3,1,2,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,1,4,3,1,6]=>[3,1,6,2,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,4,3,6,1]=>[6,4,2,5,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,4,6,1,3]=>[6,4,2,1,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,4,6,3,1]=>[6,4,2,1,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,6,1,3,4]=>[3,1,1,5,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,6,1,4,3]=>[3,1,1,5,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,6,3,1,4]=>[5,3,3,2,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,6,3,4,1]=>[4,2,2,1,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,1,6,4,1,3]=>[4,2,2,2,1,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,6,4,3,1]=>[3,1,1,1,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[3,3,1,1,4,6]=>[1,1,6,1,4,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,3,1,1,6,4]=>[3,3,1,3,1,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,3,1,4,1,6]=>[5,5,3,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,3,1,4,6,1]=>[1,1,6,4,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,1,6,1,4]=>[3,3,1,1,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,3,1,6,4,1]=>[4,4,2,2,2,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,4,1,1,6]=>[1,1,2,5,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,3,4,1,6,1]=>[1,1,2,5,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,4,6,1,1]=>[1,1,2,3,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,3,6,1,1,4]=>[1,1,4,3,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,3,6,1,4,1]=>[1,1,4,3,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,3,6,4,1,1]=>[1,1,4,6,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,4,1,1,3,6]=>[1,2,5,1,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,1,1,6,3]=>[4,5,1,4,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,4,1,3,1,6]=>[4,5,1,6,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,4,1,3,6,1]=>[1,2,5,3,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,1,6,1,3]=>[1,2,5,6,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,4,1,6,3,1]=>[4,5,1,2,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,3,1,1,6]=>[3,4,2,1,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,4,3,1,6,1]=>[3,4,2,1,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,3,6,1,1]=>[2,3,1,5,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,4,6,1,1,3]=>[1,2,3,3,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,4,6,1,3,1]=>[1,2,3,3,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,6,3,1,1]=>[1,2,3,5,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,1,1,3,4]=>[1,4,3,1,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,6,1,1,4,3]=>[2,5,4,2,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,6,1,3,1,4]=>[6,2,1,1,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,6,1,3,4,1]=>[1,4,3,3,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,6,1,4,1,3]=>[6,2,1,2,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,6,1,4,3,1]=>[6,2,1,2,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,3,1,1,4]=>[5,1,2,3,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,6,3,1,4,1]=>[5,1,2,3,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,6,3,4,1,1]=>[1,4,5,2,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,6,4,1,1,3]=>[1,4,6,5,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,6,4,1,3,1]=>[6,2,4,3,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,6,4,3,1,1]=>[3,6,1,2,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,1,3,3,6]=>[1,5,1,3,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,1,3,6,3]=>[1,5,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,1,6,3,3]=>[4,1,4,2,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,1,3,1,3,6]=>[6,3,1,4,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,1,6,3]=>[4,1,6,2,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,1,3,3,1,6]=>[4,1,6,4,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,3,3,6,1]=>[1,5,3,1,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,3,6,1,3]=>[6,3,1,2,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,1,3,6,3,1]=>[6,3,1,2,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,6,1,3,3]=>[1,5,6,3,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,6,3,1,3]=>[4,1,2,1,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,1,6,3,3,1]=>[4,1,2,1,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,3,1,1,3,6]=>[3,2,1,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,3,1,1,6,3]=>[4,3,2,4,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,1,3,1,6]=>[3,2,1,5,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,3,1,3,6,1]=>[6,5,4,1,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,1,6,1,3]=>[3,2,1,1,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,3,1,6,3,1]=>[4,3,2,2,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,3,1,1,6]=>[3,2,3,1,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,3,3,1,6,1]=>[3,2,3,1,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,3,6,1,1]=>[2,1,2,5,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,3,6,1,1,3]=>[2,1,5,4,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,3,6,1,3,1]=>[6,5,2,1,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,6,3,1,1]=>[5,4,1,2,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,6,1,1,3,3]=>[1,3,3,1,3,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[4,6,1,3,1,3]=>[6,1,1,1,4,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,6,1,3,3,1]=>[1,3,3,3,1,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[4,6,3,1,1,3]=>[1,3,5,6,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,6,3,1,3,1]=>[6,1,3,4,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,6,3,3,1,1]=>[1,3,5,1,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,1,3,3,4]=>[1,3,1,3,1,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,1,3,4,3]=>[2,4,2,4,3,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,1,4,3,3]=>[2,4,2,5,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,1,3,1,3,4]=>[1,3,3,6,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[6,1,3,1,4,3]=>[6,1,1,4,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,1,3,3,1,4]=>[1,3,3,1,6,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,3,3,4,1]=>[1,3,3,1,2,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,3,4,1,3]=>[1,3,3,2,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[6,1,3,4,3,1]=>[3,5,5,4,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,1,4,1,3,3]=>[1,3,4,5,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,1,4,3,1,3]=>[6,1,2,5,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,1,4,3,3,1]=>[3,5,6,2,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,1,3,4]=>[1,5,6,1,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,1,1,4,3]=>[5,2,3,5,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,1,3,1,4]=>[6,3,4,1,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,3,1,3,4,1]=>[4,1,2,6,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,1,4,1,3]=>[6,3,4,2,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,3,1,4,3,1]=>[5,2,3,1,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,3,3,1,1,4]=>[1,5,1,6,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,3,3,1,4,1]=>[5,2,5,3,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,3,4,1,1]=>[1,5,1,2,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[6,3,4,1,1,3]=>[1,5,2,5,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,3,4,1,3,1]=>[4,1,5,1,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,4,3,1,1]=>[4,1,5,3,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,1,1,3,3]=>[1,6,5,1,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,4,1,3,1,3]=>[6,4,3,1,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,4,1,3,3,1]=>[4,2,1,6,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,4,3,1,1,3]=>[3,1,2,1,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,4,3,1,3,1]=>[3,1,2,1,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[6,4,3,3,1,1]=>[3,1,2,3,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,3,5,5]=>[1,1,3,1,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,3,5,3,5]=>[1,1,3,3,6,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,3,5,5,3]=>[1,1,3,3,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,5,3,3,5]=>[1,1,5,6,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,5,3,5,3]=>[4,4,1,2,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,5,5,3,3]=>[1,1,5,1,6,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,3,1,3,5,5]=>[1,3,6,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,3,1,5,3,5]=>[6,1,4,3,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,1,5,5,3]=>[4,6,2,1,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,3,1,5,5]=>[1,3,1,6,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,3,5,1,5]=>[1,3,1,3,4,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,3,5,5,1]=>[1,3,1,3,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,3,5,1,3,5]=>[6,1,1,2,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,3,5,1,5,3]=>[6,1,1,2,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,5,3,1,5]=>[6,1,1,4,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,5,3,5,1]=>[6,1,1,4,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,5,5,1,3]=>[1,3,3,1,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,3,5,5,3,1]=>[3,5,5,3,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,5,1,3,3,5]=>[1,5,4,3,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,1,3,5,3]=>[6,3,2,1,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,1,5,3,3]=>[5,2,1,2,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,3,1,3,5]=>[6,3,4,4,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,3,1,5,3]=>[4,1,2,2,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,5,3,3,1,5]=>[4,1,2,4,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,5,3,3,5,1]=>[1,5,6,1,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,3,5,1,3]=>[6,3,4,1,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,3,5,3,1]=>[4,1,2,6,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,5,5,1,3,3]=>[1,5,1,4,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,5,3,1,3]=>[4,1,4,2,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,5,5,3,3,1]=>[4,1,4,2,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,1,3,5,5]=>[1,6,1,3,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[3,1,1,5,3,5]=>[4,2,4,1,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,1,5,5,3]=>[4,2,4,1,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,1,3,1,5,5]=>[4,2,6,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,3,5,1,5]=>[6,4,1,1,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,3,5,5,1]=>[1,6,3,3,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,5,1,3,5]=>[6,4,3,2,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,5,1,5,3]=>[5,3,2,1,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,1,5,3,1,5]=>[4,2,1,2,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,1,5,3,5,1]=>[6,4,3,4,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,5,5,1,3]=>[1,6,5,1,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,5,5,3,1]=>[4,2,1,4,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,3,1,1,5,5]=>[1,1,6,1,5,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[3,3,1,5,1,5]=>[5,5,3,2,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,3,1,5,5,1]=>[1,1,6,5,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,3,5,1,1,5]=>[1,1,3,4,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,3,5,1,5,1]=>[1,1,3,4,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,3,5,5,1,1]=>[1,1,3,1,4,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[3,5,1,1,3,5]=>[1,3,4,1,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,5,1,1,5,3]=>[1,3,4,1,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,1,3,1,5]=>[6,1,2,1,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,1,3,5,1]=>[6,1,2,1,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,5,1,5,1,3]=>[6,1,2,3,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,5,1,5,3,1]=>[6,1,2,3,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,3,1,1,5]=>[4,6,2,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,5,3,1,5,1]=>[6,1,4,4,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,3,5,1,1]=>[1,3,6,3,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,5,1,1,3]=>[1,3,1,4,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,5,5,1,3,1]=>[1,3,1,4,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,5,3,1,1]=>[3,5,3,1,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,1,1,3,3,5]=>[1,4,1,3,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[5,1,1,3,5,3]=>[1,4,1,3,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,1,5,3,3]=>[1,4,1,5,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[5,1,3,1,3,5]=>[6,2,1,4,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,1,3,1,5,3]=>[6,2,1,4,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,3,3,1,5]=>[1,4,3,1,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,3,3,5,1]=>[1,4,3,1,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,3,5,1,3]=>[6,2,1,1,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[5,1,3,5,3,1]=>[6,2,1,1,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,5,1,3,3]=>[1,4,5,4,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,5,3,1,3]=>[6,2,3,4,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,5,3,3,1]=>[5,1,2,3,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,1,3,5]=>[3,1,1,3,5,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,3,1,1,5,3]=>[4,2,2,4,1,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[5,3,1,3,1,5]=>[4,2,2,6,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,3,1,3,5,1]=>[6,4,4,1,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,3,1,5,1,3]=>[6,4,4,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,1,5,3,1]=>[4,2,2,1,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[5,3,3,1,1,5]=>[4,2,4,2,4,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[5,3,3,1,5,1]=>[5,3,5,3,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,3,5,1,1]=>[1,6,1,3,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,5,1,1,3]=>[1,6,3,4,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,5,1,3,1]=>[6,4,1,2,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,3,5,3,1,1]=>[3,1,5,1,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,5,1,1,3,3]=>[1,1,4,1,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[5,5,1,3,1,3]=>[1,1,4,3,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,5,1,3,3,1]=>[1,1,4,3,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,5,3,1,1,3]=>[3,3,1,1,3,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,5,3,1,3,1]=>[3,3,1,1,5,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,5,3,3,1,1]=>[3,3,1,3,1,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,3,3,5,6]=>[1,1,3,1,3,2]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,3,3,6,5]=>[2,2,4,2,5,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,3,5,3,6]=>[1,1,3,3,6,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,3,5,6,3]=>[1,1,3,3,2,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,3,6,3,5]=>[1,1,3,4,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,3,6,5,3]=>[3,3,5,6,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,5,3,3,6]=>[1,1,5,6,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,5,3,6,3]=>[5,5,2,3,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,5,6,3,3]=>[1,1,5,2,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,6,3,3,5]=>[1,1,6,5,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,6,3,5,3]=>[4,4,2,1,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,6,5,3,3]=>[3,3,1,2,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,1,3,5,6]=>[1,3,6,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,3,1,3,6,5]=>[6,1,4,1,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,5,3,6]=>[6,1,4,3,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,1,5,6,3]=>[4,6,2,1,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,6,3,5]=>[6,1,4,4,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,1,6,5,3]=>[3,5,1,1,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,3,1,5,6]=>[1,3,1,6,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,3,1,6,5]=>[3,5,3,1,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,3,5,1,6]=>[1,3,1,3,4,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,3,5,6,1]=>[1,3,1,3,2,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,3,6,1,5]=>[1,3,1,4,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,3,6,5,1]=>[2,4,2,5,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,3,5,1,3,6]=>[6,1,1,2,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,5,1,6,3]=>[6,1,1,2,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,5,3,1,6]=>[3,5,5,1,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,3,5,3,6,1]=>[6,1,1,4,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,5,6,1,3]=>[1,3,3,2,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,3,5,6,3,1]=>[1,3,3,2,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,6,1,3,5]=>[6,1,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,3,6,1,5,3]=>[6,1,2,1,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,6,3,1,5]=>[6,1,2,3,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,6,3,5,1]=>[6,1,2,3,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,6,5,1,3]=>[6,1,2,5,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,6,5,3,1]=>[3,5,6,2,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,3,3,6]=>[1,5,4,3,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,1,3,6,3]=>[6,3,2,1,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,5,1,6,3,3]=>[5,2,1,3,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,3,1,3,6]=>[6,3,4,4,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,3,1,6,3]=>[4,1,2,2,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,5,3,3,1,6]=>[4,1,2,4,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,5,3,3,6,1]=>[1,5,6,1,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,3,6,1,3]=>[6,3,4,2,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,3,6,3,1]=>[5,2,3,1,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,6,1,3,3]=>[1,5,2,3,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,5,6,3,1,3]=>[4,1,5,1,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,6,3,3,1]=>[4,1,5,1,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,6,1,3,3,5]=>[1,6,3,3,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,6,1,3,5,3]=>[6,4,1,1,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,6,1,5,3,3]=>[4,2,6,1,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,3,1,3,5]=>[6,4,3,4,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,6,3,1,5,3]=>[4,2,1,2,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,6,3,3,1,5]=>[4,2,1,4,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,6,3,3,5,1]=>[1,6,5,1,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,3,5,1,3]=>[6,4,3,1,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,3,5,3,1]=>[4,2,1,6,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,6,5,1,3,3]=>[3,1,2,6,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,5,3,1,3]=>[3,1,2,1,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,6,5,3,3,1]=>[3,1,2,1,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,1,1,3,5,6]=>[1,6,1,3,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,1,3,6,5]=>[3,1,3,5,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,1,5,3,6]=>[5,3,5,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,1,5,6,3]=>[4,2,4,1,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,1,6,3,5]=>[4,2,4,2,1,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,1,6,5,3]=>[3,1,3,1,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,1,3,1,5,6]=>[4,2,6,2,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,3,1,6,5]=>[3,1,5,1,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,1,3,5,1,6]=>[6,4,1,1,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,3,5,6,1]=>[1,6,3,3,2,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,3,6,1,5]=>[6,4,1,2,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,3,6,5,1]=>[6,4,1,2,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,5,1,3,6]=>[6,4,3,2,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,5,1,6,3]=>[5,3,2,1,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,1,5,3,1,6]=>[4,2,1,2,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[3,1,5,3,6,1]=>[6,4,3,4,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,5,6,1,3]=>[1,6,5,2,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,5,6,3,1]=>[4,2,1,5,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,1,6,1,3,5]=>[6,4,4,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[3,1,6,1,5,3]=>[4,2,2,6,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,6,3,1,5]=>[4,2,2,1,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,1,6,3,5,1]=>[6,4,4,3,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,6,5,1,3]=>[3,1,1,2,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,6,5,3,1]=>[3,1,1,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[3,3,1,1,5,6]=>[1,1,6,1,5,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,3,1,1,6,5]=>[3,3,1,3,1,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,3,1,5,1,6]=>[5,5,3,2,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,3,1,5,6,1]=>[1,1,6,5,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,1,6,1,5]=>[4,4,2,2,6,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,3,1,6,5,1]=>[3,3,1,1,2,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,5,1,1,6]=>[1,1,3,4,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,3,5,1,6,1]=>[1,1,3,4,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,5,6,1,1]=>[1,1,3,2,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,3,6,1,1,5]=>[1,1,4,3,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,3,6,1,5,1]=>[1,1,4,3,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,3,6,5,1,1]=>[2,2,5,1,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,5,1,1,3,6]=>[1,3,4,1,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,5,1,1,6,3]=>[1,3,4,1,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,1,3,1,6]=>[6,1,2,1,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,5,1,3,6,1]=>[6,1,2,1,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,5,1,6,1,3]=>[6,1,2,4,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,5,1,6,3,1]=>[6,1,2,4,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,3,1,1,6]=>[3,5,1,1,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,5,3,1,6,1]=>[3,5,1,1,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[3,5,3,6,1,1]=>[1,3,6,4,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,6,1,1,3]=>[1,3,2,3,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,5,6,1,3,1]=>[1,3,2,3,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,5,6,3,1,1]=>[1,3,2,5,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,1,1,3,5]=>[1,4,3,1,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,6,1,1,5,3]=>[1,4,3,1,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,6,1,3,1,5]=>[6,2,1,1,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,6,1,3,5,1]=>[6,2,1,1,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,6,1,5,1,3]=>[6,2,1,3,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,6,1,5,3,1]=>[6,2,1,3,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,6,3,1,1,5]=>[5,1,2,3,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,6,3,1,5,1]=>[5,1,2,3,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,6,3,5,1,1]=>[1,4,5,3,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,5,1,1,3]=>[2,5,1,5,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,6,5,1,3,1]=>[6,2,5,2,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,5,3,1,1]=>[3,6,2,1,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,1,1,3,3,6]=>[1,4,1,3,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,1,1,3,6,3]=>[1,4,1,3,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,1,6,3,3]=>[1,4,1,6,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[5,1,3,1,3,6]=>[6,2,1,4,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,3,1,6,3]=>[6,2,1,4,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,3,3,1,6]=>[3,6,5,3,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,1,3,3,6,1]=>[1,4,3,1,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,3,6,1,3]=>[6,2,1,2,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[5,1,3,6,3,1]=>[6,2,1,2,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,6,1,3,3]=>[1,4,6,3,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,1,6,3,1,3]=>[6,2,4,3,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,6,3,3,1]=>[5,1,3,2,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,1,3,6]=>[3,1,1,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,3,1,1,6,3]=>[4,2,2,4,2,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[5,3,1,3,1,6]=>[3,1,1,5,1,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[5,3,1,3,6,1]=>[6,4,4,1,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,3,1,6,1,3]=>[3,1,1,1,5,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,3,1,6,3,1]=>[4,2,2,2,1,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[5,3,3,1,1,6]=>[3,1,3,1,3,1]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[5,3,3,1,6,1]=>[3,1,3,1,1,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,3,3,6,1,1]=>[1,6,1,4,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,6,1,1,3]=>[1,6,4,3,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,6,1,3,1]=>[6,4,2,1,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,3,6,3,1,1]=>[5,3,1,2,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,6,1,1,3,3]=>[1,2,3,1,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[5,6,1,3,1,3]=>[1,2,3,3,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,6,1,3,3,1]=>[1,2,3,3,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,6,3,1,1,3]=>[1,2,5,6,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,6,3,1,3,1]=>[4,5,1,2,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,6,3,3,1,1]=>[1,2,5,1,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,1,1,3,3,5]=>[1,3,1,3,1,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[6,1,1,3,5,3]=>[1,3,1,3,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[6,1,1,5,3,3]=>[1,3,1,5,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,3,1,3,5]=>[6,1,1,4,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[6,1,3,1,5,3]=>[6,1,1,4,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,1,3,3,1,5]=>[1,3,3,1,6,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,1,3,3,5,1]=>[1,3,3,1,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[6,1,3,5,1,3]=>[6,1,1,1,2,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[6,1,3,5,3,1]=>[6,1,1,1,4,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[6,1,5,1,3,3]=>[1,3,5,4,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,1,5,3,1,3]=>[6,1,3,4,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,1,5,3,3,1]=>[4,6,1,2,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,3,1,1,3,5]=>[1,5,6,1,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,3,1,1,5,3]=>[4,1,2,4,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[6,3,1,3,1,5]=>[4,1,2,6,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,3,1,3,5,1]=>[6,3,4,1,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,3,1,5,1,3]=>[6,3,4,3,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,3,1,5,3,1]=>[4,1,2,1,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[6,3,3,1,1,5]=>[4,1,4,2,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,3,3,1,5,1]=>[5,2,5,3,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,3,5,1,1]=>[1,5,1,3,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,3,5,1,1,3]=>[1,5,3,4,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,3,5,1,3,1]=>[6,3,1,2,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,3,5,3,1,1]=>[4,1,6,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,5,1,1,3,3]=>[2,1,5,2,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,5,1,3,1,3]=>[6,5,2,1,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,5,1,3,3,1]=>[3,2,6,5,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,5,3,1,1,3]=>[3,2,1,1,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,5,3,1,3,1]=>[3,2,1,1,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[6,5,3,3,1,1]=>[3,2,1,3,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,4,4,4]=>[1,1,3,2,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,4,3,4,4]=>[2,2,5,1,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,4,4,3,4]=>[2,2,5,2,1,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,4,4,4,3]=>[2,2,5,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,3,1,4,4,4]=>[1,3,6,4,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,4,1,4,4]=>[1,3,2,5,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,4,4,1,4]=>[1,3,2,1,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,4,4,4,1]=>[1,3,2,1,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,1,3,4,4]=>[1,4,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,1,4,3,4]=>[5,1,2,1,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,1,4,4,3]=>[5,1,2,1,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,3,1,4,4]=>[5,1,4,3,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,3,4,1,4]=>[5,1,4,6,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,3,4,4,1]=>[2,5,1,3,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,4,1,3,4]=>[1,4,1,5,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,4,1,4,3]=>[5,1,5,2,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,4,3,1,4]=>[5,1,5,4,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,4,3,4,1]=>[2,5,2,1,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,4,4,1,3]=>[1,4,1,1,5,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,4,4,4,3,1]=>[3,6,3,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,1,1,4,4,4]=>[1,6,1,4,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[3,1,4,1,4,4]=>[5,3,1,2,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,4,4,1,4]=>[5,3,1,5,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,4,4,4,1]=>[1,6,4,1,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,4,1,1,4,4]=>[1,2,5,1,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,4,1,4,1,4]=>[5,6,2,1,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,4,1,4,4,1]=>[1,2,5,4,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,4,1,1,4]=>[1,2,1,5,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,4,4,1,4,1]=>[1,2,1,5,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,4,4,1,1]=>[1,2,1,1,5,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,1,1,3,4,4]=>[1,5,1,3,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,1,4,3,4]=>[2,6,2,5,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,1,4,4,3]=>[2,6,2,5,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,3,1,4,4]=>[1,5,3,6,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,3,4,1,4]=>[1,5,3,2,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,3,4,4,1]=>[1,5,3,2,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,4,1,3,4]=>[1,5,4,5,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,4,1,4,3]=>[5,2,1,2,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,4,3,1,4]=>[5,2,1,4,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,4,3,4,1]=>[5,2,1,4,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,4,4,1,3]=>[1,5,4,1,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,4,4,3,1]=>[5,2,1,5,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,1,4,4]=>[3,2,1,3,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,3,1,4,1,4]=>[5,4,3,1,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,4,4,1]=>[5,4,3,1,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,4,1,1,4]=>[2,1,3,6,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,4,1,4,1]=>[5,4,6,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,4,4,1,1]=>[2,1,3,2,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,4,1,1,3,4]=>[1,1,5,1,3,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,4,1,1,4,3]=>[2,2,6,2,5,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,4,1,3,1,4]=>[1,1,5,3,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,4,1,3,4,1]=>[1,1,5,3,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,4,1,4,1,3]=>[1,1,5,4,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,4,1,4,3,1]=>[5,5,2,1,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,3,1,1,4]=>[3,3,2,1,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,4,3,1,4,1]=>[5,5,4,3,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,3,4,1,1]=>[2,2,1,3,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,4,4,1,1,3]=>[1,1,1,5,1,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[4,4,4,1,3,1]=>[1,1,1,5,3,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,4,3,1,1]=>[3,3,3,2,1,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,3,4,4,5]=>[1,1,3,2,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,3,4,5,4]=>[2,2,4,3,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,3,5,4,4]=>[2,2,4,4,1,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,4,3,4,5]=>[2,2,5,1,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,4,3,5,4]=>[2,2,5,1,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,4,4,3,5]=>[2,2,5,2,1,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,4,4,5,3]=>[1,1,4,1,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,4,5,3,4]=>[1,1,4,2,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,4,5,4,3]=>[2,2,5,3,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,5,3,4,4]=>[1,1,5,6,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,5,4,3,4]=>[2,2,6,1,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,5,4,4,3]=>[2,2,6,1,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,3,1,4,4,5]=>[1,3,6,4,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,4,5,4]=>[3,5,1,6,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,4,4]=>[4,6,2,1,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,1,4,5]=>[1,3,2,5,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,4,1,5,4]=>[4,6,5,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,4,4,1,5]=>[1,3,2,1,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,4,4,5,1]=>[1,3,2,1,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,4,5,1,4]=>[1,3,2,2,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,4,5,4,1]=>[2,4,3,3,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,5,1,4,4]=>[1,3,3,4,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,5,4,1,4]=>[6,1,1,5,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,5,4,4,1]=>[2,4,4,1,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,4,1,3,4,5]=>[1,4,5,3,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,1,3,5,4]=>[6,2,3,1,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,4,3,5]=>[6,2,3,2,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,4,5,3]=>[5,1,2,1,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,1,5,3,4]=>[5,1,2,2,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,5,4,3]=>[5,1,2,2,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,3,1,4,5]=>[5,1,4,3,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,3,1,5,4]=>[5,1,4,3,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,4,3,4,1,5]=>[5,1,4,6,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,3,4,5,1]=>[2,5,1,3,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,3,5,1,4]=>[6,2,5,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,3,5,4,1]=>[2,5,1,4,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,4,1,3,5]=>[1,4,1,5,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,4,1,5,3]=>[5,1,5,2,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,4,3,1,5]=>[5,1,5,4,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,4,3,5,1]=>[2,5,2,1,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,4,5,1,3]=>[1,4,1,2,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,4,5,3,1]=>[3,6,3,4,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,4,5,1,3,4]=>[1,4,2,4,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,4,5,1,4,3]=>[5,1,6,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,5,3,1,4]=>[5,1,6,3,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,5,3,4,1]=>[1,4,2,6,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,5,4,1,3]=>[2,5,3,1,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,4,3,1]=>[3,6,4,2,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,3,4,4]=>[1,5,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,1,4,3,4]=>[5,2,1,1,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,1,4,4,3]=>[5,2,1,1,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,3,1,4,4]=>[5,2,3,3,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,3,4,1,4]=>[5,2,3,6,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,3,4,4,1]=>[4,1,2,5,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,4,1,3,4]=>[4,1,3,1,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,4,1,4,3]=>[5,2,4,2,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,4,3,1,4]=>[5,2,4,4,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,4,3,4,1]=>[4,1,3,3,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,5,4,4,1,3]=>[4,1,3,4,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,4,4,3,1]=>[4,1,3,4,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,1,4,4,5]=>[1,6,1,4,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,1,4,5,4]=>[3,1,3,6,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,1,5,4,4]=>[4,2,4,1,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,4,1,4,5]=>[5,3,1,2,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,1,5,4]=>[5,3,1,2,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,4,4,1,5]=>[5,3,1,5,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,4,4,5,1]=>[1,6,4,1,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,4,5,1,4]=>[5,3,1,6,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,4,5,4,1]=>[5,3,1,6,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,1,4,4]=>[5,3,2,1,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,5,4,1,4]=>[5,3,2,4,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,5,4,4,1]=>[4,2,1,3,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,1,4,5]=>[1,2,5,1,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,1,1,5,4]=>[4,5,1,4,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,4,1,4,1,5]=>[5,6,2,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,1,4,5,1]=>[1,2,5,4,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,4,1,5,1,4]=>[5,6,2,2,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,4,1,5,4,1]=>[4,5,1,1,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,4,4,1,1,5]=>[1,2,1,5,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[3,4,4,1,5,1]=>[1,2,1,5,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,4,5,1,1]=>[1,2,1,2,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,4,5,1,1,4]=>[1,2,2,4,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[3,4,5,1,4,1]=>[1,2,2,4,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,4,5,4,1,1]=>[2,3,3,1,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,5,1,1,4,4]=>[1,3,4,1,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,5,1,4,1,4]=>[6,1,2,2,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,5,1,4,4,1]=>[1,3,4,4,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,4,1,1,4]=>[2,4,1,6,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,4,1,4,1]=>[6,1,5,3,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,4,4,1,1]=>[2,4,1,2,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,1,1,3,4,5]=>[1,5,1,3,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,1,3,5,4]=>[2,6,2,4,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,1,4,3,5]=>[2,6,2,5,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,1,4,5,3]=>[1,5,1,4,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,1,5,3,4]=>[4,1,4,1,2,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,1,5,4,3]=>[4,1,4,1,3,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,1,3,1,4,5]=>[1,5,3,6,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,1,5,4]=>[4,1,6,2,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,4,1,5]=>[4,1,6,5,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,3,4,5,1]=>[1,5,3,2,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,3,5,1,4]=>[6,3,1,1,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,1,3,5,4,1]=>[6,3,1,1,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,1,4,1,3,5]=>[6,3,2,3,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,4,1,5,3]=>[5,2,1,2,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,4,3,1,5]=>[5,2,1,4,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,4,3,5,1]=>[6,3,2,5,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,4,5,1,3]=>[1,5,4,2,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,1,4,5,3,1]=>[5,2,1,6,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,5,1,3,4]=>[1,5,5,4,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,5,1,4,3]=>[5,2,2,1,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,5,3,1,4]=>[5,2,2,3,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,5,3,4,1]=>[4,1,1,2,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,5,4,1,3]=>[4,1,1,3,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,1,5,4,3,1]=>[4,1,1,3,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,3,1,1,4,5]=>[3,2,1,3,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,1,1,5,4]=>[4,3,2,4,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,1,4,1,5]=>[5,4,3,1,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,1,4,5,1]=>[5,4,3,1,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,3,1,5,1,4]=>[5,4,3,2,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,5,4,1]=>[4,3,2,1,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,3,4,1,1,5]=>[4,3,5,1,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,3,4,1,5,1]=>[5,4,6,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,4,5,1,1]=>[2,1,3,3,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,3,5,1,1,4]=>[2,1,4,5,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,3,5,1,4,1]=>[6,5,1,2,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,5,4,1,1]=>[2,1,4,1,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,4,1,1,3,5]=>[1,1,5,1,3,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[4,4,1,1,5,3]=>[4,4,1,4,1,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,4,1,3,1,5]=>[4,4,1,6,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,4,1,3,5,1]=>[1,1,5,3,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,4,1,5,1,3]=>[1,1,5,5,4,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,4,1,5,3,1]=>[4,4,1,1,2,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,4,3,1,1,5]=>[4,4,3,2,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,4,3,1,5,1]=>[5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,3,5,1,1]=>[2,2,1,4,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,4,5,1,1,3]=>[1,1,2,4,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,4,5,1,3,1]=>[1,1,2,4,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,4,5,3,1,1]=>[3,3,4,1,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,5,1,1,3,4]=>[1,2,4,1,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,5,1,1,4,3]=>[2,3,5,2,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,5,1,3,1,4]=>[1,2,4,3,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,5,1,3,4,1]=>[1,2,4,3,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,1,4,1,3]=>[1,2,4,4,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,5,1,4,3,1]=>[5,6,1,1,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,5,3,1,1,4]=>[3,4,1,1,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,5,3,1,4,1]=>[5,6,3,3,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,5,3,4,1,1]=>[1,2,6,2,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,5,4,1,1,3]=>[2,3,1,6,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,4,1,3,1]=>[4,5,3,1,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,4,3,1,1]=>[3,4,2,2,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,1,3,4,4]=>[1,4,1,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,1,4,3,4]=>[2,5,2,5,1,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,1,1,4,4,3]=>[2,5,2,5,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[5,1,3,1,4,4]=>[1,4,3,6,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,3,4,1,4]=>[1,4,3,2,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,3,4,4,1]=>[1,4,3,2,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,4,1,3,4]=>[1,4,4,5,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,4,1,4,3]=>[5,1,1,2,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,1,4,3,1,4]=>[5,1,1,4,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,1,4,3,4,1]=>[5,1,1,4,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,4,4,1,3]=>[1,4,4,1,5,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,4,4,3,1]=>[5,1,1,5,4,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,1,1,4,4]=>[3,1,1,3,6,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[5,3,1,4,1,4]=>[5,3,3,1,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,3,1,4,4,1]=>[5,3,3,1,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,4,1,1,4]=>[1,6,2,5,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,3,4,1,4,1]=>[5,3,6,2,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,3,4,4,1,1]=>[1,6,2,1,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,4,1,1,3,4]=>[2,1,6,2,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,4,1,1,4,3]=>[2,1,6,2,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,4,1,3,1,4]=>[6,5,3,1,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,3,4,1]=>[4,3,1,6,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,1,4,1,3]=>[6,5,3,2,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,4,1,4,3,1]=>[5,4,2,1,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,3,1,1,4]=>[3,2,2,1,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,4,3,1,4,1]=>[5,4,4,3,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,3,4,1,1]=>[2,1,1,3,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,4,1,1,3]=>[2,1,2,6,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,4,4,1,3,1]=>[4,3,4,1,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,4,3,1,1]=>[3,2,3,2,1,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,3,4,4,6]=>[1,1,3,2,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,3,4,6,4]=>[1,1,3,2,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,3,6,4,4]=>[1,1,3,4,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,4,3,4,6]=>[2,2,5,1,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,4,3,6,4]=>[5,5,1,4,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,4,4,3,6]=>[2,2,5,2,1,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,4,4,6,3]=>[1,1,4,1,3,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,4,6,3,4]=>[1,1,4,3,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,4,6,4,3]=>[3,3,6,5,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,6,3,4,4]=>[1,1,6,5,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,6,4,3,4]=>[3,3,1,1,2,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,6,4,4,3]=>[3,3,1,1,3,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,1,4,4,6]=>[1,3,6,4,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,1,4,6,4]=>[6,1,4,2,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,1,6,4,4]=>[3,5,1,1,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,4,1,4,6]=>[1,3,2,5,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,4,1,6,4]=>[4,6,5,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,4,4,1,6]=>[1,3,2,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,4,4,6,1]=>[1,3,2,1,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,3,4,6,1,4]=>[1,3,2,3,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,4,6,4,1]=>[1,3,2,3,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,6,1,4,4]=>[1,3,4,3,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,6,4,1,4]=>[6,1,2,4,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,6,4,4,1]=>[1,3,4,6,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,1,3,4,6]=>[1,4,5,3,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,3,6,4]=>[6,2,3,1,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,1,4,3,6]=>[5,1,2,1,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,1,4,6,3]=>[6,2,3,2,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,4,1,6,3,4]=>[5,1,2,3,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,6,4,3]=>[5,1,2,3,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,3,1,4,6]=>[6,2,5,4,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,3,1,6,4]=>[3,6,2,1,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,3,4,1,6]=>[5,1,4,6,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,4,6,1]=>[2,5,1,3,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,4,3,6,1,4]=>[6,2,5,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,3,6,4,1]=>[5,1,4,1,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,4,1,3,6]=>[1,4,1,5,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,4,1,6,3]=>[5,1,5,2,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,4,3,1,6]=>[3,6,3,2,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,4,3,6,1]=>[2,5,2,1,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,4,6,1,3]=>[1,4,1,3,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,4,4,6,3,1]=>[1,4,1,3,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,6,1,3,4]=>[1,4,3,3,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,4,6,1,4,3]=>[6,2,1,1,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,6,3,1,4]=>[6,2,1,3,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,6,3,4,1]=>[1,4,3,5,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,6,4,1,3]=>[6,2,1,4,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,6,4,3,1]=>[3,6,5,1,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,1,3,4,4]=>[1,6,3,3,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,6,1,4,3,4]=>[3,1,5,6,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,1,4,4,3]=>[3,1,5,6,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,3,1,4,4]=>[5,3,2,3,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,6,3,4,1,4]=>[5,3,2,6,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,3,4,4,1]=>[4,2,1,5,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,6,4,1,3,4]=>[4,2,2,1,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,4,1,4,3]=>[5,3,3,2,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,4,3,1,4]=>[3,1,1,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,6,4,3,4,1]=>[4,2,2,3,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,4,4,1,3]=>[4,2,2,4,1,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,4,4,3,1]=>[3,1,1,3,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,1,1,4,4,6]=>[1,6,1,4,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,1,4,6,4]=>[3,1,3,6,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,1,6,4,4]=>[3,1,3,1,1,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[3,1,4,1,4,6]=>[6,4,2,3,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,4,1,6,4]=>[5,3,1,2,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,4,4,1,6]=>[5,3,1,5,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,4,4,6,1]=>[1,6,4,1,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,4,6,1,4]=>[6,4,2,1,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,4,6,4,1]=>[6,4,2,1,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,6,1,4,4]=>[3,1,1,5,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,6,4,1,4]=>[5,3,3,3,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,6,4,4,1]=>[4,2,2,2,4,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,4,1,1,4,6]=>[1,2,5,1,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,1,1,6,4]=>[4,5,1,4,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,4,1,4,1,6]=>[5,6,2,1,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,4,6,1]=>[1,2,5,4,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,1,6,1,4]=>[1,2,5,6,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,1,6,4,1]=>[4,5,1,2,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,4,1,1,6]=>[1,2,1,5,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,4,4,1,6,1]=>[1,2,1,5,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,4,6,1,1]=>[1,2,1,3,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,4,6,1,1,4]=>[1,2,3,3,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,4,6,1,4,1]=>[1,2,3,3,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,6,4,1,1]=>[1,2,3,6,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,1,1,4,4]=>[1,4,3,1,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,6,1,4,1,4]=>[6,2,1,2,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,6,1,4,4,1]=>[1,4,3,4,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,4,1,1,4]=>[5,1,3,2,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,6,4,1,4,1]=>[5,1,3,2,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,6,4,4,1,1]=>[1,4,6,1,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,1,3,4,6]=>[1,5,1,3,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,1,1,3,6,4]=>[1,5,1,3,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,1,4,3,6]=>[5,2,5,1,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,1,4,6,3]=>[1,5,1,4,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,1,6,3,4]=>[4,1,4,2,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,1,6,4,3]=>[4,1,4,2,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,1,3,1,4,6]=>[6,3,1,4,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,1,6,4]=>[4,1,6,2,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,1,3,4,1,6]=>[4,1,6,5,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,4,6,1]=>[1,5,3,2,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,3,6,1,4]=>[6,3,1,2,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,1,3,6,4,1]=>[6,3,1,2,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,4,1,3,6]=>[6,3,2,3,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,4,1,6,3]=>[5,2,1,2,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,4,3,1,6]=>[5,2,1,4,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,4,3,6,1]=>[6,3,2,5,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,4,6,1,3]=>[6,3,2,1,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,1,4,6,3,1]=>[6,3,2,1,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,6,1,3,4]=>[1,5,6,3,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,6,1,4,3]=>[6,3,4,1,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,3,1,4]=>[5,2,3,2,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,6,3,4,1]=>[4,1,2,1,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,6,4,1,3]=>[4,1,2,2,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,1,6,4,3,1]=>[4,1,2,2,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,1,1,4,6]=>[3,2,1,3,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,3,1,1,6,4]=>[3,2,1,3,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,3,1,4,1,6]=>[5,4,3,1,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,4,6,1]=>[6,5,4,2,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,1,6,1,4]=>[3,2,1,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,3,1,6,4,1]=>[4,3,2,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,4,1,1,6]=>[4,3,5,1,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,4,1,6,1]=>[4,3,5,1,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,4,6,1,1]=>[2,1,3,4,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,6,1,1,4]=>[2,1,5,4,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,3,6,1,4,1]=>[6,5,2,1,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,6,4,1,1]=>[5,4,1,3,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,1,1,3,6]=>[1,1,5,1,3,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,4,1,1,6,3]=>[4,4,1,4,2,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,4,1,3,1,6]=>[4,4,1,6,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,4,1,3,6,1]=>[1,1,5,3,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,4,1,6,1,3]=>[1,1,5,6,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,4,1,6,3,1]=>[4,4,1,2,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,4,3,1,1,6]=>[3,3,2,1,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,4,3,1,6,1]=>[3,3,2,1,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,3,6,1,1]=>[2,2,1,5,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,4,6,1,1,3]=>[1,1,3,3,1,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[4,4,6,1,3,1]=>[1,1,3,3,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[4,4,6,3,1,1]=>[1,1,3,5,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,6,1,1,3,4]=>[1,3,3,1,3,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,6,1,1,4,3]=>[2,4,4,2,5,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,6,1,3,1,4]=>[6,1,1,1,4,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,6,1,3,4,1]=>[1,3,3,3,2,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,6,1,4,1,3]=>[6,1,1,2,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,6,1,4,3,1]=>[6,1,1,2,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,6,3,1,1,4]=>[1,3,5,6,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,6,3,1,4,1]=>[6,1,3,4,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,6,3,4,1,1]=>[1,3,5,2,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,6,4,1,1,3]=>[1,3,6,5,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,6,4,1,3,1]=>[6,1,4,3,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,6,4,3,1,1]=>[3,5,1,2,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,1,3,4,4]=>[1,3,1,3,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,1,4,3,4]=>[2,4,2,5,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,1,4,4,3]=>[2,4,2,5,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,1,3,1,4,4]=>[1,3,3,6,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,3,4,1,4]=>[1,3,3,2,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,3,4,4,1]=>[1,3,3,2,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,4,1,3,4]=>[1,3,4,5,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,4,1,4,3]=>[6,1,2,3,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,1,4,3,1,4]=>[6,1,2,5,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,1,4,3,4,1]=>[2,4,5,1,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,4,1,3]=>[1,3,4,1,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,1,4,4,3,1]=>[3,5,6,3,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,1,4,4]=>[1,5,6,1,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,3,1,4,1,4]=>[5,2,3,1,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,3,1,4,4,1]=>[5,2,3,1,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,4,1,1,4]=>[1,5,2,5,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,3,4,1,4,1]=>[5,2,6,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,3,4,4,1,1]=>[1,5,2,1,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[6,4,1,1,3,4]=>[1,6,5,1,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,4,1,1,4,3]=>[5,3,2,5,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,4,1,3,1,4]=>[6,4,3,1,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,1,3,4,1]=>[4,2,1,6,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,4,1,4,1,3]=>[6,4,3,2,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,4,1,4,3,1]=>[5,3,2,1,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,4,3,1,1,4]=>[3,1,2,1,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,4,3,1,4,1]=>[5,3,4,3,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,4,3,4,1,1]=>[4,2,3,5,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,4,1,1,3]=>[1,6,1,5,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,4,4,1,3,1]=>[4,2,4,1,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,4,4,3,1,1]=>[3,1,3,2,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,3,4,5,5]=>[1,1,3,2,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,3,5,4,5]=>[2,2,4,4,1,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,3,5,5,4]=>[2,2,4,4,2,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,4,3,5,5]=>[2,2,5,1,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,4,5,3,5]=>[1,1,4,2,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,4,5,5,3]=>[1,1,4,2,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,5,3,4,5]=>[1,1,5,6,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,5,3,5,4]=>[4,4,1,2,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,5,4,3,5]=>[2,2,6,1,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,5,4,5,3]=>[4,4,1,3,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,5,5,3,4]=>[1,1,5,1,6,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,5,5,4,3]=>[2,2,6,2,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,3,1,4,5,5]=>[1,3,6,4,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,1,5,4,5]=>[4,6,2,1,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,1,5,5,4]=>[4,6,2,1,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,1,5,5]=>[1,3,2,5,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,3,4,5,1,5]=>[1,3,2,2,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,4,5,5,1]=>[1,3,2,2,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,5,1,4,5]=>[1,3,3,4,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,5,1,5,4]=>[6,1,1,2,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,5,4,1,5]=>[6,1,1,5,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,5,4,5,1]=>[2,4,4,1,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,5,5,1,4]=>[1,3,3,1,4,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,5,5,4,1]=>[2,4,4,2,1,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,4,1,3,5,5]=>[1,4,5,3,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,1,5,3,5]=>[6,2,3,3,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,1,5,5,3]=>[5,1,2,2,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,3,1,5,5]=>[5,1,4,3,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,3,5,1,5]=>[6,2,5,1,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,3,5,5,1]=>[2,5,1,4,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,4,5,1,3,5]=>[1,4,2,4,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,4,5,1,5,3]=>[5,1,6,1,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,5,3,1,5]=>[5,1,6,3,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,5,3,5,1]=>[1,4,2,6,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,5,5,1,3]=>[1,4,2,1,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,5,5,3,1]=>[3,6,4,3,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,1,3,4,5]=>[1,5,4,3,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,1,3,5,4]=>[6,3,2,1,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,4,3,5]=>[6,3,2,2,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,4,5,3]=>[5,2,1,1,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,5,3,4]=>[5,2,1,2,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,5,4,3]=>[5,2,1,2,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,3,1,4,5]=>[5,2,3,3,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,3,1,5,4]=>[4,1,2,2,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,5,3,4,1,5]=>[4,1,2,5,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,3,4,5,1]=>[1,5,6,2,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,3,5,1,4]=>[6,3,4,1,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,3,5,4,1]=>[4,1,2,6,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,4,1,3,5]=>[6,3,5,3,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,5,4,1,5,3]=>[4,1,3,1,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,5,4,3,1,5]=>[4,1,3,3,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,5,4,3,5,1]=>[2,6,1,1,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,4,5,1,3]=>[2,6,1,3,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,4,5,3,1]=>[4,1,3,5,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,5,1,3,4]=>[1,5,1,4,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,5,1,4,3]=>[5,2,5,1,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,5,3,1,4]=>[5,2,5,3,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,5,3,4,1]=>[4,1,4,2,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,5,4,1,3]=>[4,1,4,3,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,5,4,3,1]=>[4,1,4,3,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,1,4,5,5]=>[1,6,1,4,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,1,5,4,5]=>[4,2,4,1,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,1,5,5,4]=>[4,2,4,1,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,4,1,5,5]=>[5,3,1,2,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,4,5,1,5]=>[5,3,1,6,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,5,5,1]=>[1,6,4,2,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,5,1,4,5]=>[5,3,2,1,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,5,1,5,4]=>[5,3,2,1,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,5,4,1,5]=>[4,2,1,3,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,1,5,4,5,1]=>[5,3,2,4,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,5,1,4]=>[5,3,2,5,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,5,5,4,1]=>[4,2,1,4,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,1,5,5]=>[1,2,5,1,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[3,4,1,5,1,5]=>[5,6,2,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,1,5,5,1]=>[1,2,5,5,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,5,1,1,5]=>[1,2,2,4,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,5,1,5,1]=>[1,2,2,4,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,4,5,5,1,1]=>[1,2,2,1,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,5,1,1,4,5]=>[1,3,4,1,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,5,1,1,5,4]=>[2,4,5,2,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,1,4,1,5]=>[6,1,2,2,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,5,1,4,5,1]=>[1,3,4,4,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,5,1,5,1,4]=>[6,1,2,3,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,5,1,5,4,1]=>[6,1,2,3,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,4,1,1,5]=>[4,6,3,1,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,4,1,5,1]=>[6,1,5,3,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,4,5,1,1]=>[2,4,1,3,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,5,1,1,4]=>[1,3,1,4,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,5,5,1,4,1]=>[1,3,1,4,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,5,4,1,1]=>[2,4,2,1,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,1,1,3,5,5]=>[1,5,1,3,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[4,1,1,5,3,5]=>[4,1,4,1,2,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,1,5,5,3]=>[4,1,4,1,4,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,1,3,1,5,5]=>[4,1,6,2,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,3,5,1,5]=>[6,3,1,1,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,3,5,5,1]=>[1,5,3,3,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,1,5,1,3,5]=>[6,3,3,2,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,5,1,5,3]=>[5,2,2,1,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,5,3,1,5]=>[4,1,1,2,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,1,5,3,5,1]=>[6,3,3,4,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,5,5,1,3]=>[1,5,5,1,4,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,5,5,3,1]=>[4,1,1,4,2,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,3,1,1,5,5]=>[4,3,2,4,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,1,5,1,5]=>[5,4,3,2,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,1,5,5,1]=>[5,4,3,2,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,5,1,1,5]=>[2,1,4,5,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,5,1,5,1]=>[6,5,1,2,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,5,5,1,1]=>[2,1,4,2,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,5,1,1,3,5]=>[1,2,4,1,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,5,1,1,5,3]=>[1,2,4,1,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,5,1,3,1,5]=>[1,2,4,3,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,1,3,5,1]=>[1,2,4,3,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,5,1,5,1,3]=>[1,2,4,5,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,5,1,5,3,1]=>[5,6,1,2,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,5,3,1,1,5]=>[4,5,2,2,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,5,3,1,5,1]=>[5,6,3,3,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,5,3,5,1,1]=>[1,2,6,3,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,5,1,1,3]=>[1,2,1,4,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,5,5,1,3,1]=>[1,2,1,4,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,5,3,1,1]=>[3,4,3,1,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,1,1,3,4,5]=>[1,4,1,3,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,1,1,3,5,4]=>[2,5,2,4,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,1,4,3,5]=>[2,5,2,5,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,1,4,5,3]=>[1,4,1,4,2,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,1,5,3,4]=>[1,4,1,5,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,1,5,4,3]=>[2,5,2,6,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,1,3,1,4,5]=>[1,4,3,6,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,3,1,5,4]=>[6,2,1,4,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,4,1,5]=>[1,4,3,2,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,3,4,5,1]=>[1,4,3,2,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,1,3,5,1,4]=>[6,2,1,1,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[5,1,3,5,4,1]=>[6,2,1,1,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,1,4,1,3,5]=>[6,2,2,3,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,1,4,1,5,3]=>[5,1,1,2,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,1,4,3,1,5]=>[5,1,1,4,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,4,3,5,1]=>[6,2,2,5,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,4,5,1,3]=>[1,4,4,2,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,1,4,5,3,1]=>[5,1,1,6,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,1,5,1,3,4]=>[1,4,5,4,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,5,1,4,3]=>[5,1,2,1,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,1,5,3,1,4]=>[5,1,2,3,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,1,5,3,4,1]=>[5,1,2,3,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,5,4,1,3]=>[6,2,3,5,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,5,4,3,1]=>[5,1,2,4,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,1,1,4,5]=>[3,1,1,3,6,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,1,1,5,4]=>[4,2,2,4,1,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,3,1,4,1,5]=>[5,3,3,1,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,3,1,4,5,1]=>[5,3,3,1,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,3,1,5,1,4]=>[5,3,3,2,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,3,1,5,4,1]=>[4,2,2,1,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,3,4,1,1,5]=>[4,2,5,1,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,3,4,1,5,1]=>[5,3,6,2,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,3,4,5,1,1]=>[1,6,2,2,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,3,5,1,1,4]=>[1,6,3,4,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,3,5,1,4,1]=>[6,4,1,2,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,5,4,1,1]=>[4,2,6,3,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,1,1,3,5]=>[2,1,6,2,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,4,1,1,5,3]=>[4,3,1,4,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,4,1,3,1,5]=>[4,3,1,6,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,4,1,3,5,1]=>[6,5,3,1,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,4,1,5,1,3]=>[6,5,3,3,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,4,1,5,3,1]=>[4,3,1,1,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,4,3,1,1,5]=>[4,3,3,2,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,4,3,1,5,1]=>[5,4,4,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,3,5,1,1]=>[2,1,1,4,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,4,5,1,1,3]=>[2,1,3,5,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,4,5,1,3,1]=>[3,2,4,6,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,5,3,1,1]=>[3,2,4,1,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,5,1,1,3,4]=>[1,1,4,1,3,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,5,1,1,4,3]=>[2,2,5,2,5,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[5,5,1,3,1,4]=>[1,1,4,3,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,5,1,3,4,1]=>[1,1,4,3,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,5,1,4,1,3]=>[1,1,4,4,5,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,5,1,4,3,1]=>[5,5,1,1,4,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,5,3,1,1,4]=>[3,3,1,1,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[5,5,3,1,4,1]=>[5,5,3,3,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,5,3,4,1,1]=>[1,1,6,2,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,5,4,1,1,3]=>[2,2,1,6,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,5,4,1,3,1]=>[4,4,3,1,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,5,4,3,1,1]=>[3,3,2,2,1,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,3,4,5,6]=>[1,1,3,2,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,3,4,6,5]=>[2,2,4,3,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,3,5,4,6]=>[2,2,4,4,1,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,3,5,6,4]=>[1,1,3,3,2,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,3,6,4,5]=>[1,1,3,4,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,3,6,5,4]=>[2,2,4,5,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,4,3,5,6]=>[2,2,5,1,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,4,3,6,5]=>[2,2,5,1,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,4,5,3,6]=>[1,1,4,2,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,4,5,6,3]=>[1,1,4,2,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,4,6,3,5]=>[1,1,4,3,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,4,6,5,3]=>[3,3,6,5,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,5,3,4,6]=>[1,1,5,6,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,5,3,6,4]=>[5,5,2,3,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,5,4,3,6]=>[2,2,6,1,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,5,4,6,3]=>[4,4,1,3,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,5,6,3,4]=>[1,1,5,2,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,5,6,4,3]=>[4,4,1,5,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,6,3,4,5]=>[1,1,6,5,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,6,3,5,4]=>[4,4,2,1,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,6,4,3,5]=>[3,3,1,1,2,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,6,4,5,3]=>[3,3,1,1,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,6,5,3,4]=>[3,3,1,2,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,6,5,4,3]=>[3,3,1,2,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,1,4,5,6]=>[1,3,6,4,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,1,4,6,5]=>[6,1,4,2,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,1,5,4,6]=>[6,1,4,3,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,1,5,6,4]=>[4,6,2,1,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,1,6,4,5]=>[3,5,1,1,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,3,1,6,5,4]=>[3,5,1,1,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,4,1,5,6]=>[1,3,2,5,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,4,1,6,5]=>[4,6,5,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,5,1,6]=>[1,3,2,2,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,4,5,6,1]=>[1,3,2,2,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,4,6,1,5]=>[1,3,2,3,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,3,4,6,5,1]=>[2,4,3,4,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,5,1,4,6]=>[6,1,1,2,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,3,5,1,6,4]=>[6,1,1,2,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,5,4,1,6]=>[6,1,1,5,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,5,4,6,1]=>[6,1,1,5,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,3,5,6,1,4]=>[1,3,3,2,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,5,6,4,1]=>[1,3,3,2,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,6,1,4,5]=>[1,3,4,3,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,6,1,5,4]=>[6,1,2,1,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,6,4,1,5]=>[6,1,2,4,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,6,4,5,1]=>[1,3,4,6,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,6,5,1,4]=>[6,1,2,5,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,3,6,5,4,1]=>[2,4,5,1,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,1,3,5,6]=>[1,4,5,3,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,1,3,6,5]=>[6,2,3,1,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,1,5,3,6]=>[5,1,2,2,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,1,5,6,3]=>[5,1,2,2,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,1,6,3,5]=>[6,2,3,4,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,1,6,5,3]=>[5,1,2,3,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,3,1,5,6]=>[5,1,4,3,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,1,6,5]=>[3,6,2,1,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,3,5,1,6]=>[6,2,5,1,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,3,5,6,1]=>[2,5,1,4,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,4,3,6,1,5]=>[6,2,5,2,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,3,6,5,1]=>[5,1,4,1,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,4,5,1,3,6]=>[1,4,2,4,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,4,5,1,6,3]=>[5,1,6,1,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,5,3,1,6]=>[3,6,4,1,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,4,5,3,6,1]=>[1,4,2,6,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,5,6,1,3]=>[1,4,2,2,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,4,5,6,3,1]=>[1,4,2,2,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,6,1,3,5]=>[6,2,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,4,6,1,5,3]=>[6,2,1,1,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,6,3,1,5]=>[6,2,1,3,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,6,3,5,1]=>[6,2,1,3,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,4,6,5,1,3]=>[6,2,1,5,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,6,5,3,1]=>[3,6,5,2,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,1,3,4,6]=>[1,5,4,3,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,1,3,6,4]=>[6,3,2,1,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,1,4,3,6]=>[5,2,1,1,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,1,4,6,3]=>[6,3,2,2,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,5,1,6,3,4]=>[5,2,1,3,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,1,6,4,3]=>[5,2,1,3,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,3,1,4,6]=>[6,3,4,4,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,3,1,6,4]=>[4,1,2,2,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,5,3,4,1,6]=>[4,1,2,5,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,3,4,6,1]=>[1,5,6,2,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,3,6,1,4]=>[6,3,4,2,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,3,6,4,1]=>[5,2,3,1,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,4,1,3,6]=>[6,3,5,3,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,4,1,6,3]=>[4,1,3,1,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,5,4,3,1,6]=>[4,1,3,3,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,5,4,3,6,1]=>[2,6,1,1,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,4,6,1,3]=>[6,3,5,1,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,5,4,6,3,1]=>[4,1,3,6,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,5,6,1,3,4]=>[1,5,2,3,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,5,6,1,4,3]=>[2,6,3,4,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,6,3,1,4]=>[5,2,6,2,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,6,3,4,1]=>[4,1,5,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,5,6,4,1,3]=>[4,1,5,2,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,6,4,3,1]=>[4,1,5,2,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,1,3,4,5]=>[1,6,3,3,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,6,1,3,5,4]=>[6,4,1,1,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,6,1,4,3,5]=>[6,4,1,2,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,1,4,5,3]=>[3,1,5,6,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,1,5,3,4]=>[4,2,6,1,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,1,5,4,3]=>[4,2,6,1,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,3,1,4,5]=>[5,3,2,3,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,3,1,5,4]=>[4,2,1,2,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,6,3,4,1,5]=>[4,2,1,5,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,6,3,4,5,1]=>[1,6,5,2,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,3,5,1,4]=>[6,4,3,1,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,3,5,4,1]=>[4,2,1,6,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,4,1,3,5]=>[6,4,4,3,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,6,4,1,5,3]=>[4,2,2,1,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,6,4,3,1,5]=>[4,2,2,3,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,6,4,3,5,1]=>[3,1,1,2,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,4,5,1,3]=>[3,1,1,4,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,4,5,3,1]=>[3,1,1,4,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,6,5,1,3,4]=>[3,1,2,6,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,5,1,4,3]=>[5,3,4,1,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,6,5,3,1,4]=>[3,1,2,1,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,6,5,3,4,1]=>[4,2,3,2,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,5,4,1,3]=>[4,2,3,3,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,5,4,3,1]=>[3,1,2,2,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,1,1,4,5,6]=>[1,6,1,4,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,1,4,6,5]=>[3,1,3,6,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,1,5,4,6]=>[4,2,4,1,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,1,5,6,4]=>[4,2,4,1,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,1,6,4,5]=>[3,1,3,1,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,1,1,6,5,4]=>[3,1,3,1,2,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,1,4,1,5,6]=>[5,3,1,2,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,4,1,6,5]=>[5,3,1,2,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,4,5,1,6]=>[5,3,1,6,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,4,5,6,1]=>[1,6,4,2,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,4,6,1,5]=>[6,4,2,1,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,4,6,5,1]=>[6,4,2,1,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,5,1,4,6]=>[6,4,3,2,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,5,1,6,4]=>[5,3,2,1,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,5,4,1,6]=>[4,2,1,3,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,1,5,4,6,1]=>[6,4,3,5,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,5,6,1,4]=>[1,6,5,2,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,6,4,1]=>[4,2,1,5,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,1,6,1,4,5]=>[3,1,1,5,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,6,1,5,4]=>[4,2,2,6,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,6,4,1,5]=>[4,2,2,2,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,1,6,4,5,1]=>[3,1,1,1,4,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,6,5,1,4]=>[5,3,3,4,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,6,5,4,1]=>[4,2,2,3,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,4,1,1,5,6]=>[1,2,5,1,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[3,4,1,1,6,5]=>[4,5,1,4,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,1,5,1,6]=>[5,6,2,2,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,5,6,1]=>[1,2,5,5,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,4,1,6,1,5]=>[4,5,1,2,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,1,6,5,1]=>[5,6,2,3,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,5,1,1,6]=>[1,2,2,4,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,4,5,1,6,1]=>[1,2,2,4,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,5,6,1,1]=>[1,2,2,2,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,4,6,1,1,5]=>[1,2,3,3,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,4,6,1,5,1]=>[1,2,3,3,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,6,5,1,1]=>[2,3,4,1,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,1,1,4,6]=>[1,3,4,1,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,5,1,1,6,4]=>[3,5,6,3,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,5,1,4,1,6]=>[6,1,2,2,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,1,4,6,1]=>[6,1,2,2,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,5,1,6,1,4]=>[6,1,2,4,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,5,1,6,4,1]=>[6,1,2,4,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,4,1,1,6]=>[4,6,3,1,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,4,1,6,1]=>[6,1,5,3,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,4,6,1,1]=>[2,4,1,4,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,5,6,1,1,4]=>[1,3,2,3,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,5,6,1,4,1]=>[1,3,2,3,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,6,4,1,1]=>[1,3,2,6,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,1,1,4,5]=>[1,4,3,1,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,6,1,1,5,4]=>[2,5,4,2,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,1,4,1,5]=>[6,2,1,2,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,6,1,4,5,1]=>[1,4,3,4,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,6,1,5,1,4]=>[6,2,1,3,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,6,1,5,4,1]=>[6,2,1,3,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,6,4,1,1,5]=>[5,1,3,2,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,6,4,1,5,1]=>[5,1,3,2,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,6,4,5,1,1]=>[1,4,6,2,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,6,5,1,1,4]=>[5,1,4,1,5,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,6,5,1,4,1]=>[5,1,4,1,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,6,5,4,1,1]=>[2,5,1,1,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,1,3,5,6]=>[1,5,1,3,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,1,1,3,6,5]=>[2,6,2,4,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,1,5,3,6]=>[5,2,5,2,3,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,1,5,6,3]=>[4,1,4,1,5,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,1,6,3,5]=>[4,1,4,2,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,1,6,5,3]=>[4,1,4,2,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,1,3,1,5,6]=>[4,1,6,2,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,1,6,5]=>[4,1,6,2,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,3,5,1,6]=>[6,3,1,1,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,5,6,1]=>[1,5,3,3,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,3,6,1,5]=>[6,3,1,2,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,3,6,5,1]=>[6,3,1,2,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,5,1,3,6]=>[6,3,3,2,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,5,1,6,3]=>[5,2,2,1,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,5,3,1,6]=>[4,1,1,2,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[4,1,5,3,6,1]=>[6,3,3,4,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,5,6,1,3]=>[1,5,5,2,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,1,5,6,3,1]=>[4,1,1,5,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,6,1,3,5]=>[6,3,4,1,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,1,6,1,5,3]=>[4,1,2,6,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,1,6,3,1,5]=>[4,1,2,1,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,1,6,3,5,1]=>[6,3,4,3,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,6,5,1,3]=>[6,3,4,5,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,5,3,1]=>[4,1,2,3,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,1,1,5,6]=>[4,3,2,4,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,1,1,6,5]=>[3,2,1,3,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,3,1,5,1,6]=>[5,4,3,2,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,5,6,1]=>[4,3,2,1,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,6,1,5]=>[4,3,2,2,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,3,1,6,5,1]=>[3,2,1,1,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,3,5,1,1,6]=>[3,2,5,6,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,3,5,1,6,1]=>[6,5,1,2,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,5,6,1,1]=>[2,1,4,3,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,6,1,1,5]=>[2,1,5,4,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,6,1,5,1]=>[6,5,2,1,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,6,5,1,1]=>[2,1,5,1,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,5,1,1,3,6]=>[1,2,4,1,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,5,1,1,6,3]=>[1,2,4,1,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,5,1,3,1,6]=>[3,4,6,5,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,5,1,3,6,1]=>[1,2,4,3,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,5,1,6,1,3]=>[1,2,4,6,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,5,1,6,3,1]=>[5,6,1,3,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,5,3,1,1,6]=>[3,4,1,1,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[4,5,3,1,6,1]=>[3,4,1,1,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,5,3,6,1,1]=>[1,2,6,4,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,6,1,1,3]=>[1,2,2,3,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,5,6,1,3,1]=>[1,2,2,3,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,5,6,3,1,1]=>[1,2,2,5,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,6,1,1,3,5]=>[1,3,3,1,3,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[4,6,1,1,5,3]=>[1,3,3,1,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,6,1,3,1,5]=>[6,1,1,1,4,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,6,1,3,5,1]=>[6,1,1,1,1,2]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[4,6,1,5,1,3]=>[6,1,1,3,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,6,1,5,3,1]=>[6,1,1,3,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,6,3,1,1,5]=>[4,6,1,2,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,6,3,1,5,1]=>[6,1,3,4,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,6,3,5,1,1]=>[1,3,5,3,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,6,5,1,1,3]=>[2,4,1,5,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,6,5,1,3,1]=>[6,1,5,2,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,6,5,3,1,1]=>[3,5,2,1,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,1,1,3,4,6]=>[1,4,1,3,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,1,1,3,6,4]=>[1,4,1,3,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,1,4,3,6]=>[5,1,5,1,4,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[5,1,1,4,6,3]=>[1,4,1,4,3,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,1,1,6,3,4]=>[1,4,1,6,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,1,6,4,3]=>[3,6,3,1,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,1,3,1,4,6]=>[6,2,1,4,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,3,1,6,4]=>[3,6,5,1,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[5,1,3,4,1,6]=>[1,4,3,2,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,4,6,1]=>[1,4,3,2,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[5,1,3,6,1,4]=>[6,2,1,2,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[5,1,3,6,4,1]=>[6,2,1,2,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,4,1,3,6]=>[6,2,2,3,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,4,1,6,3]=>[5,1,1,2,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,1,4,3,1,6]=>[5,1,1,4,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,1,4,3,6,1]=>[6,2,2,5,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,4,6,1,3]=>[6,2,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[5,1,4,6,3,1]=>[6,2,2,1,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,6,1,3,4]=>[1,4,6,3,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,6,1,4,3]=>[6,2,4,1,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,6,3,1,4]=>[5,1,3,2,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,1,6,3,4,1]=>[5,1,3,2,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,6,4,1,3]=>[6,2,4,4,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,6,4,3,1]=>[3,6,1,1,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,3,1,1,4,6]=>[3,1,1,3,6,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,3,1,1,6,4]=>[3,1,1,3,1,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[5,3,1,4,1,6]=>[5,3,3,1,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,3,1,4,6,1]=>[6,4,4,2,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,3,1,6,1,4]=>[3,1,1,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[5,3,1,6,4,1]=>[4,2,2,2,2,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[5,3,4,1,1,6]=>[4,2,5,1,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,3,4,1,6,1]=>[4,2,5,1,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,4,6,1,1]=>[1,6,2,3,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,3,6,1,1,4]=>[1,6,4,3,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,3,6,1,4,1]=>[6,4,2,1,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,6,4,1,1]=>[5,3,1,3,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,4,1,1,3,6]=>[2,1,6,2,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,1,1,6,3]=>[4,3,1,4,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,4,1,3,1,6]=>[4,3,1,6,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,4,1,3,6,1]=>[6,5,3,1,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,4,1,6,1,3]=>[6,5,3,4,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,1,6,3,1]=>[4,3,1,2,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,4,3,1,1,6]=>[3,2,2,1,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,4,3,1,6,1]=>[3,2,2,1,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,4,3,6,1,1]=>[2,1,1,5,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,4,6,1,1,3]=>[2,1,4,4,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[5,4,6,1,3,1]=>[6,5,1,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[5,4,6,3,1,1]=>[4,3,6,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,6,1,1,3,4]=>[1,2,3,1,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,6,1,1,4,3]=>[2,3,4,2,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,6,1,3,1,4]=>[1,2,3,3,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,6,1,3,4,1]=>[1,2,3,3,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,6,1,4,1,3]=>[1,2,3,4,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,6,1,4,3,1]=>[3,4,5,6,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,3,1,1,4]=>[1,2,5,6,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,6,3,1,4,1]=>[5,6,2,3,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,6,3,4,1,1]=>[1,2,5,2,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,6,4,1,1,3]=>[1,2,6,5,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,6,4,1,3,1]=>[4,5,2,1,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,6,4,3,1,1]=>[3,4,1,2,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,1,1,3,4,5]=>[1,3,1,3,2,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[6,1,1,3,5,4]=>[2,4,2,4,4,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[6,1,1,4,3,5]=>[2,4,2,5,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,1,1,4,5,3]=>[1,3,1,4,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,1,5,3,4]=>[1,3,1,5,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,1,1,5,4,3]=>[2,4,2,6,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,1,3,1,4,5]=>[1,3,3,6,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,1,3,1,5,4]=>[6,1,1,4,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,3,4,1,5]=>[1,3,3,2,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,1,3,4,5,1]=>[1,3,3,2,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,3,5,1,4]=>[6,1,1,1,2,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[6,1,3,5,4,1]=>[6,1,1,1,5,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[6,1,4,1,3,5]=>[6,1,2,3,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,1,4,1,5,3]=>[6,1,2,3,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,1,4,3,1,5]=>[6,1,2,5,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,3,5,1]=>[6,1,2,5,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,1,4,5,1,3]=>[1,3,4,2,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,4,5,3,1]=>[3,5,6,4,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,5,1,3,4]=>[1,3,5,4,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,5,1,4,3]=>[6,1,3,2,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,1,5,3,1,4]=>[6,1,3,4,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,1,5,3,4,1]=>[4,6,1,2,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,1,5,4,1,3]=>[6,1,3,5,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,1,5,4,3,1]=>[4,6,1,3,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,3,1,1,4,5]=>[1,5,6,1,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,1,1,5,4]=>[4,1,2,4,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,3,1,4,1,5]=>[5,2,3,1,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,3,1,4,5,1]=>[5,2,3,1,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,1,5,1,4]=>[5,2,3,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,3,1,5,4,1]=>[4,1,2,1,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[6,3,4,1,1,5]=>[4,1,5,1,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[6,3,4,1,5,1]=>[5,2,6,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,3,4,5,1,1]=>[1,5,2,2,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,3,5,1,1,4]=>[1,5,3,4,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,3,5,1,4,1]=>[6,3,1,2,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,3,5,4,1,1]=>[4,1,6,3,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,4,1,1,3,5]=>[1,6,5,1,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,4,1,1,5,3]=>[4,2,1,4,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[6,4,1,3,1,5]=>[4,2,1,6,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,4,1,3,5,1]=>[6,4,3,1,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,4,1,5,1,3]=>[6,4,3,3,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,4,1,5,3,1]=>[4,2,1,1,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[6,4,3,1,1,5]=>[4,2,3,2,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,4,3,1,5,1]=>[5,3,4,3,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,4,3,5,1,1]=>[3,1,2,5,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,4,5,1,1,3]=>[1,6,2,4,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,4,5,1,3,1]=>[3,1,4,6,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,4,5,3,1,1]=>[3,1,4,1,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[6,5,1,1,3,4]=>[2,1,5,2,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,5,1,1,4,3]=>[2,1,5,2,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,5,1,3,1,4]=>[6,5,2,1,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,5,1,3,4,1]=>[2,1,5,4,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,1,4,1,3]=>[6,5,2,2,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,5,1,4,3,1]=>[5,4,1,1,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,5,3,1,1,4]=>[3,2,1,1,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,5,3,1,4,1]=>[5,4,3,3,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,5,3,4,1,1]=>[4,3,2,5,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,4,1,1,3]=>[2,1,1,6,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,5,4,1,3,1]=>[4,3,3,1,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,4,3,1,1]=>[3,2,2,2,1,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,2,2,2]=>[1,2,1,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[2,1,2,2,2,2]=>[2,1,3,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,1,2,2,2]=>[2,2,1,3,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,2,1,2,2]=>[2,2,2,1,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,2,2,1,2]=>[2,2,2,2,1,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,2,2,2,2,1]=>[2,2,2,2,2,1]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,2,2,2,3]=>[1,2,1,1,1,2]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,2,2,3,2]=>[2,3,2,2,3,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,3,2,2]=>[2,3,2,3,1,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,2,2,2]=>[2,3,3,1,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,2,2,2,2]=>[2,4,1,2,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,2,2,2,3]=>[2,1,3,2,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,2,2,3,2]=>[2,1,3,2,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,2,3,2,2]=>[2,1,3,3,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,2,2,2]=>[2,1,4,1,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,1,2,2,3]=>[2,2,1,3,2,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,1,2,3,2]=>[2,2,1,3,3,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,1,3,2,2]=>[2,2,1,4,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,2,1,2,3]=>[2,2,2,1,3,3]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,2,1,3,2]=>[2,2,2,1,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,2,2,1,3]=>[2,2,2,2,1,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,2,2,2,3,1]=>[1,1,1,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,2,2,3,1,2]=>[1,1,1,2,6,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,2,2,3,2,1]=>[2,2,2,3,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,3,1,2,2]=>[1,1,2,6,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,2,3,2,1,2]=>[2,2,3,1,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,3,2,2,1]=>[2,2,3,1,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,3,1,2,2,2]=>[1,2,6,2,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,2,1,2,2]=>[2,3,1,1,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,2,2,1,2]=>[2,3,1,2,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,2,2,2,1]=>[2,3,1,2,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,1,2,2,2,2]=>[1,6,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,2,1,2,2,2]=>[2,1,1,3,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,2,1,2,2]=>[2,1,2,1,3,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,2,2,1,2]=>[2,1,2,2,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,2,2,2,1]=>[2,1,2,2,2,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,2,2,2,4]=>[1,2,1,1,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,2,4,2]=>[1,2,1,1,3,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,2,4,2,2]=>[1,2,1,3,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,4,2,2,2]=>[1,2,3,6,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,2,2,2,2]=>[1,4,6,1,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,2,2,2,4]=>[2,1,3,2,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,2,2,4,2]=>[3,2,4,3,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,2,4,2,2]=>[3,2,4,5,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,2,2,2]=>[3,2,6,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,1,2,2,4]=>[2,2,1,3,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,2,4,2]=>[3,3,2,4,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,1,4,2,2]=>[3,3,2,6,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,2,1,2,4]=>[2,2,2,1,3,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,2,1,4,2]=>[3,3,3,2,6,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,2,2,1,4]=>[2,2,2,2,1,5]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,2,2,2,4,1]=>[1,1,1,1,3,5]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,2,2,4,1,2]=>[1,1,1,3,5,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,2,4,2,1]=>[3,3,3,5,1,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,4,1,2,2]=>[1,1,3,5,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,4,2,1,2]=>[3,3,5,1,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,4,2,2,1]=>[3,3,5,1,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,4,1,2,2,2]=>[1,3,5,2,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,2,1,2,2]=>[3,5,1,2,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,2,2,1,2]=>[3,5,1,3,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,2,2,2,1]=>[3,5,1,3,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,2,2,2,2]=>[1,5,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,2,1,2,2,2]=>[3,1,2,4,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,2,2,1,2,2]=>[3,1,3,2,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,2,2,2,1,2]=>[3,1,3,3,2,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,2,2,2,2,1]=>[3,1,3,3,3,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,2,2,2,5]=>[1,2,1,1,1,4]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,2,2,5,2]=>[1,2,1,1,4,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,2,5,2,2]=>[1,2,1,4,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,5,2,2,2]=>[1,2,4,5,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,2,2,2,2]=>[1,5,5,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[2,1,2,2,2,5]=>[2,1,3,2,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,2,2,5,2]=>[2,1,3,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,2,5,2,2]=>[2,1,3,5,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,2,2,2]=>[4,3,1,1,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,1,2,2,5]=>[2,2,1,3,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,1,2,5,2]=>[2,2,1,3,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,1,5,2,2]=>[4,4,3,1,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,2,1,2,5]=>[2,2,2,1,3,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,2,1,5,2]=>[4,4,4,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,2,2,1,5]=>[2,2,2,2,1,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,2,2,2,5,1]=>[1,1,1,1,4,4]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[2,2,2,5,1,2]=>[1,1,1,4,4,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,2,5,2,1]=>[2,2,2,5,6,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,5,1,2,2]=>[1,1,4,4,2,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,5,2,1,2]=>[2,2,5,6,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,5,2,2,1]=>[2,2,5,6,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,2,2,2]=>[1,4,4,2,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,5,2,1,2,2]=>[2,5,6,1,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,2,2,1,2]=>[2,5,6,2,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,2,2,2,1]=>[2,5,6,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,2,2,2,2]=>[1,4,2,1,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,2,1,2,2,2]=>[2,6,1,3,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,2,2,1,2,2]=>[2,6,2,1,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,2,2,2,1,2]=>[2,6,2,2,1,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,2,2,2,2,1]=>[2,6,2,2,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,2,2,2,6]=>[1,2,1,1,1,5]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,2,2,2,6,2]=>[1,2,1,1,5,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,2,6,2,2]=>[1,2,1,5,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,6,2,2,2]=>[1,2,5,4,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,6,2,2,2,2]=>[1,6,4,1,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,2,2,2,6]=>[2,1,3,2,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,1,2,2,6,2]=>[2,1,3,2,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,2,6,2,2]=>[2,1,3,6,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,6,2,2,2]=>[3,2,1,6,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,1,2,2,6]=>[2,2,1,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,2,1,2,6,2]=>[2,2,1,3,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,1,6,2,2]=>[3,3,2,1,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,2,1,2,6]=>[2,2,2,1,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,2,2,1,6,2]=>[3,3,3,2,1,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,2,2,1,6]=>[3,3,3,3,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,2,2,2,6,1]=>[1,1,1,1,5,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,2,2,6,1,2]=>[1,1,1,5,3,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,2,6,2,1]=>[2,2,2,6,5,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,6,1,2,2]=>[1,1,5,3,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,6,2,1,2]=>[2,2,6,5,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,6,2,2,1]=>[2,2,6,5,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,6,1,2,2,2]=>[1,5,3,2,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,6,2,1,2,2]=>[2,6,5,1,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,2,2,1,2]=>[2,6,5,2,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,2,2,2,1]=>[2,6,5,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,1,2,2,2,2]=>[1,3,2,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[6,2,1,2,2,2]=>[2,5,1,3,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,2,2,1,2,2]=>[2,5,2,1,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,2,2,2,1,2]=>[2,5,2,2,1,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,2,2,2,2,1]=>[2,5,2,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,2,2,2,3,3]=>[1,2,1,1,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,2,3,2,3]=>[2,3,2,3,1,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,3,3,2]=>[2,3,2,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,2,2,3]=>[2,3,3,1,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,2,3,2]=>[2,3,3,1,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,3,3,2,2]=>[2,3,3,2,1,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,2,2,2,3]=>[2,4,1,2,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,2,2,3,2]=>[2,4,1,2,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,3,2,2]=>[2,4,1,3,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,3,2,2,2]=>[2,4,2,1,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,2,2,3,3]=>[2,1,3,2,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,2,3,2,3]=>[2,1,3,3,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,1,2,3,3,2]=>[2,1,3,3,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,2,2,3]=>[2,1,4,1,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,2,3,2]=>[2,1,4,1,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,3,3,2,2]=>[2,1,4,2,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,1,2,3,3]=>[2,2,1,3,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,1,3,2,3]=>[2,2,1,4,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,1,3,3,2]=>[2,2,1,4,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,2,1,3,3]=>[2,2,2,1,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,2,2,3,1,3]=>[1,1,1,2,6,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,2,2,3,3,1]=>[1,1,1,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,2,3,1,2,3]=>[1,1,2,6,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,2,3,1,3,2]=>[3,3,4,1,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,3,2,1,3]=>[2,2,3,1,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,3,2,3,1]=>[3,3,4,2,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,3,3,1,2]=>[1,1,2,1,6,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,2,3,3,2,1]=>[2,2,3,2,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,3,1,2,2,3]=>[1,2,6,2,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,3,1,2,3,2]=>[3,4,1,4,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,1,3,2,2]=>[3,4,1,5,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,1,2,3]=>[2,3,1,1,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,3,2,1,3,2]=>[2,3,1,1,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,2,2,1,3]=>[2,3,1,2,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,2,2,3,1]=>[3,4,2,3,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,2,3,1,2]=>[3,4,2,4,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,2,3,2,1]=>[2,3,1,3,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,3,3,1,2,2]=>[1,2,1,6,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,3,2,1,2]=>[2,3,2,1,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,3,2,2,1]=>[2,3,2,1,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,1,2,2,2,3]=>[1,6,2,1,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,1,2,2,3,2]=>[3,1,4,3,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,2,3,2,2]=>[3,1,4,4,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,3,2,2,2]=>[3,1,5,2,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,2,1,2,2,3]=>[2,1,1,3,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,1,2,3,2]=>[2,1,1,3,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,2,1,3,2,2]=>[2,1,1,4,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,2,2,1,2,3]=>[2,1,2,1,3,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,2,1,3,2]=>[2,1,2,1,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,2,2,2,1,3]=>[2,1,2,2,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,2,2,2,3,1]=>[3,2,3,3,4,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,2,3,1,2]=>[3,2,3,4,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,2,3,2,1]=>[2,1,2,3,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,3,1,2,2]=>[3,2,4,1,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,2,1,2]=>[2,1,3,1,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,2,3,2,2,1]=>[2,1,3,1,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,3,1,2,2,2]=>[1,1,6,2,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,3,2,1,2,2]=>[2,2,1,1,3,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,3,2,2,1,2]=>[2,2,1,2,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,3,2,2,2,1]=>[2,2,1,2,2,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,2,2,3,4]=>[1,2,1,1,2,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,2,4,3]=>[2,3,2,2,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,2,3,2,4]=>[2,3,2,3,1,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,3,4,2]=>[1,2,1,2,2,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,2,4,2,3]=>[1,2,1,3,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,2,4,3,2]=>[2,3,2,4,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,2,3,2,2,4]=>[2,3,3,1,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,2,4,2]=>[3,4,4,2,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,4,2,2]=>[1,2,2,2,6,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,4,2,2,3]=>[1,2,3,6,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,2,3,2]=>[3,4,5,1,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,3,2,2]=>[2,3,4,1,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,2,2,4]=>[2,4,1,2,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,2,2,4,2]=>[3,5,2,3,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,2,4,2,2]=>[3,5,2,5,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,4,2,2,2]=>[1,3,2,6,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,2,2,2,3]=>[1,4,6,1,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,2,2,3,2]=>[3,6,1,3,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,3,2,2]=>[3,6,1,4,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,3,2,2,2]=>[2,5,1,1,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,2,2,3,4]=>[2,1,3,2,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,2,2,4,3]=>[2,1,3,2,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,2,3,2,4]=>[2,1,3,3,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,2,3,4,2]=>[3,2,4,4,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,4,2,3]=>[3,2,4,5,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,2,4,3,2]=>[2,1,3,4,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,3,2,2,4]=>[2,1,4,1,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,3,2,4,2]=>[3,2,5,2,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,3,4,2,2]=>[3,2,5,4,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,2,2,3]=>[3,2,6,1,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,4,2,3,2]=>[3,2,6,1,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,3,2,2]=>[2,1,5,1,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,1,2,3,4]=>[2,2,1,3,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,2,1,2,4,3]=>[2,2,1,3,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,1,3,2,4]=>[2,2,1,4,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,2,1,3,4,2]=>[3,3,2,5,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,1,4,2,3]=>[3,3,2,6,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,2,1,4,3,2]=>[2,2,1,5,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,2,1,3,4]=>[2,2,2,1,4,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,2,1,4,3]=>[2,2,2,1,5,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,2,2,3,1,4]=>[1,1,1,2,6,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,2,2,3,4,1]=>[1,1,1,2,2,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,2,4,1,3]=>[1,1,1,3,5,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,2,4,3,1]=>[3,3,3,5,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,2,3,1,2,4]=>[1,1,2,6,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,3,1,4,2]=>[3,3,4,1,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,2,3,2,1,4]=>[2,2,3,1,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,3,2,4,1]=>[2,2,3,1,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,3,4,1,2]=>[1,1,2,2,5,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,2,3,4,2,1]=>[3,3,4,4,1,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,4,1,2,3]=>[1,1,3,5,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,4,1,3,2]=>[2,2,4,6,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,2,4,2,1,3]=>[3,3,5,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,2,4,2,3,1]=>[3,3,5,1,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,4,3,1,2]=>[3,3,5,2,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,2,4,3,2,1]=>[2,2,4,1,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,3,1,2,2,4]=>[1,2,6,2,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,1,2,4,2]=>[3,4,1,4,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,3,1,4,2,2]=>[3,4,1,6,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,3,2,1,2,4]=>[2,3,1,1,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,2,1,4,2]=>[3,4,2,2,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,2,2,1,4]=>[2,3,1,2,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,2,2,4,1]=>[2,3,1,2,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,2,4,1,2]=>[2,3,1,4,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,2,4,2,1]=>[3,4,2,5,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,4,1,2,2]=>[1,2,2,5,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,4,2,1,2]=>[3,4,4,1,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,4,2,2,1]=>[3,4,4,1,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,1,2,2,3]=>[1,3,5,2,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,4,1,2,3,2]=>[2,4,6,3,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,1,3,2,2]=>[2,4,6,4,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,4,2,1,2,3]=>[3,5,1,2,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,2,1,3,2]=>[3,5,1,2,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,4,2,2,1,3]=>[3,5,1,3,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,2,2,3,1]=>[3,5,1,3,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,2,3,1,2]=>[3,5,1,4,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,4,2,3,2,1]=>[3,5,1,4,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,3,1,2,2]=>[3,5,2,1,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,3,2,1,2]=>[2,4,1,1,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,4,3,2,2,1]=>[2,4,1,1,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,1,2,2,2,4]=>[1,6,2,1,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,2,2,4,2]=>[3,1,4,3,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,2,4,2,2]=>[3,1,4,5,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,4,2,2,2]=>[3,1,6,1,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,1,2,2,4]=>[2,1,1,3,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,2,4,2]=>[3,2,2,4,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,1,4,2,2]=>[3,2,2,6,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,2,1,2,4]=>[2,1,2,1,3,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,2,1,4,2]=>[3,2,3,2,6,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,2,2,1,4]=>[2,1,2,2,1,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,2,2,2,4,1]=>[2,1,2,2,4,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,2,2,4,1,2]=>[2,1,2,4,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,2,4,2,1]=>[3,2,3,5,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,4,1,2,2]=>[2,1,4,6,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,4,2,1,2]=>[3,2,5,1,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,4,2,2,1]=>[3,2,5,1,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,4,1,2,2,2]=>[1,2,5,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,4,2,1,2,2]=>[3,4,1,2,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,2,2,1,2]=>[3,4,1,3,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,2,2,2,1]=>[3,4,1,3,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,2,2,2,3]=>[1,5,2,1,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,1,2,2,3,2]=>[2,6,3,2,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,2,3,2,2]=>[2,6,3,3,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,3,2,2,2]=>[2,6,4,1,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,2,1,2,2,3]=>[3,1,2,4,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,2,1,2,3,2]=>[3,1,2,4,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,1,3,2,2]=>[3,1,2,5,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,2,2,1,2,3]=>[3,1,3,2,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,2,2,1,3,2]=>[3,1,3,2,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,2,2,2,1,3]=>[3,1,3,3,2,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,2,2,2,3,1]=>[3,1,3,3,4,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,2,2,3,1,2]=>[3,1,3,4,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,2,2,3,2,1]=>[3,1,3,4,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,3,1,2,2]=>[3,1,4,1,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,2,3,2,1,2]=>[3,1,4,2,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,3,2,2,1]=>[3,1,4,2,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,1,2,2,2]=>[3,2,1,4,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,2,1,2,2]=>[2,1,1,1,3,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,3,2,2,1,2]=>[2,1,1,2,1,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,3,2,2,2,1]=>[2,1,1,2,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,2,3,5]=>[1,2,1,1,2,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,2,5,3]=>[1,2,1,1,4,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,2,3,2,5]=>[2,3,2,3,1,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,2,3,5,2]=>[1,2,1,2,3,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,2,5,2,3]=>[1,2,1,4,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,2,5,3,2]=>[3,4,3,6,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,3,2,2,5]=>[2,3,3,1,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,3,2,5,2]=>[2,3,3,1,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,3,5,2,2]=>[1,2,2,3,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,5,2,2,3]=>[1,2,4,5,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,5,2,3,2]=>[2,3,5,6,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,5,3,2,2]=>[3,4,6,1,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,2,2,5]=>[2,4,1,2,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,3,2,2,5,2]=>[2,4,1,2,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,2,5,2,2]=>[2,4,1,5,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,5,2,2,2]=>[1,3,3,5,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,5,2,2,2,3]=>[1,5,5,1,1,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,5,2,2,3,2]=>[4,1,1,4,5,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,2,3,2,2]=>[4,1,1,5,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,3,2,2,2]=>[4,1,2,3,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,2,3,5]=>[2,1,3,2,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,2,5,3]=>[3,2,4,3,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,2,3,2,5]=>[2,1,3,3,1,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,2,3,5,2]=>[2,1,3,3,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,2,5,2,3]=>[2,1,3,5,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,2,5,3,2]=>[3,2,4,6,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,3,2,2,5]=>[2,1,4,1,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,3,2,5,2]=>[2,1,4,1,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,3,5,2,2]=>[2,1,4,4,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,1,5,2,2,3]=>[4,3,1,1,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,5,2,3,2]=>[4,3,1,1,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,5,3,2,2]=>[4,3,1,2,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,2,3,5]=>[2,2,1,3,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,1,2,5,3]=>[3,3,2,4,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,2,1,3,2,5]=>[2,2,1,4,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,2,1,3,5,2]=>[2,2,1,4,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,2,1,5,2,3]=>[4,4,3,1,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,2,1,5,3,2]=>[4,4,3,1,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,2,1,3,5]=>[2,2,2,1,4,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,2,2,1,5,3]=>[4,4,4,3,1,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,2,2,3,1,5]=>[1,1,1,2,6,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,2,2,3,5,1]=>[1,1,1,2,3,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,2,5,1,3]=>[1,1,1,4,4,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,2,2,5,3,1]=>[3,3,3,6,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[2,2,3,1,2,5]=>[1,1,2,6,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,2,3,1,5,2]=>[4,4,5,2,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,2,3,2,1,5]=>[2,2,3,1,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,3,2,5,1]=>[2,2,3,1,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,3,5,1,2]=>[1,1,2,3,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,3,5,2,1]=>[2,2,3,4,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,5,1,2,3]=>[1,1,4,4,2,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,2,5,1,3,2]=>[2,2,5,5,4,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,5,2,1,3]=>[2,2,5,6,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,5,2,3,1]=>[1,1,4,5,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,5,3,1,2]=>[3,3,6,1,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,2,5,3,2,1]=>[3,3,6,1,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,2,2,5]=>[1,2,6,2,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,1,2,5,2]=>[1,2,6,2,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,5,2,2]=>[4,5,2,1,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,3,2,1,2,5]=>[2,3,1,1,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,3,2,1,5,2]=>[4,5,3,3,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,2,2,1,5]=>[2,3,1,2,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,2,2,5,1]=>[2,3,1,2,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,3,2,5,1,2]=>[2,3,1,5,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,2,5,2,1]=>[2,3,1,5,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,5,1,2,2]=>[1,2,3,4,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,5,2,1,2]=>[2,3,4,6,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,5,2,2,1]=>[2,3,4,6,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,2,2,3]=>[1,4,4,2,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,5,1,2,3,2]=>[2,5,5,3,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,5,1,3,2,2]=>[2,5,5,4,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,2,1,2,3]=>[2,5,6,1,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,5,2,1,3,2]=>[2,5,6,1,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,2,2,1,3]=>[2,5,6,2,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,2,2,3,1]=>[1,4,5,1,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,2,3,1,2]=>[1,4,5,2,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,2,3,2,1]=>[2,5,6,3,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,3,1,2,2]=>[3,6,1,1,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,5,3,2,1,2]=>[3,6,1,2,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,3,2,2,1]=>[3,6,1,2,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,2,2,2,5]=>[1,6,2,1,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,2,2,5,2]=>[1,6,2,1,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,2,5,2,2]=>[1,6,2,4,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,2,2]=>[4,2,1,1,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,2,1,2,2,5]=>[2,1,1,3,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,2,5,2]=>[2,1,1,3,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,5,2,2]=>[4,3,3,1,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,2,2,1,2,5]=>[2,1,2,1,3,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,2,1,5,2]=>[4,3,4,3,1,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,2,2,2,1,5]=>[2,1,2,2,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,2,2,2,5,1]=>[2,1,2,2,5,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,2,2,5,1,2]=>[2,1,2,5,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,2,5,2,1]=>[2,1,2,5,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,5,1,2,2]=>[2,1,5,5,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,5,2,1,2]=>[2,1,5,6,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,5,2,2,1]=>[2,1,5,6,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,5,1,2,2,2]=>[1,3,4,2,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,5,2,1,2,2]=>[2,4,6,1,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,2,2,1,2]=>[2,4,6,2,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,2,2,2,1]=>[2,4,6,2,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,2,2,2,3]=>[1,4,2,1,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,1,2,2,3,2]=>[2,5,3,2,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,2,3,2,2]=>[2,5,3,3,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,3,2,2,2]=>[2,5,4,1,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,2,1,2,2,3]=>[2,6,1,3,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,2,1,2,3,2]=>[2,6,1,3,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,2,1,3,2,2]=>[2,6,1,4,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,2,2,1,2,3]=>[2,6,2,1,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,2,2,1,3,2]=>[2,6,2,1,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,2,2,2,1,3]=>[2,6,2,2,1,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,2,2,3,1]=>[1,5,1,1,2,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,2,2,3,1,2]=>[1,5,1,2,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,2,3,2,1]=>[2,6,2,3,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,2,3,1,2,2]=>[1,5,2,6,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,3,2,1,2]=>[2,6,3,1,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,2,3,2,2,1]=>[2,6,3,1,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,1,2,2,2]=>[3,1,1,4,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,3,2,1,2,2]=>[3,1,2,2,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,3,2,2,1,2]=>[3,1,2,3,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,3,2,2,2,1]=>[3,1,2,3,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,2,3,6]=>[1,2,1,1,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,2,2,2,6,3]=>[1,2,1,1,5,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,2,3,2,6]=>[2,3,2,3,1,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,2,3,6,2]=>[1,2,1,2,4,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,2,6,2,3]=>[1,2,1,5,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,2,6,3,2]=>[4,5,4,1,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,3,2,2,6]=>[2,3,3,1,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,3,2,6,2]=>[2,3,3,1,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,3,6,2,2]=>[1,2,2,4,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,6,2,2,3]=>[1,2,5,4,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,6,2,3,2]=>[2,3,6,5,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,3,2,2]=>[4,5,1,1,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,2,2,2,6]=>[2,4,1,2,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,3,2,2,6,2]=>[2,4,1,2,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,2,6,2,2]=>[2,4,1,6,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,6,2,2,2]=>[1,3,4,4,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,6,2,2,2,3]=>[1,6,4,1,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,6,2,2,3,2]=>[3,1,6,3,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,2,3,2,2]=>[3,1,6,4,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,3,2,2,2]=>[4,2,1,3,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,2,3,6]=>[2,1,3,2,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,1,2,2,6,3]=>[4,3,5,4,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,2,3,2,6]=>[2,1,3,3,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,1,2,3,6,2]=>[2,1,3,3,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,2,6,2,3]=>[2,1,3,6,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,2,6,3,2]=>[4,3,5,1,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,3,2,2,6]=>[2,1,4,1,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,1,3,2,6,2]=>[2,1,4,1,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,3,6,2,2]=>[2,1,4,5,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,6,2,2,3]=>[3,2,1,6,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,6,2,3,2]=>[3,2,1,6,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,3,2,2]=>[4,3,2,1,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,2,3,6]=>[2,2,1,3,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,2,1,2,6,3]=>[4,4,3,5,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,2,1,3,2,6]=>[2,2,1,4,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,2,1,3,6,2]=>[2,2,1,4,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,1,6,2,3]=>[3,3,2,1,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,2,1,6,3,2]=>[4,4,3,2,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,2,1,3,6]=>[2,2,2,1,4,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,2,2,1,6,3]=>[4,4,4,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,2,2,3,1,6]=>[3,3,3,4,1,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,2,2,3,6,1]=>[1,1,1,2,4,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,2,6,1,3]=>[1,1,1,5,3,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,2,6,3,1]=>[4,4,4,1,1,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,2,3,1,2,6]=>[1,1,2,6,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,2,3,1,6,2]=>[3,3,4,1,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,2,3,2,1,6]=>[3,3,4,2,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,3,2,6,1]=>[2,2,3,1,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,3,6,1,2]=>[1,1,2,4,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,3,6,2,1]=>[2,2,3,5,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,6,1,2,3]=>[1,1,5,3,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,6,1,3,2]=>[2,2,6,4,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,2,6,2,1,3]=>[2,2,6,5,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,6,2,3,1]=>[1,1,5,4,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,6,3,1,2]=>[4,4,1,1,2,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,2,6,3,2,1]=>[4,4,1,1,3,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,3,1,2,2,6]=>[1,2,6,2,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,1,2,6,2]=>[1,2,6,2,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,6,2,2]=>[3,4,1,1,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,3,2,1,2,6]=>[2,3,1,1,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,2,1,6,2]=>[3,4,2,2,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,2,2,1,6]=>[3,4,2,3,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,2,2,6,1]=>[2,3,1,2,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,2,6,1,2]=>[2,3,1,6,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,2,6,2,1]=>[2,3,1,6,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,6,1,2,2]=>[1,2,4,3,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,6,2,1,2]=>[2,3,5,5,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,6,2,2,1]=>[2,3,5,5,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,1,2,2,3]=>[1,5,3,2,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,6,1,2,3,2]=>[2,6,4,3,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,6,1,3,2,2]=>[2,6,4,4,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,6,2,1,2,3]=>[2,6,5,1,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,6,2,1,3,2]=>[2,6,5,1,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,2,2,1,3]=>[2,6,5,2,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,2,2,3,1]=>[1,5,4,1,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,2,3,1,2]=>[1,5,4,2,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,2,3,2,1]=>[2,6,5,3,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,3,1,2,2]=>[4,1,1,2,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,3,2,1,2]=>[4,1,1,3,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,6,3,2,2,1]=>[4,1,1,3,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,1,2,2,2,6]=>[1,6,2,1,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,1,2,2,6,2]=>[1,6,2,1,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,2,6,2,2]=>[1,6,2,5,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,6,2,2,2]=>[3,1,1,6,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,1,2,2,6]=>[2,1,1,3,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,2,1,2,6,2]=>[2,1,1,3,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,6,2,2]=>[3,2,2,1,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,2,1,2,6]=>[2,1,2,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,2,2,1,6,2]=>[3,2,3,2,1,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,2,2,1,6]=>[3,2,3,3,2,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,2,2,2,6,1]=>[2,1,2,2,6,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,2,2,6,1,2]=>[2,1,2,6,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,2,6,2,1]=>[2,1,2,6,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,6,1,2,2]=>[2,1,6,4,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,6,2,1,2]=>[2,1,6,5,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,6,2,2,1]=>[2,1,6,5,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,6,1,2,2,2]=>[1,4,3,2,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,6,2,1,2,2]=>[2,5,5,1,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,6,2,2,1,2]=>[2,5,5,2,1,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,6,2,2,2,1]=>[2,5,5,2,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,1,2,2,2,3]=>[1,3,2,1,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[6,1,2,2,3,2]=>[2,4,3,2,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,2,3,2,2]=>[2,4,3,3,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,3,2,2,2]=>[2,4,4,1,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[6,2,1,2,2,3]=>[2,5,1,3,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,2,1,2,3,2]=>[2,5,1,3,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,2,1,3,2,2]=>[2,5,1,4,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,2,1,2,3]=>[2,5,2,1,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,2,2,1,3,2]=>[2,5,2,1,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,2,2,1,3]=>[2,5,2,2,1,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,2,2,2,3,1]=>[1,4,1,1,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,2,2,3,1,2]=>[1,4,1,2,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,2,2,3,2,1]=>[2,5,2,3,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,2,3,1,2,2]=>[1,4,2,6,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,2,3,2,1,2]=>[2,5,3,1,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,2,3,2,2,1]=>[2,5,3,1,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,3,1,2,2,2]=>[1,5,6,2,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,3,2,1,2,2]=>[2,6,1,1,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,3,2,2,1,2]=>[2,6,1,2,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,3,2,2,2,1]=>[2,6,1,2,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,2,2,4,4]=>[1,2,1,1,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,2,4,2,4]=>[1,2,1,3,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,2,4,4,2]=>[1,2,1,3,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,2,4,2,2,4]=>[1,2,3,6,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,4,2,4,2]=>[3,4,5,1,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,4,4,2,2]=>[1,2,3,1,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,2,2,2,4]=>[1,4,6,1,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,4,2,2,4,2]=>[3,6,1,3,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,2,4,2,2]=>[3,6,1,5,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,4,2,2,2]=>[1,4,1,6,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,2,2,4,4]=>[2,1,3,2,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,2,4,2,4]=>[3,2,4,5,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,2,4,4,2]=>[3,2,4,5,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,2,2,4]=>[3,2,6,1,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,4,2,4,2]=>[3,2,6,1,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,4,2,2]=>[3,2,6,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,1,2,4,4]=>[2,2,1,3,4,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,4,2,4]=>[3,3,2,6,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,1,4,4,2]=>[3,3,2,6,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,2,1,4,4]=>[2,2,2,1,5,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,2,2,4,1,4]=>[1,1,1,3,5,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,2,4,4,1]=>[1,1,1,3,1,5]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,2,4,1,2,4]=>[1,1,3,5,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,2,4,1,4,2]=>[1,1,3,5,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,4,2,1,4]=>[3,3,5,1,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,4,2,4,1]=>[1,1,3,6,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,4,4,1,2]=>[1,1,3,1,5,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,2,4,4,2,1]=>[3,3,5,3,1,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,4,1,2,2,4]=>[1,3,5,2,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,1,2,4,2]=>[1,3,5,2,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,1,4,2,2]=>[1,3,5,4,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,2,1,2,4]=>[3,5,1,2,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,2,1,4,2]=>[3,5,1,2,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,2,2,1,4]=>[3,5,1,3,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,2,2,4,1]=>[1,3,6,1,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,2,4,1,2]=>[1,3,6,3,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,2,4,2,1]=>[3,5,1,5,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,4,1,2,2]=>[1,3,1,5,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,4,2,1,2]=>[3,5,3,1,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,4,2,2,1]=>[3,5,3,1,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,2,2,2,4]=>[1,5,2,1,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,2,2,4,2]=>[1,5,2,1,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,2,4,2,2]=>[1,5,2,3,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,4,2,2,2]=>[1,5,4,6,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,2,1,2,2,4]=>[3,1,2,4,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,2,4,2]=>[3,1,2,4,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,4,2,2]=>[3,1,2,6,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,2,2,1,2,4]=>[3,1,3,2,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,2,1,4,2]=>[3,1,3,2,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,2,2,2,1,4]=>[3,1,3,3,2,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,2,2,2,4,1]=>[1,6,1,1,3,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,2,2,4,1,2]=>[1,6,1,3,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,2,4,2,1]=>[3,1,3,5,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,4,1,2,2]=>[1,6,3,5,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,4,2,1,2]=>[3,1,5,1,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,4,2,2,1]=>[3,1,5,1,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,1,2,2,2]=>[1,1,5,2,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,4,2,1,2,2]=>[3,3,1,2,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,2,2,1,2]=>[3,3,1,3,2,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,2,2,2,1]=>[3,3,1,3,3,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,2,2,4,5]=>[1,2,1,1,3,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,2,5,4]=>[2,3,2,2,5,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,2,4,2,5]=>[1,2,1,3,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,2,4,5,2]=>[1,2,1,3,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,2,5,2,4]=>[1,2,1,4,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,5,4,2]=>[3,4,3,6,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,2,4,2,2,5]=>[1,2,3,6,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,4,2,5,2]=>[1,2,3,6,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,5,2,2]=>[1,2,3,2,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,5,2,2,4]=>[1,2,4,5,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,5,2,4,2]=>[1,2,4,5,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,4,2,2]=>[3,4,6,2,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,2,2,5]=>[1,4,6,1,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,4,2,2,5,2]=>[5,1,3,5,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,2,5,2,2]=>[5,1,3,1,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,5,2,2,2]=>[1,4,2,5,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,2,2,2,4]=>[1,5,5,1,1,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,5,2,2,4,2]=>[4,1,1,4,6,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,5,2,4,2,2]=>[4,1,1,6,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,5,4,2,2,2]=>[4,1,3,2,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,2,4,5]=>[2,1,3,2,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,2,5,4]=>[2,1,3,2,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,2,4,2,5]=>[3,2,4,5,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,4,5,2]=>[2,1,3,4,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,2,5,2,4]=>[2,1,3,5,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,5,4,2]=>[3,2,4,6,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,2,2,5]=>[5,4,1,3,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,2,5,2]=>[5,4,1,3,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,4,5,2,2]=>[2,1,5,3,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,2,2,4]=>[4,3,1,1,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,1,5,2,4,2]=>[4,3,1,1,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,5,4,2,2]=>[4,3,1,3,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,2,4,5]=>[2,2,1,3,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,1,2,5,4]=>[2,2,1,3,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,1,4,2,5]=>[5,5,4,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,1,4,5,2]=>[2,2,1,5,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,1,5,2,4]=>[4,4,3,1,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,1,5,4,2]=>[4,4,3,1,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,2,1,4,5]=>[2,2,2,1,5,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,2,1,5,4]=>[2,2,2,1,6,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,2,2,4,1,5]=>[1,1,1,3,5,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,2,4,5,1]=>[1,1,1,3,2,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,2,5,1,4]=>[1,1,1,4,4,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,2,5,4,1]=>[2,2,2,5,1,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,4,1,2,5]=>[1,1,3,5,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,4,1,5,2]=>[4,4,6,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,2,4,2,1,5]=>[4,4,6,2,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,2,4,2,5,1]=>[1,1,3,6,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,4,5,1,2]=>[1,1,3,2,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,4,5,2,1]=>[2,2,4,3,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,5,1,2,4]=>[1,1,4,4,2,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,2,5,1,4,2]=>[5,5,1,1,1,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,5,2,1,4]=>[5,5,1,2,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,2,5,2,4,1]=>[1,1,4,5,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,5,4,1,2]=>[2,2,5,1,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,5,4,2,1]=>[3,3,6,2,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,4,1,2,2,5]=>[1,3,5,2,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,4,1,2,5,2]=>[1,3,5,2,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,1,5,2,2]=>[4,6,1,1,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,4,2,1,2,5]=>[3,5,1,2,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,1,5,2]=>[4,6,2,3,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,2,2,1,5]=>[4,6,2,4,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,2,2,5,1]=>[1,3,6,1,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,4,2,5,1,2]=>[1,3,6,4,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,2,5,2,1]=>[6,1,4,2,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,5,1,2,2]=>[1,3,2,4,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,4,5,2,1,2]=>[2,4,3,6,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,5,2,2,1]=>[2,4,3,6,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,2,2,4]=>[1,4,4,2,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,1,2,4,2]=>[1,4,4,2,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,5,1,4,2,2]=>[5,1,1,1,3,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,5,2,1,2,4]=>[2,5,6,1,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,2,1,4,2]=>[5,1,2,4,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,5,2,2,1,4]=>[5,1,2,5,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,2,2,4,1]=>[1,4,5,1,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,5,2,4,1,2]=>[1,4,5,3,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,2,4,2,1]=>[6,2,3,1,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,1,2,2]=>[2,5,1,6,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,4,2,1,2]=>[3,6,2,1,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,4,2,2,1]=>[3,6,2,1,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,2,2,2,5]=>[1,5,2,1,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,2,2,5,2]=>[1,5,2,1,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,2,5,2,2]=>[1,5,2,4,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,5,2,2,2]=>[4,1,1,1,4,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,2,1,2,2,5]=>[3,1,2,4,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,1,2,5,2]=>[5,3,4,6,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,5,2,2]=>[4,2,3,1,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,2,1,2,5]=>[3,1,3,2,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,2,1,5,2]=>[4,2,4,3,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,2,2,1,5]=>[4,2,4,4,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,2,2,5,1]=>[1,6,1,1,4,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,2,2,5,1,2]=>[1,6,1,4,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,2,5,2,1]=>[5,3,5,1,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,5,1,2,2]=>[1,6,4,4,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,5,2,1,2]=>[5,3,1,2,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,5,2,2,1]=>[5,3,1,2,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,5,1,2,2,2]=>[1,2,4,2,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,5,2,1,2,2]=>[2,3,6,1,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,5,2,2,1,2]=>[2,3,6,2,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,5,2,2,2,1]=>[2,3,6,2,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,2,2,2,4]=>[1,4,2,1,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,2,2,4,2]=>[1,4,2,1,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,2,4,2,2]=>[1,4,2,3,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,4,2,2,2]=>[1,4,4,6,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,2,1,2,2,4]=>[2,6,1,3,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,1,2,4,2]=>[4,1,3,5,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,4,2,2]=>[5,2,4,1,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,1,2,4]=>[2,6,2,1,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,2,1,4,2]=>[5,2,5,4,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,1,4]=>[2,6,2,2,1,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,2,2,2,4,1]=>[1,5,1,1,3,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,2,2,4,1,2]=>[1,5,1,3,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,2,2,4,2,1]=>[4,1,4,6,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,4,1,2,2]=>[1,5,3,5,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,2,4,2,1,2]=>[4,1,6,2,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,4,2,2,1]=>[4,1,6,2,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,1,2,2,2]=>[2,1,6,3,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,4,2,1,2,2]=>[3,2,1,2,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,2,2,1,2]=>[3,2,1,3,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,2,2,2,1]=>[3,2,1,3,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,2,4,6]=>[1,2,1,1,3,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,2,2,6,4]=>[1,2,1,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,2,4,2,6]=>[1,2,1,3,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,2,4,6,2]=>[1,2,1,3,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,2,6,2,4]=>[1,2,1,5,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,2,6,4,2]=>[4,5,4,1,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,2,4,2,2,6]=>[1,2,3,6,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,4,2,6,2]=>[1,2,3,6,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,6,2,2]=>[1,2,3,3,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,6,2,2,4]=>[1,2,5,4,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,6,2,4,2]=>[1,2,5,4,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,6,4,2,2]=>[4,5,1,2,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,2,2,2,6]=>[1,4,6,1,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,2,2,6,2]=>[5,1,3,5,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,2,6,2,2]=>[5,1,3,2,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,6,2,2,2]=>[1,4,3,4,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,6,2,2,2,4]=>[1,6,4,1,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,6,2,2,4,2]=>[3,1,6,3,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,2,4,2,2]=>[3,1,6,5,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,4,2,2,2]=>[3,1,1,1,3,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[2,1,2,2,4,6]=>[2,1,3,2,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,2,2,6,4]=>[4,3,5,4,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,2,4,2,6]=>[4,3,5,6,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,4,6,2]=>[2,1,3,4,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,2,6,2,4]=>[2,1,3,6,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,6,4,2]=>[4,3,5,1,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,4,2,2,6]=>[5,4,1,3,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,2,6,2]=>[5,4,1,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,4,6,2,2]=>[2,1,5,4,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,6,2,2,4]=>[3,2,1,6,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,6,2,4,2]=>[3,2,1,6,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,6,4,2,2]=>[3,2,1,1,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,2,1,2,4,6]=>[2,2,1,3,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,2,1,2,6,4]=>[4,4,3,5,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,2,1,4,2,6]=>[5,5,4,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,4,6,2]=>[2,2,1,5,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,1,6,2,4]=>[3,3,2,1,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,1,6,4,2]=>[3,3,2,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,2,2,1,4,6]=>[2,2,2,1,5,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,2,2,1,6,4]=>[3,3,3,2,1,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,2,2,4,1,6]=>[1,1,1,3,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,2,2,4,6,1]=>[1,1,1,3,3,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[2,2,2,6,1,4]=>[1,1,1,5,3,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,2,6,4,1]=>[4,4,4,1,2,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,2,4,1,2,6]=>[1,1,3,5,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,4,1,6,2]=>[1,1,3,5,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,4,2,1,6]=>[3,3,5,1,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,2,4,2,6,1]=>[1,1,3,6,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,4,6,1,2]=>[1,1,3,3,3,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,2,4,6,2,1]=>[2,2,4,4,5,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,6,1,2,4]=>[1,1,5,3,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,2,6,1,4,2]=>[1,1,5,3,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,2,6,2,1,4]=>[5,5,2,1,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,2,6,2,4,1]=>[1,1,5,4,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,6,4,1,2]=>[4,4,1,2,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,2,6,4,2,1]=>[4,4,1,2,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,4,1,2,2,6]=>[1,3,5,2,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,1,2,6,2]=>[1,3,5,2,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,1,6,2,2]=>[1,3,5,6,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,2,1,2,6]=>[4,6,2,3,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,1,6,2]=>[3,5,1,2,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,2,2,1,6]=>[3,5,1,3,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,2,2,6,1]=>[1,3,6,1,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,2,6,1,2]=>[1,3,6,5,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,2,6,2,1]=>[6,1,4,3,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,6,1,2,2]=>[1,3,3,3,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,4,6,2,1,2]=>[2,4,4,5,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,6,2,2,1]=>[2,4,4,5,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,6,1,2,2,4]=>[1,5,3,2,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,1,2,4,2]=>[1,5,3,2,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,6,1,4,2,2]=>[1,5,3,4,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,6,2,1,2,4]=>[2,6,5,1,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,2,1,4,2]=>[5,2,1,4,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,2,2,1,4]=>[5,2,1,5,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,6,2,2,4,1]=>[1,5,4,1,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,2,4,1,2]=>[1,5,4,3,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,6,2,4,2,1]=>[6,3,2,1,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,4,1,2,2]=>[4,1,2,1,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,4,2,1,2]=>[4,1,2,2,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,6,4,2,2,1]=>[4,1,2,2,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,1,2,2,2,6]=>[1,5,2,1,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[4,1,2,2,6,2]=>[1,5,2,1,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,2,6,2,2]=>[1,5,2,5,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,6,2,2,2]=>[1,5,6,4,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,2,1,2,2,6]=>[4,2,3,5,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,1,2,6,2]=>[5,3,4,6,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,6,2,2]=>[3,1,2,1,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,2,2,1,2,6]=>[4,2,4,3,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,2,1,6,2]=>[3,1,3,2,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,2,2,2,1,6]=>[3,1,3,3,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,2,2,2,6,1]=>[1,6,1,1,5,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,2,2,6,1,2]=>[1,6,1,5,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,2,6,2,1]=>[5,3,5,2,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,6,1,2,2]=>[1,6,5,3,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,6,2,1,2]=>[5,3,2,1,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,6,2,2,1]=>[5,3,2,1,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,6,1,2,2,2]=>[1,3,3,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,6,2,1,2,2]=>[2,4,5,1,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,6,2,2,1,2]=>[2,4,5,2,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,6,2,2,2,1]=>[2,4,5,2,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,1,2,2,2,4]=>[1,3,2,1,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,2,2,4,2]=>[1,3,2,1,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,2,4,2,2]=>[1,3,2,3,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,4,2,2,2]=>[1,3,4,6,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[6,2,1,2,2,4]=>[2,5,1,3,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,1,2,4,2]=>[3,6,2,4,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,1,4,2,2]=>[5,1,4,1,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,2,2,1,2,4]=>[2,5,2,1,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,2,1,4,2]=>[5,1,5,4,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,2,2,2,1,4]=>[2,5,2,2,1,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,2,2,2,4,1]=>[1,4,1,1,3,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,2,2,4,1,2]=>[1,4,1,3,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,2,4,2,1]=>[3,6,3,5,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,4,1,2,2]=>[1,4,3,5,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,4,2,1,2]=>[3,6,5,1,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,4,2,2,1]=>[3,6,5,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,4,1,2,2,2]=>[1,6,5,2,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,4,2,1,2,2]=>[3,1,1,2,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,2,2,1,2]=>[3,1,1,3,2,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,2,2,2,1]=>[3,1,1,3,3,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,2,2,5,5]=>[1,2,1,1,4,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,2,2,5,2,5]=>[1,2,1,4,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,5,5,2]=>[1,2,1,4,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,2,5,2,2,5]=>[1,2,4,5,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,5,2,5,2]=>[5,6,1,2,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,5,5,2,2]=>[1,2,4,1,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,2,2,2,5]=>[1,5,5,1,1,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,5,2,2,5,2]=>[5,2,2,5,1,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,5,2,5,2,2]=>[5,2,2,1,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,5,5,2,2,2]=>[1,5,1,5,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[2,1,2,2,5,5]=>[2,1,3,2,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,1,2,5,2,5]=>[5,4,6,1,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,2,5,5,2]=>[2,1,3,5,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,2,2,5]=>[5,4,2,2,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,5,2,5,2]=>[5,4,2,2,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,5,5,2,2]=>[4,3,1,4,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,1,2,5,5]=>[2,2,1,3,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,1,5,2,5]=>[5,5,4,2,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,1,5,5,2]=>[4,4,3,1,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,2,1,5,5]=>[2,2,2,1,6,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,2,2,5,1,5]=>[1,1,1,4,4,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,2,2,5,5,1]=>[1,1,1,4,1,4]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[2,2,5,1,2,5]=>[1,1,4,4,2,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,2,5,1,5,2]=>[5,5,1,1,2,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,2,5,2,1,5]=>[5,5,1,2,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,5,2,5,1]=>[5,5,1,2,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,2,5,5,1,2]=>[1,1,4,1,4,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,5,5,2,1]=>[2,2,5,2,6,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,2,2,5]=>[1,4,4,2,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,5,1,2,5,2]=>[5,1,1,6,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,5,1,5,2,2]=>[5,1,1,2,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,5,2,1,2,5]=>[5,1,2,4,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,2,1,5,2]=>[5,1,2,4,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,5,2,2,1,5]=>[5,1,2,5,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,2,2,5,1]=>[5,1,2,5,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,5,2,5,1,2]=>[5,1,2,1,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,5,2,5,2,1]=>[5,1,2,1,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,5,1,2,2]=>[1,4,1,4,2,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,5,5,2,1,2]=>[2,5,2,6,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,5,2,2,1]=>[2,5,2,6,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,1,2,2,2,5]=>[1,4,2,1,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,1,2,2,5,2]=>[1,4,2,1,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,2,5,2,2]=>[1,4,2,4,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,5,2,2,2]=>[1,4,5,5,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[5,2,1,2,2,5]=>[2,6,1,3,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,1,2,5,2]=>[5,2,4,6,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,5,2,2]=>[4,1,3,1,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,2,2,1,2,5]=>[2,6,2,1,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,2,1,5,2]=>[4,1,4,3,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,2,2,2,1,5]=>[4,1,4,4,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,2,2,2,5,1]=>[1,5,1,1,4,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,2,2,5,1,2]=>[1,5,1,4,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,2,2,5,2,1]=>[5,2,5,1,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,5,1,2,2]=>[1,5,4,4,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,2,5,2,1,2]=>[5,2,1,2,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,5,2,2,1]=>[5,2,1,2,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,5,1,2,2,2]=>[1,1,4,2,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,5,2,1,2,2]=>[2,2,6,1,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,5,2,2,1,2]=>[2,2,6,2,1,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,5,2,2,2,1]=>[2,2,6,2,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,2,2,5,6]=>[1,2,1,1,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,2,2,2,6,5]=>[2,3,2,2,6,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,2,5,2,6]=>[1,2,1,4,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,2,5,6,2]=>[1,2,1,4,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,2,6,2,5]=>[1,2,1,5,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,2,6,5,2]=>[4,5,4,1,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,2,5,2,2,6]=>[1,2,4,5,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,5,2,6,2]=>[5,6,1,2,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,5,6,2,2]=>[1,2,4,2,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,6,2,2,5]=>[1,2,5,4,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,2,6,2,5,2]=>[5,6,2,1,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,6,5,2,2]=>[4,5,1,3,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,2,2,2,6]=>[4,1,1,4,4,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,5,2,2,6,2]=>[5,2,2,5,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,5,2,6,2,2]=>[5,2,2,2,1,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,5,6,2,2,2]=>[1,5,2,4,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,6,2,2,2,5]=>[1,6,4,1,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,6,2,2,5,2]=>[5,3,1,5,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,6,2,5,2,2]=>[5,3,1,1,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,6,5,2,2,2]=>[4,2,3,1,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,2,5,6]=>[2,1,3,2,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,1,2,2,6,5]=>[2,1,3,2,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,1,2,5,2,6]=>[5,4,6,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,2,5,6,2]=>[2,1,3,5,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,2,6,2,5]=>[5,4,6,2,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,2,6,5,2]=>[4,3,5,1,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,5,2,2,6]=>[4,3,1,1,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,1,5,2,6,2]=>[5,4,2,2,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,5,6,2,2]=>[2,1,6,3,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,6,2,2,5]=>[5,4,3,1,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,6,2,5,2]=>[5,4,3,1,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,6,5,2,2]=>[4,3,2,3,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,2,5,6]=>[2,2,1,3,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,2,1,2,6,5]=>[2,2,1,3,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,1,5,2,6]=>[4,4,3,1,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,2,1,5,6,2]=>[2,2,1,6,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,1,6,2,5]=>[5,5,4,3,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,1,6,5,2]=>[4,4,3,2,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,2,1,5,6]=>[2,2,2,1,6,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,2,2,1,6,5]=>[3,3,3,2,1,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,2,2,5,1,6]=>[1,1,1,4,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,2,2,5,6,1]=>[1,1,1,4,2,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,2,6,1,5]=>[1,1,1,5,3,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,2,6,5,1]=>[2,2,2,6,1,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,2,5,1,2,6]=>[1,1,4,4,2,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,2,5,1,6,2]=>[5,5,1,1,3,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,5,2,1,6]=>[5,5,1,2,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,2,5,2,6,1]=>[1,1,4,5,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,5,6,1,2]=>[1,1,4,2,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,5,6,2,1]=>[2,2,5,3,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,6,1,2,5]=>[1,1,5,3,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,6,1,5,2]=>[4,4,1,6,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,2,6,2,1,5]=>[5,5,2,1,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,6,2,5,1]=>[5,5,2,1,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,2,6,5,1,2]=>[2,2,6,1,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,2,6,5,2,1]=>[4,4,1,3,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,5,1,2,2,6]=>[1,4,4,2,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,5,1,2,6,2]=>[5,1,1,6,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,5,1,6,2,2]=>[5,1,1,3,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,5,2,1,2,6]=>[5,1,2,4,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,2,1,6,2]=>[5,1,2,4,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,5,2,2,1,6]=>[5,1,2,5,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,2,2,6,1]=>[1,4,5,1,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,5,2,6,1,2]=>[1,4,5,5,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,2,6,2,1]=>[5,1,2,2,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,6,1,2,2]=>[1,4,2,3,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,5,6,2,1,2]=>[2,5,3,5,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,5,6,2,2,1]=>[2,5,3,5,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,1,2,2,5]=>[1,5,3,2,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,1,2,5,2]=>[1,5,3,2,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,6,1,5,2,2]=>[4,1,6,1,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,6,2,1,2,5]=>[5,2,1,4,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,2,1,5,2]=>[5,2,1,4,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,6,2,2,1,5]=>[5,2,1,5,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,6,2,2,5,1]=>[5,2,1,5,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,6,2,5,1,2]=>[5,2,1,1,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,6,2,5,2,1]=>[5,2,1,1,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,6,5,1,2,2]=>[2,6,1,5,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,5,2,1,2]=>[4,1,3,1,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,6,5,2,2,1]=>[4,1,3,1,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,1,2,2,2,6]=>[1,4,2,1,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,1,2,2,6,2]=>[1,4,2,1,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,2,6,2,2]=>[1,4,2,5,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,6,2,2,2]=>[1,4,6,4,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,2,1,2,2,6]=>[4,1,3,5,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,2,1,2,6,2]=>[5,2,4,6,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,6,2,2]=>[5,2,4,3,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,1,2,6]=>[4,1,4,3,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,2,2,1,6,2]=>[5,2,5,4,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,2,1,6]=>[4,1,4,4,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,2,2,2,6,1]=>[1,5,1,1,5,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,2,2,6,1,2]=>[1,5,1,5,3,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,2,2,6,2,1]=>[5,2,5,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,6,1,2,2]=>[1,5,5,3,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,2,6,2,1,2]=>[5,2,2,1,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,6,2,2,1]=>[5,2,2,1,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,6,1,2,2,2]=>[1,2,3,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[5,6,2,1,2,2]=>[2,3,5,1,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,6,2,2,1,2]=>[2,3,5,2,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,6,2,2,2,1]=>[2,3,5,2,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,1,2,2,2,5]=>[1,3,2,1,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[6,1,2,2,5,2]=>[1,3,2,1,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,2,5,2,2]=>[1,3,2,4,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,5,2,2,2]=>[1,3,5,5,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[6,2,1,2,2,5]=>[2,5,1,3,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,2,1,2,5,2]=>[5,1,4,6,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,1,5,2,2]=>[5,1,4,2,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,2,2,1,2,5]=>[2,5,2,1,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,2,2,1,5,2]=>[5,1,5,4,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,2,2,2,1,5]=>[2,5,2,2,1,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,2,2,2,5,1]=>[1,4,1,1,4,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[6,2,2,5,1,2]=>[1,4,1,4,4,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,2,2,5,2,1]=>[5,1,5,1,2,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,5,1,2,2]=>[1,4,4,4,2,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,2,5,2,1,2]=>[5,1,1,2,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,5,2,2,1]=>[5,1,1,2,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,5,1,2,2,2]=>[2,1,5,3,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,5,2,1,2,2]=>[2,1,6,1,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,5,2,2,1,2]=>[2,1,6,2,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,5,2,2,2,1]=>[2,1,6,2,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,2,3,3,3]=>[1,2,1,2,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,3,2,3,3]=>[2,3,3,1,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,3,2,3]=>[2,3,3,2,1,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,3,3,2]=>[2,3,3,2,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,3,2,2,3,3]=>[2,4,1,2,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,2,3,2,3]=>[2,4,1,3,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,2,3,3,2]=>[2,4,1,3,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,3,2,2,3]=>[2,4,2,1,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,3,2,3,2]=>[2,4,2,1,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,3,3,2,2]=>[2,4,2,2,1,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,2,3,3,3]=>[2,1,3,3,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,1,3,2,3,3]=>[2,1,4,1,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,3,2,3]=>[2,1,4,2,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,3,3,2]=>[2,1,4,2,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,1,3,3,3]=>[2,2,1,4,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,2,3,1,3,3]=>[1,1,2,6,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,2,3,3,1,3]=>[1,1,2,1,6,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,2,3,3,3,1]=>[1,1,2,1,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,3,1,2,3,3]=>[1,2,6,2,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,3,1,3,2,3]=>[3,4,1,5,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,3,3,2]=>[3,4,1,5,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,1,3,3]=>[2,3,1,1,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,2,3,1,3]=>[3,4,2,4,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,2,3,3,1]=>[3,4,2,4,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,3,1,2,3]=>[1,2,1,6,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,3,3,1,3,2]=>[3,4,3,1,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,3,2,1,3]=>[2,3,2,1,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,3,2,3,1]=>[3,4,3,2,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,3,3,1,2]=>[1,2,1,1,6,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,3,3,2,1]=>[2,3,2,2,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,1,2,2,3,3]=>[1,6,2,1,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,1,2,3,2,3]=>[3,1,4,4,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,2,3,3,2]=>[3,1,4,4,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,1,3,2,2,3]=>[3,1,5,2,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,3,2,3,2]=>[3,1,5,2,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,3,3,2,2]=>[3,1,5,3,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,2,1,2,3,3]=>[2,1,1,3,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,1,3,2,3]=>[2,1,1,4,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,1,3,3,2]=>[2,1,1,4,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,2,2,1,3,3]=>[2,1,2,1,4,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,2,2,3,1,3]=>[3,2,3,4,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,2,3,3,1]=>[3,2,3,4,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,3,1,2,3]=>[3,2,4,1,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,2,3,1,3,2]=>[3,2,4,1,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,3,2,1,3]=>[2,1,3,1,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,3,2,3,1]=>[3,2,4,2,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,3,3,1,2]=>[3,2,4,3,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,3,2,1]=>[2,1,3,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,3,1,2,2,3]=>[1,1,6,2,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,3,1,2,3,2]=>[3,3,1,4,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,3,1,3,2,2]=>[3,3,1,5,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,3,2,1,2,3]=>[2,2,1,1,3,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,2,1,3,2]=>[2,2,1,1,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,3,2,2,1,3]=>[2,2,1,2,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,3,2,2,3,1]=>[3,3,2,3,4,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,2,3,1,2]=>[3,3,2,4,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,3,2,3,2,1]=>[2,2,1,3,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,3,3,1,2,2]=>[1,1,1,6,2,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,3,3,2,1,2]=>[2,2,2,1,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,3,3,2,2,1]=>[2,2,2,1,2,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,2,3,3,4]=>[1,2,1,2,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,3,4,3]=>[2,3,2,3,3,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,4,3,3]=>[2,3,2,4,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,2,3,4]=>[2,3,3,1,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,3,2,4,3]=>[2,3,3,1,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,3,3,2,4]=>[2,3,3,2,1,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,3,4,2]=>[1,2,2,1,2,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,3,4,2,3]=>[1,2,2,2,6,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,3,4,3,2]=>[2,3,3,3,1,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,4,2,3,3]=>[1,2,3,6,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,3,2,3]=>[2,3,4,1,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,4,3,3,2]=>[2,3,4,1,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,2,3,4]=>[2,4,1,2,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,2,2,4,3]=>[2,4,1,2,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,2,3,2,4]=>[2,4,1,3,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,2,3,4,2]=>[3,5,2,4,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,4,2,3]=>[3,5,2,5,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,2,4,3,2]=>[2,4,1,4,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,3,3,2,2,4]=>[2,4,2,1,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,3,2,4,2]=>[3,5,3,2,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,3,4,2,2]=>[1,3,1,2,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,4,2,2,3]=>[1,3,2,6,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,4,2,3,2]=>[3,5,4,1,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,3,2,2]=>[2,4,3,1,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,4,2,2,3,3]=>[1,4,6,1,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,2,3,2,3]=>[3,6,1,4,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,3,3,2]=>[3,6,1,4,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,3,2,2,3]=>[2,5,1,1,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,3,2,3,2]=>[2,5,1,1,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,3,3,2,2]=>[2,5,1,2,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,2,3,3,4]=>[2,1,3,3,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,2,3,4,3]=>[2,1,3,3,3,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,1,2,4,3,3]=>[2,1,3,4,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,2,3,4]=>[2,1,4,1,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,3,2,4,3]=>[2,1,4,1,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,3,3,2,4]=>[2,1,4,2,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,3,3,4,2]=>[3,2,5,3,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,4,2,3]=>[3,2,5,4,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,4,3,2]=>[2,1,4,3,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,4,2,3,3]=>[3,2,6,1,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,4,3,2,3]=>[2,1,5,1,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,4,3,3,2]=>[2,1,5,1,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,1,3,3,4]=>[2,2,1,4,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,3,4,3]=>[2,2,1,4,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,2,1,4,3,3]=>[2,2,1,5,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,2,3,1,3,4]=>[1,1,2,6,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,3,1,4,3]=>[3,3,4,1,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,2,3,3,1,4]=>[1,1,2,1,6,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,2,3,3,4,1]=>[1,1,2,1,2,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,3,4,1,3]=>[1,1,2,2,5,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,3,4,3,1]=>[3,3,4,4,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,4,1,3,3]=>[1,1,3,5,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,4,3,1,3]=>[3,3,5,2,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,2,4,3,3,1]=>[3,3,5,2,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,3,1,2,3,4]=>[1,2,6,2,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,3,1,2,4,3]=>[3,4,1,4,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,3,2,4]=>[3,4,1,5,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,1,3,4,2]=>[3,4,1,5,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,3,1,4,2,3]=>[3,4,1,6,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,3,1,4,3,2]=>[3,4,1,6,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,2,1,3,4]=>[2,3,1,1,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,2,1,4,3]=>[2,3,1,1,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,3,2,3,1,4]=>[3,4,2,4,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,2,3,4,1]=>[2,3,1,3,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,3,2,4,1,3]=>[2,3,1,4,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,2,4,3,1]=>[3,4,2,5,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,3,1,2,4]=>[1,2,1,6,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,3,1,4,2]=>[3,4,3,1,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,3,3,2,1,4]=>[2,3,2,1,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,3,2,4,1]=>[2,3,2,1,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,3,4,1,2]=>[1,2,1,2,5,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,3,4,2,1]=>[3,4,3,4,1,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,4,1,2,3]=>[1,2,2,5,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,3,4,1,3,2]=>[2,3,3,6,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,4,2,1,3]=>[3,4,4,1,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,4,2,3,1]=>[3,4,4,1,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,3,4,3,1,2]=>[3,4,4,2,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,4,3,2,1]=>[2,3,3,1,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,4,1,2,3,3]=>[1,3,5,2,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,4,1,3,2,3]=>[2,4,6,4,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,1,3,3,2]=>[2,4,6,4,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,4,2,1,3,3]=>[3,5,1,2,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,2,3,1,3]=>[3,5,1,4,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,2,3,3,1]=>[3,5,1,4,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,3,1,2,3]=>[3,5,2,1,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,3,1,3,2]=>[3,5,2,1,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,4,3,2,1,3]=>[2,4,1,1,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,4,3,2,3,1]=>[3,5,2,2,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,3,3,1,2]=>[3,5,2,3,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,3,3,2,1]=>[2,4,1,2,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,1,2,2,3,4]=>[1,6,2,1,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,1,2,2,4,3]=>[3,1,4,3,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,2,3,2,4]=>[3,1,4,4,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,3,4,2]=>[3,1,4,4,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,1,2,4,2,3]=>[3,1,4,5,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,2,4,3,2]=>[3,1,4,5,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,3,2,2,4]=>[3,1,5,2,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,3,2,4,2]=>[3,1,5,2,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,3,4,2,2]=>[3,1,5,4,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,4,2,2,3]=>[3,1,6,1,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,4,2,3,2]=>[3,1,6,1,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,4,3,2,2]=>[3,1,6,2,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,1,2,3,4]=>[2,1,1,3,3,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[3,2,1,2,4,3]=>[2,1,1,3,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,1,3,2,4]=>[2,1,1,4,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[3,2,1,3,4,2]=>[3,2,2,5,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,1,4,2,3]=>[3,2,2,6,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,1,4,3,2]=>[2,1,1,5,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[3,2,2,1,3,4]=>[2,1,2,1,4,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,2,1,4,3]=>[2,1,2,1,5,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,2,2,3,1,4]=>[3,2,3,4,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,2,3,4,1]=>[2,1,2,3,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,2,4,1,3]=>[2,1,2,4,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,2,4,3,1]=>[3,2,3,5,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,2,3,1,2,4]=>[3,2,4,1,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,3,1,4,2]=>[3,2,4,1,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,3,2,1,4]=>[2,1,3,1,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,2,3,2,4,1]=>[2,1,3,1,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,3,4,1,2]=>[2,1,3,3,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,2,3,4,2,1]=>[3,2,4,4,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,4,1,2,3]=>[2,1,4,6,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,4,1,3,2]=>[2,1,4,6,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,2,4,2,1,3]=>[3,2,5,1,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,4,2,3,1]=>[3,2,5,1,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,4,3,1,2]=>[3,2,5,2,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,4,3,2,1]=>[2,1,4,1,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[3,3,1,2,2,4]=>[1,1,6,2,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,3,1,2,4,2]=>[3,3,1,4,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,3,1,4,2,2]=>[3,3,1,6,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,3,2,1,2,4]=>[2,2,1,1,3,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,3,2,1,4,2]=>[3,3,2,2,6,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,3,2,2,1,4]=>[2,2,1,2,1,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,3,2,2,4,1]=>[2,2,1,2,4,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,2,4,1,2]=>[2,2,1,4,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,3,2,4,2,1]=>[3,3,2,5,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,4,1,2,2]=>[1,1,2,5,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,3,4,2,1,2]=>[3,3,4,1,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,3,4,2,2,1]=>[3,3,4,1,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,4,1,2,2,3]=>[1,2,5,2,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,4,1,2,3,2]=>[2,3,6,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,1,3,2,2]=>[2,3,6,4,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,2,1,2,3]=>[3,4,1,2,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,4,2,1,3,2]=>[3,4,1,2,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,4,2,2,1,3]=>[3,4,1,3,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,2,2,3,1]=>[3,4,1,3,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,4,2,3,1,2]=>[3,4,1,4,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,4,2,3,2,1]=>[3,4,1,4,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,4,3,1,2,2]=>[3,4,2,1,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,3,2,1,2]=>[2,3,1,1,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[3,4,3,2,2,1]=>[2,3,1,1,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,1,2,2,3,3]=>[1,5,2,1,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,1,2,3,2,3]=>[2,6,3,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,1,2,3,3,2]=>[2,6,3,3,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,3,2,2,3]=>[2,6,4,1,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,3,2,3,2]=>[2,6,4,1,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,3,2,2]=>[2,6,4,2,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,2,1,2,3,3]=>[3,1,2,4,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,2,1,3,2,3]=>[3,1,2,5,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,3,3,2]=>[3,1,2,5,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,2,2,1,3,3]=>[3,1,3,2,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,2,2,3,1,3]=>[3,1,3,4,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,2,2,3,3,1]=>[3,1,3,4,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,2,3,1,2,3]=>[3,1,4,1,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,2,3,1,3,2]=>[3,1,4,1,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,3,2,1,3]=>[3,1,4,2,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,3,2,3,1]=>[3,1,4,2,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,3,3,1,2]=>[3,1,4,3,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,2,3,3,2,1]=>[3,1,4,3,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,1,2,2,3]=>[3,2,1,4,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,1,2,3,2]=>[3,2,1,4,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,1,3,2,2]=>[3,2,1,5,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,3,2,1,2,3]=>[2,1,1,1,3,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,3,2,1,3,2]=>[2,1,1,1,4,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[4,3,2,2,1,3]=>[2,1,1,2,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,3,2,2,3,1]=>[3,2,2,3,4,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,2,3,1,2]=>[3,2,2,4,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,2,3,2,1]=>[2,1,1,3,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[4,3,3,1,2,2]=>[3,2,3,1,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,3,2,1,2]=>[2,1,2,1,1,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,3,3,2,2,1]=>[2,1,2,1,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,3,3,5]=>[1,2,1,2,1,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,3,5,3]=>[1,2,1,2,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,2,5,3,3]=>[1,2,1,4,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,3,2,3,5]=>[2,3,3,1,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,3,2,5,3]=>[3,4,4,2,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,3,3,2,5]=>[2,3,3,2,1,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,3,3,5,2]=>[1,2,2,1,3,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,3,5,2,3]=>[1,2,2,3,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,3,5,3,2]=>[3,4,4,5,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,5,2,3,3]=>[1,2,4,5,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,5,3,2,3]=>[3,4,6,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,3,3,2]=>[3,4,6,1,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,2,3,5]=>[2,4,1,2,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,2,2,5,3]=>[3,5,2,3,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,2,3,2,5]=>[2,4,1,3,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,3,5,2]=>[2,4,1,3,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,2,5,2,3]=>[2,4,1,5,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,5,3,2]=>[3,5,2,6,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,3,2,2,5]=>[2,4,2,1,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,3,3,2,5,2]=>[2,4,2,1,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,3,5,2,2]=>[1,3,1,3,5,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,5,2,2,3]=>[1,3,3,5,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,5,2,3,2]=>[2,4,4,6,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,5,3,2,2]=>[3,5,5,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,2,2,3,3]=>[1,5,5,1,2,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,5,2,3,2,3]=>[4,1,1,5,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,5,2,3,3,2]=>[4,1,1,5,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,3,2,2,3]=>[4,1,2,3,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,3,2,3,2]=>[4,1,2,3,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,3,3,2,2]=>[4,1,2,4,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,3,3,5]=>[2,1,3,3,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,3,5,3]=>[3,2,4,4,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,2,5,3,3]=>[3,2,4,6,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,3,2,3,5]=>[2,1,4,1,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,3,2,5,3]=>[3,2,5,2,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,3,3,2,5]=>[2,1,4,2,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,3,3,5,2]=>[2,1,4,2,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,1,3,5,2,3]=>[2,1,4,4,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,3,5,3,2]=>[3,2,5,5,1,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,5,2,3,3]=>[4,3,1,1,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,5,3,2,3]=>[4,3,1,2,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,5,3,3,2]=>[4,3,1,2,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,3,3,5]=>[2,2,1,4,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,2,1,3,5,3]=>[3,3,2,5,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,2,1,5,3,3]=>[4,4,3,1,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,2,3,1,3,5]=>[1,1,2,6,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,2,3,1,5,3]=>[4,4,5,2,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,3,3,1,5]=>[1,1,2,1,6,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,2,3,3,5,1]=>[1,1,2,1,3,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,3,5,1,3]=>[1,1,2,3,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,2,3,5,3,1]=>[3,3,4,5,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,5,1,3,3]=>[1,1,4,4,3,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,2,5,3,1,3]=>[3,3,6,1,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,5,3,3,1]=>[3,3,6,1,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[2,3,1,2,3,5]=>[1,2,6,2,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,3,1,2,5,3]=>[3,4,1,4,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,3,1,3,2,5]=>[3,4,1,5,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,3,5,2]=>[1,2,6,3,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,3,1,5,2,3]=>[4,5,2,1,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,3,1,5,3,2]=>[4,5,2,1,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,2,1,3,5]=>[2,3,1,1,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,2,1,5,3]=>[4,5,3,3,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,3,1,5]=>[4,5,3,5,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,2,3,5,1]=>[2,3,1,3,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,5,1,3]=>[2,3,1,5,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,2,5,3,1]=>[3,4,2,6,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,3,1,2,5]=>[1,2,1,6,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,3,1,5,2]=>[4,5,4,2,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,3,3,2,1,5]=>[2,3,2,1,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,3,2,5,1]=>[2,3,2,1,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,3,3,5,1,2]=>[1,2,1,3,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,3,5,2,1]=>[2,3,2,4,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,5,1,2,3]=>[1,2,3,4,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,5,1,3,2]=>[2,3,4,5,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,5,2,1,3]=>[2,3,4,6,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,5,2,3,1]=>[1,2,3,5,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,5,3,1,2]=>[3,4,5,1,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,3,5,3,2,1]=>[3,4,5,1,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,1,2,3,3]=>[1,4,4,2,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,5,1,3,2,3]=>[2,5,5,4,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,1,3,3,2]=>[2,5,5,4,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,2,1,3,3]=>[2,5,6,1,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,2,3,1,3]=>[1,4,5,2,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,2,3,3,1]=>[1,4,5,2,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,3,1,2,3]=>[3,6,1,1,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,3,1,3,2]=>[3,6,1,1,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,3,2,1,3]=>[3,6,1,2,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,3,2,3,1]=>[3,6,1,2,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,5,3,3,1,2]=>[3,6,1,3,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,5,3,3,2,1]=>[3,6,1,3,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,2,2,3,5]=>[1,6,2,1,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,2,2,5,3]=>[3,1,4,3,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,2,3,2,5]=>[3,1,4,4,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,2,3,5,2]=>[1,6,2,2,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,2,5,2,3]=>[1,6,2,4,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,2,5,3,2]=>[3,1,4,6,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,3,2,2,5]=>[3,1,5,2,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,3,2,5,2]=>[6,4,1,5,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,3,5,2,2]=>[1,6,3,3,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,5,2,2,3]=>[4,2,1,1,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,5,2,3,2]=>[4,2,1,1,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,5,3,2,2]=>[4,2,1,2,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,2,3,5]=>[2,1,1,3,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,1,2,5,3]=>[3,2,2,4,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,1,3,2,5]=>[2,1,1,4,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,1,3,5,2]=>[2,1,1,4,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,2,1,5,2,3]=>[4,3,3,1,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,2,1,5,3,2]=>[4,3,3,1,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,2,1,3,5]=>[2,1,2,1,4,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[3,2,2,1,5,3]=>[4,3,4,3,1,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,2,3,1,5]=>[4,3,4,5,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,2,3,5,1]=>[2,1,2,3,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,2,5,1,3]=>[2,1,2,5,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,2,2,5,3,1]=>[3,2,3,6,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,2,3,1,2,5]=>[3,2,4,1,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,3,1,5,2]=>[4,3,5,2,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,3,2,1,5]=>[2,1,3,1,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,2,3,2,5,1]=>[2,1,3,1,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,3,5,1,2]=>[2,1,3,4,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,3,5,2,1]=>[2,1,3,4,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,5,1,2,3]=>[2,1,5,5,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,2,5,1,3,2]=>[2,1,5,5,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,2,5,2,1,3]=>[2,1,5,6,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,5,2,3,1]=>[5,4,1,2,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,5,3,1,2]=>[3,2,6,1,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,5,3,2,1]=>[3,2,6,1,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,3,1,2,2,5]=>[1,1,6,2,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,3,1,2,5,2]=>[1,1,6,2,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,1,5,2,2]=>[4,4,2,1,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,3,2,1,2,5]=>[2,2,1,1,3,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,3,2,1,5,2]=>[4,4,3,3,1,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,3,2,2,1,5]=>[2,2,1,2,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,3,2,2,5,1]=>[2,2,1,2,5,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,3,2,5,1,2]=>[2,2,1,5,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,3,2,5,2,1]=>[2,2,1,5,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,3,5,1,2,2]=>[1,1,3,4,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,5,2,1,2]=>[2,2,4,6,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,3,5,2,2,1]=>[2,2,4,6,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,5,1,2,2,3]=>[1,3,4,2,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,5,1,2,3,2]=>[2,4,5,3,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,1,3,2,2]=>[2,4,5,4,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,5,2,1,2,3]=>[2,4,6,1,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,2,1,3,2]=>[2,4,6,1,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,5,2,2,1,3]=>[2,4,6,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,5,2,2,3,1]=>[1,3,5,1,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,2,3,1,2]=>[1,3,5,2,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,5,2,3,2,1]=>[2,4,6,3,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,3,1,2,2]=>[3,5,1,1,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,5,3,2,1,2]=>[3,5,1,2,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,3,2,2,1]=>[3,5,1,2,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,2,2,3,3]=>[1,4,2,1,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,1,2,3,2,3]=>[2,5,3,3,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,1,2,3,3,2]=>[2,5,3,3,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,3,2,2,3]=>[2,5,4,1,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,3,2,3,2]=>[2,5,4,1,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,3,3,2,2]=>[2,5,4,2,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,2,1,2,3,3]=>[2,6,1,3,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,2,1,3,2,3]=>[2,6,1,4,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,1,3,3,2]=>[2,6,1,4,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,2,2,1,3,3]=>[2,6,2,1,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,2,3,1,3]=>[1,5,1,2,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,2,3,3,1]=>[1,5,1,2,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,2,3,1,2,3]=>[1,5,2,6,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,2,3,1,3,2]=>[4,1,5,2,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,3,2,1,3]=>[2,6,3,1,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,3,2,3,1]=>[4,1,5,3,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,3,3,1,2]=>[1,5,2,1,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,3,3,2,1]=>[2,6,3,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,1,2,2,3]=>[3,1,1,4,3,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,3,1,2,3,2]=>[3,1,1,4,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,3,1,3,2,2]=>[3,1,1,5,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,3,2,1,2,3]=>[3,1,2,2,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,3,2,1,3,2]=>[3,1,2,2,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,3,2,2,1,3]=>[3,1,2,3,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,3,2,2,3,1]=>[3,1,2,3,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,2,3,1,2]=>[3,1,2,4,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,3,2,3,2,1]=>[3,1,2,4,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,3,3,1,2,2]=>[3,1,3,1,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,3,3,2,1,2]=>[3,1,3,2,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,3,3,2,2,1]=>[3,1,3,2,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,3,3,6]=>[1,2,1,2,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,2,2,3,6,3]=>[1,2,1,2,4,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,2,6,3,3]=>[1,2,1,5,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,2,3,2,3,6]=>[2,3,3,1,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,3,2,6,3]=>[4,5,5,3,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,3,3,2,6]=>[2,3,3,2,1,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,3,3,6,2]=>[1,2,2,1,4,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,2,3,6,2,3]=>[1,2,2,4,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,2,3,6,3,2]=>[2,3,3,5,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,2,3,3]=>[1,2,5,4,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,6,3,2,3]=>[4,5,1,1,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,6,3,3,2]=>[4,5,1,1,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,3,2,2,3,6]=>[2,4,1,2,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,2,2,6,3]=>[4,6,3,4,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,2,3,2,6]=>[2,4,1,3,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,2,3,6,2]=>[2,4,1,3,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,2,6,2,3]=>[2,4,1,6,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,6,3,2]=>[4,6,3,1,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,3,2,2,6]=>[2,4,2,1,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,3,3,2,6,2]=>[2,4,2,1,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,3,6,2,2]=>[1,3,1,4,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,3,6,2,2,3]=>[1,3,4,4,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,6,2,3,2]=>[2,4,5,5,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,6,3,2,2]=>[2,4,5,6,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,2,2,3,3]=>[1,6,4,1,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,6,2,3,2,3]=>[3,1,6,4,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,2,3,3,2]=>[3,1,6,4,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,3,2,2,3]=>[4,2,1,3,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,3,2,3,2]=>[4,2,1,3,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,3,3,2,2]=>[4,2,1,4,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,3,3,6]=>[2,1,3,3,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,1,2,3,6,3]=>[2,1,3,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,2,6,3,3]=>[4,3,5,1,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,3,2,3,6]=>[2,1,4,1,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,2,6,3]=>[4,3,6,3,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,3,3,2,6]=>[2,1,4,2,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,1,3,3,6,2]=>[2,1,4,2,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,3,6,2,3]=>[2,1,4,5,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,3,6,3,2]=>[2,1,4,5,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,6,2,3,3]=>[3,2,1,6,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,6,3,2,3]=>[4,3,2,1,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,3,3,2]=>[4,3,2,1,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,3,3,6]=>[2,2,1,4,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,2,1,3,6,3]=>[2,2,1,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,1,6,3,3]=>[4,4,3,2,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,2,3,1,3,6]=>[1,1,2,6,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,2,3,1,6,3]=>[4,4,5,2,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,3,3,1,6]=>[3,3,4,3,1,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,2,3,3,6,1]=>[1,1,2,1,4,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,3,6,1,3]=>[1,1,2,4,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,2,3,6,3,1]=>[1,1,2,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,6,1,3,3]=>[1,1,5,3,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,6,3,1,3]=>[4,4,1,1,2,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,6,3,3,1]=>[4,4,1,1,4,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,3,1,2,3,6]=>[1,2,6,2,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,3,1,2,6,3]=>[4,5,2,5,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,3,1,3,2,6]=>[4,5,2,6,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,3,6,2]=>[1,2,6,3,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,1,6,2,3]=>[3,4,1,1,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,3,1,6,3,2]=>[4,5,2,2,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,2,1,3,6]=>[2,3,1,1,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,2,1,6,3]=>[4,5,3,3,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,3,1,6]=>[3,4,2,4,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,2,3,6,1]=>[2,3,1,3,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,6,1,3]=>[2,3,1,6,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,2,6,3,1]=>[4,5,3,1,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,3,1,2,6]=>[1,2,1,6,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,3,1,6,2]=>[3,4,3,1,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,3,3,2,1,6]=>[3,4,3,2,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,3,2,6,1]=>[2,3,2,1,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,3,6,1,2]=>[1,2,1,4,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,3,6,2,1]=>[2,3,2,5,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,3,6,1,2,3]=>[1,2,4,3,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,6,1,3,2]=>[2,3,5,4,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,6,2,1,3]=>[2,3,5,5,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,6,2,3,1]=>[1,2,4,4,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,3,6,3,1,2]=>[1,2,4,5,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,6,3,2,1]=>[2,3,5,6,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,1,2,3,3]=>[1,5,3,2,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,6,1,3,2,3]=>[2,6,4,4,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,6,1,3,3,2]=>[2,6,4,4,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,6,2,1,3,3]=>[2,6,5,1,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,2,3,1,3]=>[1,5,4,2,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,2,3,3,1]=>[1,5,4,2,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,3,1,2,3]=>[4,1,1,2,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,6,3,1,3,2]=>[4,1,1,2,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,3,2,1,3]=>[4,1,1,3,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,6,3,2,3,1]=>[4,1,1,3,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,3,3,1,2]=>[4,1,1,4,2,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,3,3,2,1]=>[4,1,1,4,3,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,1,2,2,3,6]=>[1,6,2,1,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,2,2,6,3]=>[4,2,5,4,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,2,3,2,6]=>[4,2,5,5,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,2,3,6,2]=>[1,6,2,2,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,2,6,2,3]=>[1,6,2,5,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,2,6,3,2]=>[4,2,5,1,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,3,2,2,6]=>[4,2,6,3,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,3,2,6,2]=>[6,4,1,5,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,3,6,2,2]=>[1,6,3,4,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,6,2,2,3]=>[3,1,1,6,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,6,2,3,2]=>[3,1,1,6,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,6,3,2,2]=>[4,2,2,1,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,2,3,6]=>[2,1,1,3,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,2,1,2,6,3]=>[4,3,3,5,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,2,1,3,2,6]=>[2,1,1,4,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,2,1,3,6,2]=>[2,1,1,4,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,2,1,6,2,3]=>[3,2,2,1,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,1,6,3,2]=>[4,3,3,2,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,2,1,3,6]=>[2,1,2,1,4,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,2,2,1,6,3]=>[4,3,4,3,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,2,3,1,6]=>[3,2,3,4,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,2,3,6,1]=>[2,1,2,3,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,2,6,1,3]=>[2,1,2,6,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,2,6,3,1]=>[4,3,4,1,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,3,1,2,6]=>[4,3,5,2,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,3,1,6,2]=>[3,2,4,1,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,3,2,1,6]=>[3,2,4,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[3,2,3,2,6,1]=>[2,1,3,1,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,3,6,1,2]=>[2,1,3,5,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,3,6,2,1]=>[2,1,3,5,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,6,1,2,3]=>[2,1,6,4,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,6,1,3,2]=>[2,1,6,4,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,2,6,2,1,3]=>[2,1,6,5,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,6,2,3,1]=>[5,4,2,1,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,3,1,2]=>[4,3,1,1,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,6,3,2,1]=>[4,3,1,1,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,3,1,2,2,6]=>[1,1,6,2,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,3,1,2,6,2]=>[1,1,6,2,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,1,6,2,2]=>[3,3,1,1,6,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,3,2,1,2,6]=>[2,2,1,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,3,2,1,6,2]=>[3,3,2,2,1,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,3,2,2,1,6]=>[3,3,2,3,2,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,3,2,2,6,1]=>[2,2,1,2,6,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,2,6,1,2]=>[2,2,1,6,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,3,2,6,2,1]=>[2,2,1,6,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,3,6,1,2,2]=>[1,1,4,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,6,2,1,2]=>[2,2,5,5,1,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,3,6,2,2,1]=>[2,2,5,5,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,6,1,2,2,3]=>[1,4,3,2,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,6,1,2,3,2]=>[2,5,4,3,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,6,1,3,2,2]=>[2,5,4,4,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,6,2,1,2,3]=>[2,5,5,1,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,6,2,1,3,2]=>[2,5,5,1,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,6,2,2,1,3]=>[2,5,5,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,6,2,2,3,1]=>[1,4,4,1,2,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,6,2,3,1,2]=>[1,4,4,2,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,6,2,3,2,1]=>[2,5,5,3,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,6,3,1,2,2]=>[1,4,5,6,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,3,2,1,2]=>[2,5,6,1,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,3,2,2,1]=>[2,5,6,1,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,1,2,2,3,3]=>[1,3,2,1,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[6,1,2,3,2,3]=>[2,4,3,3,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[6,1,2,3,3,2]=>[2,4,3,3,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[6,1,3,2,2,3]=>[2,4,4,1,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,3,2,3,2]=>[2,4,4,1,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,3,3,2,2]=>[2,4,4,2,1,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[6,2,1,2,3,3]=>[2,5,1,3,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,2,1,3,2,3]=>[2,5,1,4,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,1,3,3,2]=>[2,5,1,4,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,2,1,3,3]=>[2,5,2,1,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,2,2,3,1,3]=>[1,4,1,2,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,2,2,3,3,1]=>[1,4,1,2,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,2,3,1,2,3]=>[1,4,2,6,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[6,2,3,1,3,2]=>[3,6,4,1,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,3,2,1,3]=>[2,5,3,1,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,3,2,3,1]=>[3,6,4,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,3,3,1,2]=>[1,4,2,1,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,2,3,3,2,1]=>[2,5,3,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,3,1,2,2,3]=>[1,5,6,2,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,1,2,3,2]=>[4,1,2,5,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,1,3,2,2]=>[4,1,2,6,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,3,2,1,2,3]=>[2,6,1,1,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,3,2,1,3,2]=>[2,6,1,1,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,3,2,2,1,3]=>[2,6,1,2,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,3,2,2,3,1]=>[4,1,3,4,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,2,3,1,2]=>[4,1,3,5,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,2,3,2,1]=>[2,6,1,3,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,3,3,1,2,2]=>[1,5,1,6,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,3,3,2,1,2]=>[2,6,2,1,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,3,3,2,2,1]=>[2,6,2,1,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,2,3,4,4]=>[1,2,1,2,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,4,3,4]=>[2,3,2,4,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,4,4,3]=>[2,3,2,4,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,2,4,4]=>[2,3,3,1,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,4,2,4]=>[1,2,2,2,6,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,4,4,2]=>[1,2,2,2,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,4,2,3,4]=>[1,2,3,6,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,4,2,4,3]=>[3,4,5,1,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,3,2,4]=>[2,3,4,1,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,4,3,4,2]=>[3,4,5,2,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,4,2,3]=>[1,2,3,1,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,4,3,2]=>[2,3,4,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,2,2,4,4]=>[2,4,1,2,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,2,4,2,4]=>[6,1,5,1,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,2,4,4,2]=>[3,5,2,5,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,4,2,2,4]=>[1,3,2,6,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,4,2,4,2]=>[3,5,4,1,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,4,4,2,2]=>[1,3,2,1,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,2,2,3,4]=>[1,4,6,1,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,4,2,2,4,3]=>[3,6,1,3,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,2,3,2,4]=>[3,6,1,4,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,3,4,2]=>[3,6,1,4,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,4,2,4,2,3]=>[3,6,1,5,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,4,3,2]=>[3,6,1,5,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,3,2,2,4]=>[2,5,1,1,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,3,2,4,2]=>[3,6,2,2,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,3,4,2,2]=>[3,6,2,4,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,4,2,2,3]=>[1,4,1,6,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,4,2,3,2]=>[3,6,3,1,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,4,3,2,2]=>[2,5,2,1,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,2,3,4,4]=>[2,1,3,3,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,1,2,4,3,4]=>[2,1,3,4,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,2,4,4,3]=>[2,1,3,4,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,2,4,4]=>[2,1,4,1,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,3,4,2,4]=>[3,2,5,4,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,3,4,4,2]=>[3,2,5,4,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,2,3,4]=>[3,2,6,1,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,4,2,4,3]=>[3,2,6,1,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,3,2,4]=>[2,1,5,1,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,4,3,4,2]=>[3,2,6,2,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,4,4,2,3]=>[3,2,6,3,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,4,4,3,2]=>[2,1,5,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,1,3,4,4]=>[2,2,1,4,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,2,1,4,3,4]=>[2,2,1,5,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,1,4,4,3]=>[2,2,1,5,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,2,3,1,4,4]=>[1,1,2,6,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,2,3,4,1,4]=>[1,1,2,2,5,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,2,3,4,4,1]=>[1,1,2,2,1,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,2,4,1,3,4]=>[1,1,3,5,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,2,4,1,4,3]=>[2,2,4,6,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,4,3,1,4]=>[3,3,5,2,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,4,3,4,1]=>[2,2,4,1,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,4,4,1,3]=>[1,1,3,1,5,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,2,4,4,3,1]=>[3,3,5,3,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,3,1,2,4,4]=>[1,2,6,2,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,1,4,2,4]=>[3,4,1,6,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,4,4,2]=>[3,4,1,6,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,3,2,1,4,4]=>[2,3,1,1,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,2,4,1,4]=>[2,3,1,4,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,2,4,4,1]=>[2,3,1,4,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,4,1,2,4]=>[1,2,2,5,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,3,4,1,4,2]=>[1,2,2,5,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,4,2,1,4]=>[3,4,4,1,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,4,2,4,1]=>[1,2,2,6,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,4,4,1,2]=>[1,2,2,1,5,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,4,4,2,1]=>[3,4,4,3,1,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,1,2,3,4]=>[1,3,5,2,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,4,1,2,4,3]=>[2,4,6,3,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,1,3,2,4]=>[6,1,3,1,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,4,1,3,4,2]=>[1,3,5,3,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,1,4,2,3]=>[1,3,5,4,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,4,3,2]=>[2,4,6,5,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,2,1,3,4]=>[3,5,1,2,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,2,1,4,3]=>[3,5,1,2,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,2,3,1,4]=>[3,5,1,4,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,2,3,4,1]=>[1,3,6,2,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,2,4,1,3]=>[6,1,4,1,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,2,4,3,1]=>[3,5,1,5,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,3,1,2,4]=>[3,5,2,1,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,3,1,4,2]=>[3,5,2,1,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,3,2,1,4]=>[2,4,1,1,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[2,4,3,2,4,1]=>[2,4,1,1,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,3,4,1,2]=>[2,4,1,3,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,3,4,2,1]=>[3,5,2,4,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,4,1,2,3]=>[1,3,1,5,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,4,4,1,3,2]=>[2,4,2,6,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,4,4,2,1,3]=>[3,5,3,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,4,2,3,1]=>[3,5,3,1,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,4,3,1,2]=>[3,5,3,2,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,4,3,2,1]=>[2,4,2,1,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,1,2,2,4,4]=>[1,6,2,1,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,2,4,2,4]=>[3,1,4,5,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,2,4,4,2]=>[3,1,4,5,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,4,2,2,4]=>[3,1,6,1,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,4,2,4,2]=>[3,1,6,1,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,4,4,2,2]=>[3,1,6,3,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,1,2,4,4]=>[2,1,1,3,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,4,2,4]=>[3,2,2,6,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,1,4,4,2]=>[3,2,2,6,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,2,1,4,4]=>[2,1,2,1,5,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,2,2,4,1,4]=>[2,1,2,4,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,2,4,4,1]=>[2,1,2,4,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,2,4,1,2,4]=>[2,1,4,6,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,4,1,4,2]=>[6,5,1,3,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,4,2,1,4]=>[3,2,5,1,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,4,2,4,1]=>[6,5,1,4,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,4,4,1,2]=>[2,1,4,2,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,4,4,2,1]=>[3,2,5,3,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,4,1,2,2,4]=>[1,2,5,2,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,4,1,2,4,2]=>[1,2,5,2,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,4,2,2]=>[1,2,5,4,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,2,1,2,4]=>[3,4,1,2,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,2,1,4,2]=>[3,4,1,2,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,2,2,1,4]=>[3,4,1,3,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,2,2,4,1]=>[1,2,6,1,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,2,4,1,2]=>[1,2,6,3,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,2,4,2,1]=>[3,4,1,5,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,4,1,2,2]=>[1,2,1,5,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,4,4,2,1,2]=>[3,4,3,1,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,4,2,2,1]=>[3,4,3,1,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,2,2,3,4]=>[1,5,2,1,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,2,2,4,3]=>[2,6,3,2,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,2,3,2,4]=>[2,6,3,3,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,2,3,4,2]=>[1,5,2,2,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,2,4,2,3]=>[1,5,2,3,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,4,3,2]=>[2,6,3,4,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,2,2,4]=>[2,6,4,1,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,3,2,4,2]=>[6,3,1,5,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,3,4,2,2]=>[1,5,3,2,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,4,2,2,3]=>[1,5,4,6,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,4,2,3,2]=>[5,2,1,3,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,3,2,2]=>[2,6,5,1,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,2,1,2,3,4]=>[3,1,2,4,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,1,2,4,3]=>[3,1,2,4,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,3,2,4]=>[3,1,2,5,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,2,1,3,4,2]=>[3,1,2,5,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,4,2,3]=>[3,1,2,6,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,1,4,3,2]=>[3,1,2,6,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,2,2,1,3,4]=>[3,1,3,2,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,2,1,4,3]=>[3,1,3,2,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,2,2,3,1,4]=>[3,1,3,4,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,2,2,3,4,1]=>[1,6,1,2,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,2,2,4,1,3]=>[1,6,1,3,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,2,4,3,1]=>[3,1,3,5,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,3,1,2,4]=>[3,1,4,1,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,2,3,1,4,2]=>[3,1,4,1,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,2,3,2,1,4]=>[3,1,4,2,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,3,2,4,1]=>[4,2,5,3,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,3,4,1,2]=>[1,6,2,2,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,2,3,4,2,1]=>[3,1,4,4,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,4,1,2,3]=>[1,6,3,5,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,2,4,1,3,2]=>[6,4,1,3,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,4,2,1,3]=>[3,1,5,1,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,4,2,3,1]=>[3,1,5,1,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,2,4,3,1,2]=>[3,1,5,2,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,4,3,2,1]=>[3,1,5,2,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,3,1,2,2,4]=>[3,2,1,4,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,2,4,2]=>[3,2,1,4,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,4,2,2]=>[3,2,1,6,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,2,1,2,4]=>[2,1,1,1,3,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,3,2,1,4,2]=>[3,2,2,2,6,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,3,2,2,1,4]=>[2,1,1,2,1,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,3,2,2,4,1]=>[2,1,1,2,4,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,2,4,1,2]=>[2,1,1,4,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,2,4,2,1]=>[3,2,2,5,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,3,4,1,2,2]=>[2,1,3,6,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,3,4,2,1,2]=>[3,2,4,1,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,4,2,2,1]=>[3,2,4,1,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,1,2,2,3]=>[1,1,5,2,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,4,1,2,3,2]=>[2,2,6,3,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,4,1,3,2,2]=>[2,2,6,4,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,4,2,1,2,3]=>[3,3,1,2,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,4,2,1,3,2]=>[3,3,1,2,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,4,2,2,1,3]=>[3,3,1,3,2,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,4,2,2,3,1]=>[3,3,1,3,4,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,4,2,3,1,2]=>[3,3,1,4,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,4,2,3,2,1]=>[3,3,1,4,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,3,1,2,2]=>[3,3,2,1,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,3,2,1,2]=>[2,2,1,1,1,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,4,3,2,2,1]=>[2,2,1,1,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,2,3,4,5]=>[1,2,1,2,2,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,2,3,5,4]=>[2,3,2,3,4,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,4,3,5]=>[2,3,2,4,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,2,4,5,3]=>[1,2,1,3,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,2,5,3,4]=>[1,2,1,4,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,2,5,4,3]=>[2,3,2,5,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,3,2,4,5]=>[2,3,3,1,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,3,2,5,4]=>[2,3,3,1,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,3,4,2,5]=>[1,2,2,2,6,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,2,3,4,5,2]=>[1,2,2,2,2,5]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,2,3,5,2,4]=>[1,2,2,3,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,3,5,4,2]=>[3,4,4,5,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,4,2,3,5]=>[1,2,3,6,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,4,2,5,3]=>[3,4,5,1,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,4,3,2,5]=>[2,3,4,1,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,4,3,5,2]=>[2,3,4,1,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,4,5,2,3]=>[1,2,3,2,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,4,5,3,2]=>[3,4,5,4,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,5,2,3,4]=>[1,2,4,5,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,2,5,2,4,3]=>[2,3,5,6,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,3,2,4]=>[3,4,6,1,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,3,4,2]=>[3,4,6,1,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,2,5,4,2,3]=>[3,4,6,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,4,3,2]=>[2,3,5,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,3,2,2,4,5]=>[2,4,1,2,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,2,2,5,4]=>[2,4,1,2,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,2,4,2,5]=>[6,1,5,1,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,4,5,2]=>[2,4,1,4,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,2,5,2,4]=>[6,1,5,2,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,2,5,4,2]=>[3,5,2,6,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,4,2,2,5]=>[1,3,2,6,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,4,2,5,2]=>[1,3,2,6,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,5,2,2]=>[1,3,2,2,5,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,5,2,2,4]=>[1,3,3,5,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,3,5,2,4,2]=>[6,1,1,3,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,5,4,2,2]=>[3,5,5,2,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,2,2,3,5]=>[1,4,6,1,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,2,2,5,3]=>[5,1,3,5,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,4,2,3,2,5]=>[5,1,3,6,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,3,5,2]=>[1,4,6,2,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,5,2,3]=>[5,1,3,1,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,2,5,3,2]=>[5,1,3,1,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,3,2,2,5]=>[2,5,1,1,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,3,2,5,2]=>[5,1,4,4,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,3,5,2,2]=>[2,5,1,4,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,5,2,2,3]=>[1,4,2,5,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,5,2,3,2]=>[2,5,3,6,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,5,3,2,2]=>[3,6,4,1,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,2,2,3,4]=>[1,5,5,1,2,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,2,2,4,3]=>[4,1,1,4,6,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,2,3,2,4]=>[4,1,1,5,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,2,3,4,2]=>[4,1,1,5,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,2,4,2,3]=>[4,1,1,6,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,2,4,3,2]=>[4,1,1,6,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,3,2,2,4]=>[4,1,2,3,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,3,2,4,2]=>[4,1,2,3,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,3,4,2,2]=>[4,1,2,5,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,4,2,2,3]=>[4,1,3,2,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,4,2,3,2]=>[4,1,3,2,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,4,3,2,2]=>[2,6,1,1,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,1,2,3,4,5]=>[2,1,3,3,3,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,1,2,3,5,4]=>[2,1,3,3,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,2,4,3,5]=>[2,1,3,4,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,2,4,5,3]=>[3,2,4,5,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,2,5,3,4]=>[3,2,4,6,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,2,5,4,3]=>[2,1,3,5,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,3,2,4,5]=>[2,1,4,1,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,3,2,5,4]=>[2,1,4,1,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,3,4,2,5]=>[3,2,5,4,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,5,2]=>[2,1,4,3,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,3,5,2,4]=>[6,5,1,1,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,1,3,5,4,2]=>[3,2,5,5,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,1,4,2,3,5]=>[3,2,6,1,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,2,5,3]=>[5,4,1,3,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,4,3,2,5]=>[2,1,5,1,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,4,3,5,2]=>[2,1,5,1,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,5,2,3]=>[2,1,5,3,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,4,5,3,2]=>[3,2,6,4,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,5,2,3,4]=>[4,3,1,1,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,5,2,4,3]=>[4,3,1,1,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,5,3,2,4]=>[4,3,1,2,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,5,3,4,2]=>[4,3,1,2,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,5,4,2,3]=>[4,3,1,3,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,5,4,3,2]=>[2,1,6,1,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[2,2,1,3,4,5]=>[2,2,1,4,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,2,1,3,5,4]=>[2,2,1,4,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,2,1,4,3,5]=>[2,2,1,5,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,2,1,4,5,3]=>[3,3,2,6,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,2,1,5,3,4]=>[4,4,3,1,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,2,1,5,4,3]=>[2,2,1,6,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,2,3,1,4,5]=>[1,1,2,6,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,2,3,1,5,4]=>[4,4,5,2,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,2,3,4,1,5]=>[1,1,2,2,5,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,2,3,4,5,1]=>[1,1,2,2,2,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,2,3,5,1,4]=>[1,1,2,3,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,2,3,5,4,1]=>[2,2,3,4,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,4,1,3,5]=>[1,1,3,5,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,2,4,1,5,3]=>[4,4,6,1,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,4,3,1,5]=>[4,4,6,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,2,4,3,5,1]=>[2,2,4,1,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,4,5,1,3]=>[1,1,3,2,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,2,4,5,3,1]=>[3,3,5,4,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,5,1,3,4]=>[1,1,4,4,3,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,2,5,1,4,3]=>[5,5,1,1,1,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[2,2,5,3,1,4]=>[5,5,1,3,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,5,3,4,1]=>[1,1,4,6,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,5,4,1,3]=>[2,2,5,1,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,5,4,3,1]=>[3,3,6,2,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,2,4,5]=>[1,2,6,2,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,3,1,2,5,4]=>[3,4,1,4,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,1,4,2,5]=>[5,6,3,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,3,1,4,5,2]=>[1,2,6,4,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,5,2,4]=>[4,5,2,1,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,1,5,4,2]=>[4,5,2,1,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,2,1,4,5]=>[2,3,1,1,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,3,2,1,5,4]=>[2,3,1,1,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,2,4,1,5]=>[4,5,3,6,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,2,4,5,1]=>[2,3,1,4,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,5,1,4]=>[5,6,4,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,3,2,5,4,1]=>[2,3,1,5,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,4,1,2,5]=>[1,2,2,5,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,3,4,1,5,2]=>[4,5,5,1,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[2,3,4,2,1,5]=>[4,5,5,2,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,2,5,1]=>[1,2,2,6,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,3,4,5,1,2]=>[1,2,2,2,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,3,4,5,2,1]=>[2,3,3,3,6,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,3,5,1,2,4]=>[1,2,3,4,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,5,1,4,2]=>[1,2,3,4,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,5,2,1,4]=>[2,3,4,6,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,2,4,1]=>[1,2,3,5,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,5,4,1,2]=>[2,3,4,1,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,5,4,2,1]=>[3,4,5,2,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,1,2,3,5]=>[1,3,5,2,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,4,1,2,5,3]=>[1,3,5,2,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,3,2,5]=>[6,1,3,1,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,1,3,5,2]=>[6,1,3,1,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,4,1,5,2,3]=>[4,6,1,1,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,4,1,5,3,2]=>[4,6,1,1,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,2,1,3,5]=>[6,1,4,5,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,4,2,1,5,3]=>[4,6,2,3,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,2,3,1,5]=>[4,6,2,5,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,4,2,3,5,1]=>[1,3,6,2,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,2,5,1,3]=>[6,1,4,2,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,2,5,3,1]=>[3,5,1,6,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,4,3,1,2,5]=>[3,5,2,1,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,1,5,2]=>[4,6,3,2,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,3,2,1,5]=>[2,4,1,1,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,4,3,2,5,1]=>[2,4,1,1,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,4,3,5,1,2]=>[2,4,1,4,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,3,5,2,1]=>[2,4,1,4,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,5,1,2,3]=>[1,3,2,4,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,4,5,1,3,2]=>[2,4,3,5,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,5,2,1,3]=>[2,4,3,6,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,5,2,3,1]=>[1,3,2,5,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,5,3,1,2]=>[3,5,4,1,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,4,5,3,2,1]=>[3,5,4,1,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,1,2,3,4]=>[1,4,4,2,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,5,1,2,4,3]=>[2,5,5,3,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,1,3,2,4]=>[6,2,2,1,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,5,1,3,4,2]=>[1,4,4,3,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,5,1,4,2,3]=>[5,1,1,1,3,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,5,1,4,3,2]=>[5,1,1,1,4,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,5,2,1,3,4]=>[2,5,6,1,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,2,1,4,3]=>[5,1,2,4,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,5,2,3,1,4]=>[5,1,2,6,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,2,3,4,1]=>[1,4,5,2,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,2,4,1,3]=>[6,2,3,1,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,5,2,4,3,1]=>[6,2,3,1,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,3,1,2,4]=>[3,6,1,1,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,5,3,1,4,2]=>[5,1,3,3,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,5,3,2,1,4]=>[5,1,3,4,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,5,3,2,4,1]=>[6,2,4,5,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,3,4,1,2]=>[1,4,6,2,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,3,4,2,1]=>[3,6,1,4,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,5,4,1,2,3]=>[2,5,1,6,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,5,4,1,3,2]=>[2,5,1,6,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,4,2,1,3]=>[3,6,2,1,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,4,2,3,1]=>[3,6,2,1,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,5,4,3,1,2]=>[3,6,2,2,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,4,3,2,1]=>[2,5,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[3,1,2,2,4,5]=>[1,6,2,1,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,2,2,5,4]=>[3,1,4,3,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,2,4,2,5]=>[3,1,4,5,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,2,4,5,2]=>[1,6,2,3,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,2,5,2,4]=>[1,6,2,4,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,5,4,2]=>[3,1,4,6,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,4,2,2,5]=>[5,3,1,3,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,4,2,5,2]=>[5,3,1,3,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,4,5,2,2]=>[1,6,4,2,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,2,4]=>[4,2,1,1,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,5,2,4,2]=>[4,2,1,1,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,5,4,2,2]=>[4,2,1,3,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,2,4,5]=>[2,1,1,3,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,1,2,5,4]=>[2,1,1,3,5,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,2,1,4,2,5]=>[5,4,4,1,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,2,1,4,5,2]=>[2,1,1,5,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,5,2,4]=>[4,3,3,1,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,2,1,5,4,2]=>[4,3,3,1,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,2,1,4,5]=>[2,1,2,1,5,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,2,1,5,4]=>[2,1,2,1,6,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,2,2,4,1,5]=>[4,3,4,6,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,2,2,4,5,1]=>[2,1,2,4,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,2,5,1,4]=>[5,4,5,1,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,2,2,5,4,1]=>[2,1,2,5,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,4,1,2,5]=>[2,1,4,6,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,4,1,5,2]=>[4,3,6,1,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,2,4,2,1,5]=>[4,3,6,2,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,4,2,5,1]=>[6,5,1,4,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,4,5,1,2]=>[2,1,4,3,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,4,5,2,1]=>[2,1,4,3,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,5,1,2,4]=>[2,1,5,5,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,5,1,4,2]=>[5,4,1,1,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,2,5,2,1,4]=>[5,4,1,2,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,5,2,4,1]=>[6,5,2,3,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,5,4,1,2]=>[2,1,5,1,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,5,4,2,1]=>[3,2,6,2,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,4,1,2,2,5]=>[1,2,5,2,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,1,2,5,2]=>[1,2,5,2,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,1,5,2,2]=>[4,5,1,1,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,4,2,1,2,5]=>[3,4,1,2,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,4,2,1,5,2]=>[4,5,2,3,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,2,2,1,5]=>[4,5,2,4,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,2,2,5,1]=>[1,2,6,1,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,4,2,5,1,2]=>[1,2,6,4,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,4,2,5,2,1]=>[5,6,3,1,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,5,1,2,2]=>[1,2,2,4,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,4,5,2,1,2]=>[2,3,3,6,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,5,2,2,1]=>[2,3,3,6,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,5,1,2,2,4]=>[1,3,4,2,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,5,1,2,4,2]=>[1,3,4,2,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,1,4,2,2]=>[1,3,4,4,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,2,1,2,4]=>[2,4,6,1,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,2,1,4,2]=>[6,1,3,5,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,2,1,4]=>[2,4,6,2,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,2,2,4,1]=>[1,3,5,1,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,2,4,1,2]=>[1,3,5,3,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,5,2,4,2,1]=>[6,1,3,1,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,4,1,2,2]=>[2,4,1,6,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,4,2,1,2]=>[3,5,2,1,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,4,2,2,1]=>[3,5,2,1,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,2,2,3,5]=>[1,5,2,1,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,2,2,5,3]=>[1,5,2,1,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,2,3,2,5]=>[2,6,3,3,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,2,3,5,2]=>[1,5,2,2,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,2,5,2,3]=>[1,5,2,4,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,2,5,3,2]=>[5,2,6,1,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,2,2,5]=>[2,6,4,1,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,3,2,5,2]=>[6,3,1,5,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,3,5,2,2]=>[1,5,3,3,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,5,2,2,3]=>[4,1,1,1,4,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,5,2,3,2]=>[4,1,1,1,5,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,5,3,2,2]=>[4,1,1,2,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,2,3,5]=>[3,1,2,4,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,1,2,5,3]=>[3,1,2,4,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,1,3,2,5]=>[3,1,2,5,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,2,1,3,5,2]=>[6,4,5,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,1,5,2,3]=>[4,2,3,1,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,5,3,2]=>[4,2,3,1,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,2,1,3,5]=>[3,1,3,2,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,2,2,1,5,3]=>[4,2,4,3,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,2,3,1,5]=>[4,2,4,5,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,2,2,3,5,1]=>[1,6,1,2,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,2,5,1,3]=>[1,6,1,4,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,2,5,3,1]=>[3,1,3,6,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[4,2,3,1,2,5]=>[3,1,4,1,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,3,1,5,2]=>[4,2,5,2,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,2,3,2,1,5]=>[4,2,5,3,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,3,2,5,1]=>[5,3,6,4,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,3,5,1,2]=>[1,6,2,3,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,3,5,2,1]=>[4,2,5,6,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,5,1,2,3]=>[1,6,4,4,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,5,1,3,2]=>[6,4,2,2,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,2,5,2,1,3]=>[6,4,2,3,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,5,2,3,1]=>[5,3,1,2,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,5,3,1,2]=>[3,1,6,1,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,2,5,3,2,1]=>[3,1,6,1,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,3,1,2,2,5]=>[3,2,1,4,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,1,2,5,2]=>[5,4,3,6,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,5,2,2]=>[4,3,2,1,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,3,2,1,2,5]=>[2,1,1,1,3,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,3,2,1,5,2]=>[4,3,3,3,1,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,3,2,2,1,5]=>[2,1,1,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[4,3,2,2,5,1]=>[2,1,1,2,5,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,3,2,5,1,2]=>[2,1,1,5,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,3,2,5,2,1]=>[2,1,1,5,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,3,5,1,2,2]=>[2,1,4,5,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,5,2,1,2]=>[2,1,4,6,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,5,2,2,1]=>[2,1,4,6,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,5,1,2,2,3]=>[1,2,4,2,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[4,5,1,2,3,2]=>[2,3,5,3,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,5,1,3,2,2]=>[2,3,5,4,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,2,1,2,3]=>[2,3,6,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,5,2,1,3,2]=>[2,3,6,1,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,2,2,1,3]=>[2,3,6,2,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,2,2,3,1]=>[1,2,5,1,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,5,2,3,1,2]=>[1,2,5,2,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,5,2,3,2,1]=>[2,3,6,3,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,5,3,1,2,2]=>[3,4,1,1,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,5,3,2,1,2]=>[3,4,1,2,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,5,3,2,2,1]=>[3,4,1,2,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,2,2,3,4]=>[1,4,2,1,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[5,1,2,2,4,3]=>[2,5,3,2,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,3,2,4]=>[2,5,3,3,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,3,4,2]=>[1,4,2,2,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,2,4,2,3]=>[1,4,2,3,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,2,4,3,2]=>[2,5,3,4,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,3,2,2,4]=>[2,5,4,1,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,3,2,4,2]=>[6,2,1,5,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,3,4,2,2]=>[1,4,3,2,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,4,2,2,3]=>[1,4,4,6,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,4,2,3,2]=>[5,1,1,3,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,4,3,2,2]=>[2,5,5,1,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,2,1,2,3,4]=>[2,6,1,3,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,2,1,2,4,3]=>[2,6,1,3,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,1,3,2,4]=>[2,6,1,4,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,2,1,3,4,2]=>[4,1,3,6,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,4,2,3]=>[5,2,4,1,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,4,3,2]=>[2,6,1,5,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,2,2,1,3,4]=>[2,6,2,1,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,2,1,4,3]=>[2,6,2,1,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,2,3,1,4]=>[1,5,1,2,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,2,3,4,1]=>[1,5,1,2,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,2,2,4,1,3]=>[1,5,1,3,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,2,4,3,1]=>[4,1,4,6,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,3,1,2,4]=>[1,5,2,6,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,3,1,4,2]=>[5,2,6,3,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,3,2,1,4]=>[2,6,3,1,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,3,2,4,1]=>[4,1,5,3,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,3,4,1,2]=>[1,5,2,2,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[5,2,3,4,2,1]=>[4,1,5,5,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,4,1,2,3]=>[1,5,3,5,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,2,4,1,3,2]=>[6,3,1,3,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,2,4,2,1,3]=>[6,3,1,4,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,4,2,3,1]=>[4,1,6,2,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,4,3,1,2]=>[4,1,6,3,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,4,3,2,1]=>[2,6,4,1,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,3,1,2,2,4]=>[3,1,1,4,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,3,1,2,4,2]=>[3,1,1,4,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,3,1,4,2,2]=>[3,1,1,6,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,2,1,2,4]=>[3,1,2,2,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,3,2,1,4,2]=>[3,1,2,2,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,2,2,1,4]=>[3,1,2,3,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,3,2,2,4,1]=>[4,2,3,4,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,2,4,1,2]=>[4,2,3,6,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,2,4,2,1]=>[3,1,2,5,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,3,4,1,2,2]=>[1,6,2,5,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,3,4,2,1,2]=>[3,1,4,1,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,3,4,2,2,1]=>[3,1,4,1,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,1,2,2,3]=>[2,1,6,3,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,4,1,2,3,2]=>[2,1,6,3,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,4,1,3,2,2]=>[2,1,6,4,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,4,2,1,2,3]=>[3,2,1,2,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,4,2,1,3,2]=>[3,2,1,2,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,4,2,2,1,3]=>[3,2,1,3,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,4,2,2,3,1]=>[3,2,1,3,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,2,3,1,2]=>[3,2,1,4,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,4,2,3,2,1]=>[3,2,1,4,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,4,3,1,2,2]=>[3,2,2,1,4,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,3,2,1,2]=>[2,1,1,1,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[5,4,3,2,2,1]=>[2,1,1,1,2,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,2,3,4,6]=>[1,2,1,2,2,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,2,3,6,4]=>[1,2,1,2,4,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,2,4,3,6]=>[2,3,2,4,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,2,4,6,3]=>[1,2,1,3,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,2,6,3,4]=>[1,2,1,5,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,2,2,6,4,3]=>[4,5,4,1,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,2,4,6]=>[2,3,3,1,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,3,2,6,4]=>[4,5,5,3,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,3,4,2,6]=>[1,2,2,2,6,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,2,3,4,6,2]=>[1,2,2,2,3,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,6,2,4]=>[1,2,2,4,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,3,6,4,2]=>[3,4,4,6,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,2,4,2,3,6]=>[1,2,3,6,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,4,2,6,3]=>[4,5,6,2,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,4,3,2,6]=>[2,3,4,1,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,4,3,6,2]=>[2,3,4,1,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,6,2,3]=>[1,2,3,3,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,6,3,2]=>[2,3,4,4,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,6,2,3,4]=>[1,2,5,4,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,2,6,2,4,3]=>[2,3,6,5,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,6,3,2,4]=>[4,5,1,1,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,6,3,4,2]=>[4,5,1,1,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,6,4,2,3]=>[4,5,1,2,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,6,4,3,2]=>[4,5,1,2,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,2,4,6]=>[2,4,1,2,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,2,2,6,4]=>[4,6,3,4,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,2,4,2,6]=>[6,1,5,1,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,4,6,2]=>[6,1,5,1,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,2,6,2,4]=>[6,1,5,3,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,2,6,4,2]=>[4,6,3,1,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,4,2,2,6]=>[1,3,2,6,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,4,2,6,2]=>[1,3,2,6,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,6,2,2]=>[1,3,2,3,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,6,2,2,4]=>[1,3,4,4,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,6,2,4,2]=>[6,1,2,2,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,6,4,2,2]=>[3,5,6,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,2,2,3,6]=>[1,4,6,1,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,4,2,2,6,3]=>[5,1,3,5,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,2,3,2,6]=>[5,1,3,6,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,3,6,2]=>[5,1,3,6,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,2,6,2,3]=>[5,1,3,2,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,2,6,3,2]=>[5,1,3,2,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,3,2,2,6]=>[2,5,1,1,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,3,2,6,2]=>[5,1,4,4,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,3,6,2,2]=>[5,1,4,1,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,6,2,2,3]=>[1,4,3,4,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,6,2,3,2]=>[2,5,4,5,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,6,3,2,2]=>[2,5,4,6,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,2,2,3,4]=>[1,6,4,1,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,6,2,2,4,3]=>[3,1,6,3,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,2,3,2,4]=>[3,1,6,4,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,3,4,2]=>[3,1,6,4,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,6,2,4,2,3]=>[3,1,6,5,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,4,3,2]=>[3,1,6,5,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,3,2,2,4]=>[4,2,1,3,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,3,2,4,2]=>[4,2,1,3,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,3,4,2,2]=>[4,2,1,5,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,4,2,2,3]=>[3,1,1,1,3,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,6,4,2,3,2]=>[3,1,1,1,4,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,6,4,3,2,2]=>[3,1,1,2,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,2,3,4,6]=>[2,1,3,3,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,1,2,3,6,4]=>[3,2,4,4,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,2,4,3,6]=>[2,1,3,4,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,4,6,3]=>[2,1,3,4,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,2,6,3,4]=>[4,3,5,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,2,6,4,3]=>[4,3,5,1,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,2,4,6]=>[2,1,4,1,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,1,3,2,6,4]=>[4,3,6,3,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,3,4,2,6]=>[4,3,6,5,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,4,6,2]=>[2,1,4,3,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,6,2,4]=>[6,5,1,2,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,1,3,6,4,2]=>[3,2,5,6,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,2,3,6]=>[5,4,1,3,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,4,2,6,3]=>[5,4,1,3,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,4,3,2,6]=>[2,1,5,1,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,1,4,3,6,2]=>[5,4,1,4,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,1,4,6,2,3]=>[2,1,5,4,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,6,3,2]=>[2,1,5,4,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,6,2,3,4]=>[3,2,1,6,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,6,2,4,3]=>[3,2,1,6,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,6,3,2,4]=>[4,3,2,1,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,6,3,4,2]=>[4,3,2,1,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,6,4,2,3]=>[3,2,1,1,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,6,4,3,2]=>[3,2,1,1,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,3,4,6]=>[2,2,1,4,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,2,1,3,6,4]=>[3,3,2,5,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,1,4,3,6]=>[2,2,1,5,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,2,1,4,6,3]=>[2,2,1,5,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,1,6,3,4]=>[4,4,3,2,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,2,1,6,4,3]=>[3,3,2,1,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,3,1,4,6]=>[1,1,2,6,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,2,3,1,6,4]=>[3,3,4,1,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[2,2,3,4,1,6]=>[1,1,2,2,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,2,3,4,6,1]=>[1,1,2,2,3,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,3,6,1,4]=>[1,1,2,4,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,2,3,6,4,1]=>[1,1,2,4,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,4,1,3,6]=>[1,1,3,5,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,4,1,6,3]=>[4,4,6,1,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,4,3,1,6]=>[3,3,5,2,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,2,4,3,6,1]=>[2,2,4,1,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,4,6,1,3]=>[1,1,3,3,3,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[2,2,4,6,3,1]=>[1,1,3,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,6,1,3,4]=>[1,1,5,3,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,2,6,1,4,3]=>[2,2,6,4,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,6,3,1,4]=>[5,5,2,2,3,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,6,3,4,1]=>[4,4,1,1,5,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,2,6,4,1,3]=>[4,4,1,2,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,6,4,3,1]=>[4,4,1,2,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,1,2,4,6]=>[1,2,6,2,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,2,6,4]=>[4,5,2,5,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,1,4,2,6]=>[5,6,3,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,3,1,4,6,2]=>[1,2,6,4,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,1,6,2,4]=>[3,4,1,1,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,6,4,2]=>[3,4,1,1,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[2,3,2,1,4,6]=>[2,3,1,1,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,2,1,6,4]=>[3,4,2,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,2,4,1,6]=>[4,5,3,6,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,2,4,6,1]=>[2,3,1,4,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,2,6,1,4]=>[2,3,1,6,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,2,6,4,1]=>[4,5,3,1,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,4,1,2,6]=>[1,2,2,5,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[2,3,4,1,6,2]=>[1,2,2,5,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,4,2,1,6]=>[3,4,4,1,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,2,6,1]=>[1,2,2,6,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,4,6,1,2]=>[1,2,2,3,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,3,4,6,2,1]=>[2,3,3,4,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,6,1,2,4]=>[1,2,4,3,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,6,1,4,2]=>[1,2,4,3,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,6,2,1,4]=>[5,6,1,1,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,3,6,2,4,1]=>[1,2,4,4,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,6,4,1,2]=>[1,2,4,6,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,6,4,2,1]=>[3,4,6,1,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,1,2,3,6]=>[1,3,5,2,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,1,2,6,3]=>[4,6,1,5,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,4,1,3,2,6]=>[6,1,3,1,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,1,3,6,2]=>[6,1,3,1,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,4,1,6,2,3]=>[1,3,5,6,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,6,3,2]=>[4,6,1,2,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,2,1,3,6]=>[6,1,4,5,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,2,1,6,3]=>[4,6,2,3,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,2,3,1,6]=>[3,5,1,4,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,4,2,3,6,1]=>[1,3,6,2,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,2,6,1,3]=>[6,1,4,3,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,2,6,3,1]=>[4,6,2,1,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,3,1,2,6]=>[4,6,3,2,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,1,6,2]=>[3,5,2,1,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,3,2,1,6]=>[3,5,2,2,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,4,3,2,6,1]=>[2,4,1,1,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,3,6,1,2]=>[2,4,1,5,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,3,6,2,1]=>[2,4,1,5,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,4,6,1,2,3]=>[1,3,3,3,2,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,4,6,1,3,2]=>[6,1,1,1,1,5]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[2,4,6,2,1,3]=>[6,1,1,2,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,4,6,2,3,1]=>[1,3,3,4,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,6,3,1,2]=>[1,3,3,5,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,6,3,2,1]=>[2,4,4,6,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,1,2,3,4]=>[1,5,3,2,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,6,1,2,4,3]=>[2,6,4,3,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,6,1,3,2,4]=>[6,3,1,1,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,6,1,3,4,2]=>[1,5,3,3,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,6,1,4,2,3]=>[1,5,3,4,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,1,4,3,2]=>[2,6,4,5,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,2,1,3,4]=>[2,6,5,1,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,2,1,4,3]=>[5,2,1,4,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,2,3,1,4]=>[5,2,1,6,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,2,3,4,1]=>[1,5,4,2,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,6,2,4,1,3]=>[6,3,2,1,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,6,2,4,3,1]=>[6,3,2,1,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,3,1,2,4]=>[4,1,1,2,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,3,1,4,2]=>[5,2,2,3,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,6,3,2,1,4]=>[5,2,2,4,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,6,3,2,4,1]=>[4,1,1,3,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,3,4,1,2]=>[4,1,1,5,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[2,6,3,4,2,1]=>[4,1,1,5,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,4,1,2,3]=>[4,1,2,1,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,6,4,1,3,2]=>[4,1,2,1,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,4,2,1,3]=>[4,1,2,2,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,6,4,2,3,1]=>[4,1,2,2,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,6,4,3,1,2]=>[4,1,2,3,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,6,4,3,2,1]=>[4,1,2,3,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,2,2,4,6]=>[1,6,2,1,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,2,2,6,4]=>[4,2,5,4,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,2,4,2,6]=>[4,2,5,6,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,2,4,6,2]=>[1,6,2,3,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,2,6,2,4]=>[1,6,2,5,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,6,4,2]=>[4,2,5,1,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,4,2,2,6]=>[5,3,1,3,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,4,2,6,2]=>[5,3,1,3,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,4,6,2,2]=>[1,6,4,3,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,6,2,2,4]=>[3,1,1,6,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,6,2,4,2]=>[3,1,1,6,5,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,6,4,2,2]=>[3,1,1,1,1,3]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[3,2,1,2,4,6]=>[2,1,1,3,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,1,2,6,4]=>[4,3,3,5,1,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,1,4,2,6]=>[5,4,4,1,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,1,4,6,2]=>[2,1,1,5,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,2,1,6,2,4]=>[3,2,2,1,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,1,6,4,2]=>[3,2,2,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,2,1,4,6]=>[2,1,2,1,5,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,2,2,1,6,4]=>[3,2,3,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,2,4,1,6]=>[4,3,4,6,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,2,4,6,1]=>[2,1,2,4,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,2,2,6,1,4]=>[2,1,2,6,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,2,6,4,1]=>[4,3,4,1,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,4,1,2,6]=>[4,3,6,1,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,4,1,6,2]=>[6,5,1,3,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,4,2,1,6]=>[3,2,5,1,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,4,2,6,1]=>[6,5,1,4,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,4,6,1,2]=>[2,1,4,4,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,2,4,6,2,1]=>[2,1,4,4,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,6,1,2,4]=>[2,1,6,4,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,6,1,4,2]=>[6,5,3,1,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,2,1,4]=>[5,4,2,1,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,6,2,4,1]=>[6,5,3,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,6,4,1,2]=>[4,3,1,2,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,6,4,2,1]=>[4,3,1,2,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,4,1,2,2,6]=>[1,2,5,2,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[3,4,1,2,6,2]=>[1,2,5,2,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,1,6,2,2]=>[1,2,5,6,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,2,1,2,6]=>[4,5,2,3,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,2,1,6,2]=>[3,4,1,2,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,2,2,1,6]=>[3,4,1,3,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,4,2,2,6,1]=>[1,2,6,1,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,2,6,1,2]=>[1,2,6,5,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,2,6,2,1]=>[5,6,3,2,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,6,1,2,2]=>[1,2,3,3,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,4,6,2,1,2]=>[2,3,4,5,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,6,2,2,1]=>[2,3,4,5,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,6,1,2,2,4]=>[1,4,3,2,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,6,1,2,4,2]=>[1,4,3,2,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,6,1,4,2,2]=>[1,4,3,4,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,6,2,1,2,4]=>[2,5,5,1,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,6,2,1,4,2]=>[5,1,1,4,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,6,2,2,1,4]=>[5,1,1,5,4,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,6,2,2,4,1]=>[1,4,4,1,3,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,2,4,1,2]=>[1,4,4,3,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,2,4,2,1]=>[6,2,2,1,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,4,1,2,2]=>[1,4,6,5,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,4,2,1,2]=>[3,6,1,1,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,6,4,2,2,1]=>[3,6,1,1,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,2,2,3,6]=>[1,5,2,1,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,2,2,6,3]=>[4,1,5,4,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,2,3,2,6]=>[4,1,5,5,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,1,2,3,6,2]=>[1,5,2,2,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,1,2,6,2,3]=>[1,5,2,5,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,2,6,3,2]=>[4,1,5,1,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,3,2,2,6]=>[4,1,6,3,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,1,3,2,6,2]=>[6,3,1,5,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,3,6,2,2]=>[1,5,3,4,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,6,2,2,3]=>[1,5,6,4,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,6,2,3,2]=>[5,2,3,1,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,3,2,2]=>[4,1,2,1,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,2,3,6]=>[3,1,2,4,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,1,2,6,3]=>[4,2,3,5,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,3,2,6]=>[4,2,3,6,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,1,3,6,2]=>[6,4,5,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,2,1,6,2,3]=>[3,1,2,1,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,1,6,3,2]=>[4,2,3,2,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,2,1,3,6]=>[3,1,3,2,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,2,1,6,3]=>[4,2,4,3,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,2,3,1,6]=>[3,1,3,4,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[4,2,2,3,6,1]=>[1,6,1,2,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,2,6,1,3]=>[1,6,1,5,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,2,6,3,1]=>[4,2,4,1,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,2,3,1,2,6]=>[4,2,5,2,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,2,3,1,6,2]=>[3,1,4,1,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,2,3,2,1,6]=>[3,1,4,2,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,2,3,2,6,1]=>[4,2,5,3,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,3,6,1,2]=>[1,6,2,4,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,3,6,2,1]=>[5,3,6,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,6,1,2,3]=>[1,6,5,3,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,2,6,1,3,2]=>[6,4,3,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,6,2,1,3]=>[6,4,3,2,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,6,2,3,1]=>[5,3,2,1,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,6,3,1,2]=>[4,2,1,1,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,2,6,3,2,1]=>[4,2,1,1,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,3,1,2,2,6]=>[4,3,2,5,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,1,2,6,2]=>[5,4,3,6,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,6,2,2]=>[3,2,1,1,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,2,1,2,6]=>[2,1,1,1,3,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,3,2,1,6,2]=>[3,2,2,2,1,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,3,2,2,1,6]=>[3,2,2,3,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[4,3,2,2,6,1]=>[2,1,1,2,6,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,2,6,1,2]=>[2,1,1,6,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,2,6,2,1]=>[2,1,1,6,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,3,6,1,2,2]=>[2,1,5,4,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,6,2,1,2]=>[2,1,5,5,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,3,6,2,2,1]=>[2,1,5,5,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,6,1,2,2,3]=>[1,3,3,2,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,6,1,2,3,2]=>[2,4,4,3,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,6,1,3,2,2]=>[2,4,4,4,1,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,6,2,1,2,3]=>[2,4,5,1,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,6,2,1,3,2]=>[2,4,5,1,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,6,2,2,1,3]=>[2,4,5,2,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,6,2,2,3,1]=>[1,3,4,1,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,6,2,3,1,2]=>[1,3,4,2,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,6,2,3,2,1]=>[2,4,5,3,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,6,3,1,2,2]=>[1,3,5,6,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,6,3,2,1,2]=>[2,4,6,1,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,6,3,2,2,1]=>[2,4,6,1,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,1,2,2,3,4]=>[1,3,2,1,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[6,1,2,2,4,3]=>[2,4,3,2,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,2,3,2,4]=>[2,4,3,3,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,2,3,4,2]=>[1,3,2,2,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[6,1,2,4,2,3]=>[1,3,2,3,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,2,4,3,2]=>[2,4,3,4,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,3,2,2,4]=>[2,4,4,1,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[6,1,3,2,4,2]=>[6,1,1,5,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,1,3,4,2,2]=>[1,3,3,2,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,4,2,2,3]=>[1,3,4,6,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,4,2,3,2]=>[3,5,6,1,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,3,2,2]=>[2,4,5,1,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,1,2,3,4]=>[2,5,1,3,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[6,2,1,2,4,3]=>[2,5,1,3,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,1,3,2,4]=>[2,5,1,4,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[6,2,1,3,4,2]=>[3,6,2,5,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,1,4,2,3]=>[5,1,4,1,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,1,4,3,2]=>[2,5,1,5,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[6,2,2,1,3,4]=>[2,5,2,1,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,2,1,4,3]=>[2,5,2,1,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,2,2,3,1,4]=>[1,4,1,2,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,2,2,3,4,1]=>[1,4,1,2,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,2,4,1,3]=>[1,4,1,3,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,2,2,4,3,1]=>[3,6,3,5,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,3,1,2,4]=>[1,4,2,6,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,2,3,1,4,2]=>[5,1,6,3,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,2,3,2,1,4]=>[2,5,3,1,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,2,3,2,4,1]=>[2,5,3,1,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,3,4,1,2]=>[1,4,2,2,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,2,3,4,2,1]=>[3,6,4,4,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,4,1,2,3]=>[1,4,3,5,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,4,1,3,2]=>[6,2,1,3,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,4,2,1,3]=>[6,2,1,4,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,4,2,3,1]=>[3,6,5,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,4,3,1,2]=>[3,6,5,2,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,4,3,2,1]=>[2,5,4,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,3,1,2,2,4]=>[1,5,6,2,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,1,2,4,2]=>[4,1,2,5,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,3,1,4,2,2]=>[5,2,3,1,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,3,2,1,2,4]=>[2,6,1,1,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,3,2,1,4,2]=>[5,2,4,4,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,2,2,1,4]=>[2,6,1,2,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,2,2,4,1]=>[4,1,3,4,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,3,2,4,1,2]=>[4,1,3,6,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,3,2,4,2,1]=>[4,1,3,6,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,3,4,1,2,2]=>[1,5,2,5,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,3,4,2,1,2]=>[4,1,5,2,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,4,2,2,1]=>[4,1,5,2,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,1,2,2,3]=>[1,6,5,2,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,4,1,2,3,2]=>[4,2,1,5,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,4,1,3,2,2]=>[4,2,1,6,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,2,1,2,3]=>[3,1,1,2,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,4,2,1,3,2]=>[3,1,1,2,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,4,2,2,1,3]=>[3,1,1,3,2,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,4,2,2,3,1]=>[3,1,1,3,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[6,4,2,3,1,2]=>[3,1,1,4,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[6,4,2,3,2,1]=>[3,1,1,4,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,3,1,2,2]=>[3,1,2,1,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,3,2,1,2]=>[3,1,2,2,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,4,3,2,2,1]=>[3,1,2,2,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,3,5,5]=>[1,2,1,2,3,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,5,3,5]=>[1,2,1,4,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,2,5,5,3]=>[1,2,1,4,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,2,3,2,5,5]=>[2,3,3,1,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,3,5,2,5]=>[1,2,2,3,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,5,5,2]=>[1,2,2,3,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,5,2,3,5]=>[1,2,4,5,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,5,2,5,3]=>[5,6,1,2,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,5,3,2,5]=>[5,6,1,3,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,5,3,5,2]=>[1,2,4,6,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,5,2,3]=>[1,2,4,1,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,5,5,3,2]=>[3,4,6,3,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,2,2,5,5]=>[2,4,1,2,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,3,2,5,2,5]=>[6,1,5,2,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,2,5,5,2]=>[2,4,1,5,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,5,2,2,5]=>[1,3,3,5,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,5,2,5,2]=>[6,1,1,3,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,5,5,2,2]=>[1,3,3,1,5,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,5,2,2,3,5]=>[1,5,5,1,2,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,2,2,5,3]=>[5,2,2,5,1,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,2,3,2,5]=>[5,2,2,6,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,2,3,5,2]=>[4,1,1,5,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,5,2,5,2,3]=>[5,2,2,1,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,5,2,5,3,2]=>[5,2,2,1,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,3,2,2,5]=>[5,2,3,4,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,3,2,5,2]=>[5,2,3,4,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,3,5,2,2]=>[4,1,2,6,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,5,5,2,2,3]=>[1,5,1,5,1,2]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,5,5,2,3,2]=>[4,1,4,1,5,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,5,3,2,2]=>[4,1,4,2,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,3,5,5]=>[2,1,3,3,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,5,3,5]=>[3,2,4,6,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,2,5,5,3]=>[3,2,4,6,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,3,2,5,5]=>[2,1,4,1,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,3,5,2,5]=>[6,5,1,1,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,5,5,2]=>[2,1,4,4,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,1,5,2,3,5]=>[4,3,1,1,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,5,2,5,3]=>[5,4,2,2,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,5,3,2,5]=>[5,4,2,3,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,5,3,5,2]=>[4,3,1,2,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,5,5,2,3]=>[4,3,1,4,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,5,5,3,2]=>[4,3,1,4,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,3,5,5]=>[2,2,1,4,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,2,1,5,3,5]=>[4,4,3,1,2,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,2,1,5,5,3]=>[4,4,3,1,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,2,3,1,5,5]=>[1,1,2,6,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,2,3,5,1,5]=>[1,1,2,3,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,3,5,5,1]=>[1,1,2,3,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,5,1,3,5]=>[1,1,4,4,3,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,2,5,1,5,3]=>[5,5,1,1,2,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,5,3,1,5]=>[5,5,1,3,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,2,5,3,5,1]=>[1,1,4,6,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,5,5,1,3]=>[1,1,4,1,4,3]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,2,5,5,3,1]=>[3,3,6,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[2,3,1,2,5,5]=>[1,2,6,2,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,1,5,2,5]=>[5,6,3,2,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,1,5,5,2]=>[4,5,2,1,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,3,2,1,5,5]=>[2,3,1,1,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,2,5,1,5]=>[5,6,4,1,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,2,5,5,1]=>[2,3,1,5,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,3,5,1,2,5]=>[1,2,3,4,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,5,1,5,2]=>[1,2,3,4,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,5,2,1,5]=>[4,5,6,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,5,2,5,1]=>[1,2,3,5,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,5,5,1,2]=>[1,2,3,1,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,5,5,2,1]=>[2,3,4,2,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,2,3,5]=>[1,4,4,2,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,5,1,2,5,3]=>[5,1,1,6,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,5,1,3,2,5]=>[6,2,2,1,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,3,5,2]=>[6,2,2,1,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,5,1,5,2,3]=>[5,1,1,2,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,5,1,5,3,2]=>[5,1,1,2,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,5,2,1,3,5]=>[6,2,3,5,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,2,1,5,3]=>[5,1,2,4,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,2,3,1,5]=>[5,1,2,6,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,2,3,5,1]=>[1,4,5,2,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,2,5,1,3]=>[6,2,3,2,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,5,2,5,3,1]=>[5,1,2,1,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,3,1,2,5]=>[5,1,3,3,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,5,3,1,5,2]=>[5,1,3,3,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,5,3,2,1,5]=>[5,1,3,4,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,3,2,5,1]=>[5,1,3,4,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,5,3,5,1,2]=>[1,4,6,3,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,5,3,5,2,1]=>[6,2,4,1,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,5,1,2,3]=>[1,4,1,4,2,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,5,5,1,3,2]=>[2,5,2,5,4,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,5,2,1,3]=>[2,5,2,6,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,5,2,3,1]=>[1,4,1,5,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,5,3,1,2]=>[3,6,3,1,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,5,5,3,2,1]=>[3,6,3,1,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,2,2,5,5]=>[1,6,2,1,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,1,2,5,2,5]=>[5,3,6,1,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,2,5,5,2]=>[1,6,2,4,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,2,5]=>[5,3,2,2,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,5,2,5,2]=>[5,3,2,2,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,1,5,5,2,2]=>[4,2,1,4,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,2,1,2,5,5]=>[2,1,1,3,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,5,2,5]=>[5,4,4,2,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,2,1,5,5,2]=>[4,3,3,1,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,2,2,1,5,5]=>[2,1,2,1,6,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,2,2,5,1,5]=>[5,4,5,1,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,2,2,5,5,1]=>[2,1,2,5,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,2,5,1,2,5]=>[5,4,1,1,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,2,5,1,5,2]=>[5,4,1,1,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,2,5,2,1,5]=>[5,4,1,2,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,2,5,2,5,1]=>[5,4,1,2,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,5,5,1,2]=>[2,1,5,2,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,5,5,2,1]=>[2,1,5,2,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,5,1,2,2,5]=>[1,3,4,2,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,5,1,2,5,2]=>[1,3,4,2,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,5,2,2]=>[1,3,4,5,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,5,2,1,2,5]=>[2,4,6,1,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,1,5,2]=>[4,6,1,3,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,5,2,2,1,5]=>[4,6,1,4,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,2,2,5,1]=>[1,3,5,1,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,2,5,1,2]=>[1,3,5,4,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,2,5,2,1]=>[6,1,3,2,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,5,1,2,2]=>[1,3,1,4,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,5,5,2,1,2]=>[2,4,2,6,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,5,2,2,1]=>[2,4,2,6,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,1,2,2,3,5]=>[1,4,2,1,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,1,2,2,5,3]=>[1,4,2,1,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,2,3,2,5]=>[2,5,3,3,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,1,2,3,5,2]=>[1,4,2,2,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,5,2,3]=>[1,4,2,4,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,2,5,3,2]=>[5,1,6,1,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,3,2,2,5]=>[2,5,4,1,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,3,2,5,2]=>[6,2,1,5,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,3,5,2,2]=>[1,4,3,3,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,1,5,2,2,3]=>[1,4,5,5,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,5,2,3,2]=>[5,1,2,2,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,5,3,2,2]=>[5,1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,2,3,5]=>[2,6,1,3,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,2,1,2,5,3]=>[5,2,4,6,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,3,2,5]=>[2,6,1,4,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,1,3,5,2]=>[6,3,5,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,2,1,5,2,3]=>[4,1,3,1,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,2,1,5,3,2]=>[4,1,3,1,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,2,2,1,3,5]=>[2,6,2,1,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,2,2,1,5,3]=>[4,1,4,3,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,2,2,3,1,5]=>[4,1,4,5,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,2,2,3,5,1]=>[1,5,1,2,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,2,5,1,3]=>[1,5,1,4,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,2,2,5,3,1]=>[5,2,5,1,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,2,3,1,2,5]=>[1,5,2,6,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,3,1,5,2]=>[4,1,5,2,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,2,3,2,1,5]=>[4,1,5,3,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,2,3,2,5,1]=>[5,2,6,4,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,3,5,1,2]=>[1,5,2,3,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,2,3,5,2,1]=>[4,1,5,6,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,5,1,2,3]=>[1,5,4,4,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,2,5,1,3,2]=>[6,3,2,2,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,5,2,1,3]=>[6,3,2,3,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,5,2,3,1]=>[5,2,1,2,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,5,3,1,2]=>[5,2,1,3,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,5,3,2,1]=>[5,2,1,3,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,1,2,2,5]=>[3,1,1,4,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,1,2,5,2]=>[5,3,3,6,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,1,5,2,2]=>[4,2,2,1,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[5,3,2,1,2,5]=>[3,1,2,2,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,2,1,5,2]=>[4,2,3,3,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,2,2,1,5]=>[4,2,3,4,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,3,2,2,5,1]=>[5,3,4,5,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,2,5,1,2]=>[5,3,4,1,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,3,2,5,2,1]=>[5,3,4,1,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,5,1,2,2]=>[1,6,3,4,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,5,2,1,2]=>[4,2,6,1,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,5,2,2,1]=>[4,2,6,1,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,5,1,2,2,3]=>[1,1,4,2,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,5,1,2,3,2]=>[2,2,5,3,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,5,1,3,2,2]=>[2,2,5,4,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,5,2,1,2,3]=>[2,2,6,1,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,5,2,1,3,2]=>[2,2,6,1,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,5,2,2,1,3]=>[2,2,6,2,1,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,5,2,2,3,1]=>[1,1,5,1,2,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,5,2,3,1,2]=>[1,1,5,2,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,5,2,3,2,1]=>[2,2,6,3,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,5,3,1,2,2]=>[3,3,1,1,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,5,3,2,1,2]=>[3,3,1,2,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,5,3,2,2,1]=>[3,3,1,2,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,3,5,6]=>[1,2,1,2,3,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,2,3,6,5]=>[2,3,2,3,5,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,2,5,3,6]=>[1,2,1,4,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,2,5,6,3]=>[1,2,1,4,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,2,6,3,5]=>[1,2,1,5,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,2,6,5,3]=>[4,5,4,1,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,3,2,5,6]=>[2,3,3,1,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,3,2,6,5]=>[2,3,3,1,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,3,5,2,6]=>[1,2,2,3,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,2,3,5,6,2]=>[1,2,2,3,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,3,6,2,5]=>[1,2,2,4,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,2,3,6,5,2]=>[2,3,3,5,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,5,2,3,6]=>[1,2,4,5,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,2,5,2,6,3]=>[5,6,1,2,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,2,5,3,2,6]=>[5,6,1,3,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,3,6,2]=>[5,6,1,3,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,2,5,6,2,3]=>[1,2,4,2,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,2,5,6,3,2]=>[2,3,5,3,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,2,3,5]=>[1,2,5,4,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,6,2,5,3]=>[5,6,2,1,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,6,3,2,5]=>[5,6,2,2,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,3,5,2]=>[4,5,1,1,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,2,6,5,2,3]=>[4,5,1,3,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,6,5,3,2]=>[4,5,1,3,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,2,2,5,6]=>[2,4,1,2,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,2,2,6,5]=>[2,4,1,2,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,2,5,2,6]=>[6,1,5,2,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,2,5,6,2]=>[2,4,1,5,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,2,6,2,5]=>[6,1,5,3,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,2,6,5,2]=>[4,6,3,1,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,5,2,2,6]=>[1,3,3,5,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,5,2,6,2]=>[6,1,1,3,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,5,6,2,2]=>[1,3,3,2,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,6,2,2,5]=>[1,3,4,4,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,3,6,2,5,2]=>[6,1,2,2,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,3,6,5,2,2]=>[2,4,5,1,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,2,2,3,6]=>[1,5,5,1,2,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,2,2,6,3]=>[4,1,1,4,1,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,2,3,2,6]=>[4,1,1,5,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,5,2,3,6,2]=>[5,2,2,6,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,5,2,6,2,3]=>[5,2,2,2,1,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,5,2,6,3,2]=>[4,1,1,1,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,5,3,2,2,6]=>[4,1,2,3,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,5,3,2,6,2]=>[5,2,3,4,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,3,6,2,2]=>[5,2,3,1,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,6,2,2,3]=>[1,5,2,4,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,6,2,3,2]=>[2,6,3,5,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,6,3,2,2]=>[4,1,5,1,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,6,2,2,3,5]=>[1,6,4,1,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,2,2,5,3]=>[5,3,1,5,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,6,2,3,2,5]=>[5,3,1,6,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,3,5,2]=>[1,6,4,2,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,5,2,3]=>[5,3,1,1,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,6,2,5,3,2]=>[5,3,1,1,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,6,3,2,2,5]=>[5,3,2,4,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,3,2,5,2]=>[5,3,2,4,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,6,3,5,2,2]=>[4,2,1,6,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,6,5,2,2,3]=>[4,2,3,1,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,5,2,3,2]=>[4,2,3,1,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,5,3,2,2]=>[3,1,2,1,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,2,3,5,6]=>[2,1,3,3,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,1,2,3,6,5]=>[2,1,3,3,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,2,5,3,6]=>[5,4,6,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,2,5,6,3]=>[2,1,3,5,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,2,6,3,5]=>[4,3,5,1,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,2,6,5,3]=>[4,3,5,1,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,3,2,5,6]=>[2,1,4,1,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,2,6,5]=>[2,1,4,1,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,1,3,5,2,6]=>[6,5,1,1,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,3,5,6,2]=>[2,1,4,4,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,6,2,5]=>[6,5,1,2,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,3,6,5,2]=>[2,1,4,5,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,5,2,3,6]=>[5,4,2,2,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,5,2,6,3]=>[4,3,1,1,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[2,1,5,3,2,6]=>[4,3,1,2,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,5,3,6,2]=>[5,4,2,3,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,5,6,2,3]=>[2,1,6,3,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,5,6,3,2]=>[4,3,1,5,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,6,2,3,5]=>[3,2,1,6,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,2,5,3]=>[5,4,3,1,1,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,6,3,2,5]=>[5,4,3,2,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,6,3,5,2]=>[4,3,2,1,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,1,6,5,2,3]=>[4,3,2,3,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,5,3,2]=>[3,2,1,2,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,3,5,6]=>[2,2,1,4,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,2,1,3,6,5]=>[2,2,1,4,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,2,1,5,3,6]=>[5,5,4,2,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,2,1,5,6,3]=>[4,4,3,1,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,2,1,6,3,5]=>[4,4,3,2,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,2,1,6,5,3]=>[3,3,2,1,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,3,1,5,6]=>[1,1,2,6,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,2,3,1,6,5]=>[3,3,4,1,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,2,3,5,1,6]=>[1,1,2,3,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,2,3,5,6,1]=>[1,1,2,3,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,3,6,1,5]=>[1,1,2,4,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,3,6,5,1]=>[2,2,3,5,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,5,1,3,6]=>[1,1,4,4,3,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,5,1,6,3]=>[5,5,1,1,3,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,5,3,1,6]=>[3,3,6,1,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,2,5,3,6,1]=>[1,1,4,6,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,5,6,1,3]=>[1,1,4,2,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,2,5,6,3,1]=>[1,1,4,2,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,6,1,3,5]=>[1,1,5,3,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,2,6,1,5,3]=>[4,4,1,6,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,2,6,3,1,5]=>[4,4,1,1,2,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,6,3,5,1]=>[1,1,5,5,3,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,2,6,5,1,3]=>[2,2,6,1,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,2,6,5,3,1]=>[4,4,1,3,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,1,2,5,6]=>[1,2,6,2,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,3,1,2,6,5]=>[4,5,2,5,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,1,5,2,6]=>[4,5,2,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[2,3,1,5,6,2]=>[1,2,6,5,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,6,2,5]=>[5,6,3,3,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,3,1,6,5,2]=>[4,5,2,2,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,2,1,5,6]=>[2,3,1,1,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,2,1,6,5]=>[3,4,2,2,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,2,5,1,6]=>[5,6,4,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,2,5,6,1]=>[2,3,1,5,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,2,6,1,5]=>[4,5,3,1,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,2,6,5,1]=>[2,3,1,6,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,5,1,2,6]=>[1,2,3,4,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,5,1,6,2]=>[1,2,3,4,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,5,2,1,6]=>[4,5,6,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,2,6,1]=>[1,2,3,5,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,5,6,1,2]=>[1,2,3,2,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,3,5,6,2,1]=>[2,3,4,3,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,6,1,2,5]=>[1,2,4,3,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,6,1,5,2]=>[1,2,4,3,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,6,2,1,5]=>[5,6,1,1,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,6,2,5,1]=>[5,6,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[2,3,6,5,1,2]=>[2,3,5,1,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,3,6,5,2,1]=>[2,3,5,1,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,1,2,3,6]=>[1,4,4,2,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[2,5,1,2,6,3]=>[5,1,1,6,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,5,1,3,2,6]=>[6,2,2,1,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,1,3,6,2]=>[6,2,2,1,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,5,1,6,2,3]=>[5,1,1,3,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,5,1,6,3,2]=>[5,1,1,3,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,5,2,1,3,6]=>[6,2,3,5,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,2,1,6,3]=>[5,1,2,4,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,2,3,1,6]=>[5,1,2,6,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,5,2,3,6,1]=>[1,4,5,2,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,2,6,1,3]=>[6,2,3,3,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,5,2,6,3,1]=>[5,1,2,2,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,5,3,1,2,6]=>[5,1,3,3,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,5,3,1,6,2]=>[5,1,3,3,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,5,3,2,1,6]=>[3,6,1,2,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,5,3,2,6,1]=>[6,2,4,5,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,3,6,1,2]=>[1,4,6,4,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,5,3,6,2,1]=>[5,1,3,1,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,5,6,1,2,3]=>[1,4,2,3,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,5,6,1,3,2]=>[2,5,3,4,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,6,2,1,3]=>[2,5,3,5,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,6,2,3,1]=>[1,4,2,4,2,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,5,6,3,1,2]=>[1,4,2,5,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,6,3,2,1]=>[2,5,3,6,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,1,2,3,5]=>[1,5,3,2,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,6,1,2,5,3]=>[1,5,3,2,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,1,3,2,5]=>[6,3,1,1,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,1,3,5,2]=>[6,3,1,1,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,6,1,5,2,3]=>[4,1,6,1,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,6,1,5,3,2]=>[4,1,6,1,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,2,1,3,5]=>[6,3,2,5,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,2,1,5,3]=>[5,2,1,4,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,6,2,3,1,5]=>[5,2,1,6,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,2,3,5,1]=>[1,5,4,2,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,6,2,5,1,3]=>[6,3,2,2,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,6,2,5,3,1]=>[5,2,1,1,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,3,1,2,5]=>[5,2,2,3,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,3,1,5,2]=>[4,1,1,2,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[2,6,3,2,1,5]=>[4,1,1,3,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[2,6,3,2,5,1]=>[5,2,2,4,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,6,3,5,1,2]=>[1,5,5,3,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,6,3,5,2,1]=>[4,1,1,6,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,5,1,2,3]=>[2,6,1,5,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,6,5,1,3,2]=>[2,6,1,5,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,5,2,1,3]=>[4,1,3,1,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,6,5,2,3,1]=>[4,1,3,1,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,5,3,1,2]=>[4,1,3,2,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,6,5,3,2,1]=>[4,1,3,2,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,2,2,5,6]=>[1,6,2,1,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,2,2,6,5]=>[4,2,5,4,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,5,2,6]=>[5,3,6,1,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,2,5,6,2]=>[1,6,2,4,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,2,6,2,5]=>[5,3,6,2,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,2,6,5,2]=>[4,2,5,1,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,5,2,2,6]=>[4,2,1,1,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[3,1,5,2,6,2]=>[5,3,2,2,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,1,5,6,2,2]=>[1,6,5,2,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,6,2,2,5]=>[5,3,3,1,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,6,2,5,2]=>[5,3,3,1,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,6,5,2,2]=>[4,2,2,3,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,2,5,6]=>[2,1,1,3,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,2,1,2,6,5]=>[2,1,1,3,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,2,1,5,2,6]=>[4,3,3,1,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[3,2,1,5,6,2]=>[2,1,1,6,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,1,6,2,5]=>[5,4,4,3,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,2,1,6,5,2]=>[4,3,3,2,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,2,1,5,6]=>[2,1,2,1,6,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,2,2,1,6,5]=>[3,2,3,2,1,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[3,2,2,5,1,6]=>[5,4,5,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,2,2,5,6,1]=>[2,1,2,5,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,2,6,1,5]=>[4,3,4,1,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,2,2,6,5,1]=>[2,1,2,6,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,5,1,2,6]=>[5,4,1,1,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,5,1,6,2]=>[5,4,1,1,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,2,5,2,1,6]=>[5,4,1,2,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,5,2,6,1]=>[6,5,2,3,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,5,6,1,2]=>[2,1,5,3,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,5,6,2,1]=>[2,1,5,3,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,6,1,2,5]=>[2,1,6,4,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,1,5,2]=>[4,3,1,6,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,2,6,2,1,5]=>[5,4,2,1,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,2,6,2,5,1]=>[5,4,2,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,6,5,1,2]=>[2,1,6,1,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,6,5,2,1]=>[4,3,1,3,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,5,1,2,2,6]=>[1,3,4,2,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,5,1,2,6,2]=>[1,3,4,2,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,6,2,2]=>[1,3,4,6,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,2,1,2,6]=>[4,6,1,3,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,2,1,6,2]=>[6,1,3,5,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,2,1,6]=>[4,6,1,4,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,2,2,6,1]=>[1,3,5,1,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,2,6,1,2]=>[1,3,5,5,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,5,2,6,2,1]=>[6,1,3,3,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,6,1,2,2]=>[1,3,2,3,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,5,6,2,1,2]=>[2,4,3,5,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,6,2,2,1]=>[2,4,3,5,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,6,1,2,2,5]=>[1,4,3,2,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,6,1,2,5,2]=>[1,4,3,2,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,1,5,2,2]=>[1,4,3,5,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,6,2,1,2,5]=>[5,1,1,4,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,6,2,1,5,2]=>[5,1,1,4,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,6,2,2,1,5]=>[5,1,1,5,4,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,6,2,2,5,1]=>[5,1,1,5,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[3,6,2,5,1,2]=>[5,1,1,1,1,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[3,6,2,5,2,1]=>[5,1,1,1,2,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,6,5,1,2,2]=>[2,5,1,5,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,6,5,2,1,2]=>[2,5,1,6,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,5,2,2,1]=>[2,5,1,6,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,1,2,2,3,6]=>[1,4,2,1,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[5,1,2,2,6,3]=>[1,4,2,1,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,2,3,2,6]=>[2,5,3,3,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,2,3,6,2]=>[1,4,2,2,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[5,1,2,6,2,3]=>[1,4,2,5,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,2,6,3,2]=>[5,1,6,2,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,3,2,2,6]=>[2,5,4,1,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,3,2,6,2]=>[6,2,1,5,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,3,6,2,2]=>[1,4,3,4,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,1,6,2,2,3]=>[1,4,6,4,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,6,2,3,2]=>[5,1,3,1,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,6,3,2,2]=>[5,1,3,2,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,2,3,6]=>[2,6,1,3,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,1,2,6,3]=>[4,1,3,5,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,2,1,3,2,6]=>[4,1,3,6,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,2,1,3,6,2]=>[6,3,5,1,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,1,6,2,3]=>[5,2,4,3,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,6,3,2]=>[4,1,3,2,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,2,2,1,3,6]=>[2,6,2,1,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,2,1,6,3]=>[4,1,4,3,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,2,2,3,1,6]=>[4,1,4,5,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,2,2,3,6,1]=>[1,5,1,2,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,2,6,1,3]=>[1,5,1,5,3,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,2,6,3,1]=>[4,1,4,1,1,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,2,3,1,2,6]=>[4,1,5,2,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,2,3,1,6,2]=>[5,2,6,3,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,3,2,1,6]=>[4,1,5,3,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,2,3,2,6,1]=>[4,1,5,3,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,3,6,1,2]=>[1,5,2,4,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,2,3,6,2,1]=>[5,2,6,1,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,6,1,2,3]=>[1,5,5,3,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,2,6,1,3,2]=>[6,3,3,1,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,2,6,2,1,3]=>[6,3,3,2,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,6,2,3,1]=>[5,2,2,1,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,6,3,1,2]=>[4,1,1,1,2,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,2,6,3,2,1]=>[4,1,1,1,3,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[5,3,1,2,2,6]=>[4,2,2,5,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,3,1,2,6,2]=>[5,3,3,6,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,1,6,2,2]=>[3,1,1,1,6,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,2,1,2,6]=>[4,2,3,3,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,3,2,1,6,2]=>[3,1,2,2,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,2,2,1,6]=>[3,1,2,3,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,3,2,2,6,1]=>[4,2,3,4,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,2,6,1,2]=>[4,2,3,1,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,2,6,2,1]=>[5,3,4,2,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,6,1,2,2]=>[1,6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,6,2,1,2]=>[5,3,1,1,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,3,6,2,2,1]=>[5,3,1,1,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,6,1,2,2,3]=>[1,2,3,2,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[5,6,1,2,3,2]=>[2,3,4,3,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[5,6,1,3,2,2]=>[2,3,4,4,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,6,2,1,2,3]=>[2,3,5,1,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,6,2,1,3,2]=>[2,3,5,1,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,6,2,2,1,3]=>[2,3,5,2,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,6,2,2,3,1]=>[1,2,4,1,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,6,2,3,1,2]=>[1,2,4,2,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,6,2,3,2,1]=>[2,3,5,3,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,6,3,1,2,2]=>[1,2,5,6,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,6,3,2,1,2]=>[2,3,6,1,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,6,3,2,2,1]=>[2,3,6,1,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,1,2,2,3,5]=>[1,3,2,1,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[6,1,2,2,5,3]=>[1,3,2,1,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,2,3,2,5]=>[2,4,3,3,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,2,3,5,2]=>[1,3,2,2,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,1,2,5,2,3]=>[1,3,2,4,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,2,5,3,2]=>[3,5,4,6,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,3,2,2,5]=>[2,4,4,1,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,1,3,2,5,2]=>[6,1,1,5,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,1,3,5,2,2]=>[1,3,3,3,5,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[6,1,5,2,2,3]=>[1,3,5,5,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,1,5,2,3,2]=>[4,6,1,1,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,5,3,2,2]=>[4,6,1,2,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,1,2,3,5]=>[2,5,1,3,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,2,1,2,5,3]=>[5,1,4,6,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,1,3,2,5]=>[2,5,1,4,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,1,3,5,2]=>[6,2,5,1,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,1,5,2,3]=>[5,1,4,2,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,2,1,5,3,2]=>[5,1,4,2,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,2,2,1,3,5]=>[2,5,2,1,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,2,2,1,5,3]=>[5,1,5,4,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,2,2,3,1,5]=>[1,4,1,2,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,2,3,5,1]=>[1,4,1,2,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,2,2,5,1,3]=>[1,4,1,4,4,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[6,2,2,5,3,1]=>[5,1,5,1,3,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[6,2,3,1,2,5]=>[1,4,2,6,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,2,3,1,5,2]=>[5,1,6,3,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,2,3,2,1,5]=>[2,5,3,1,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,3,2,5,1]=>[5,1,6,4,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,2,3,5,1,2]=>[1,4,2,3,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,2,3,5,2,1]=>[2,5,3,4,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,5,1,2,3]=>[1,4,4,4,2,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[6,2,5,1,3,2]=>[6,2,2,2,1,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,2,5,2,1,3]=>[6,2,2,3,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,2,5,2,3,1]=>[5,1,1,2,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,5,3,1,2]=>[5,1,1,3,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,2,5,3,2,1]=>[5,1,1,3,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,3,1,2,2,5]=>[1,5,6,2,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,1,2,5,2]=>[5,2,3,6,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,1,5,2,2]=>[4,1,2,1,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[6,3,2,1,2,5]=>[2,6,1,1,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,2,1,5,2]=>[4,1,3,3,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[6,3,2,2,1,5]=>[4,1,3,4,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[6,3,2,2,5,1]=>[5,2,4,5,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,3,2,5,1,2]=>[5,2,4,1,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,2,5,2,1]=>[5,2,4,1,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,3,5,1,2,2]=>[1,5,3,4,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,3,5,2,1,2]=>[4,1,6,1,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,3,5,2,2,1]=>[4,1,6,1,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,5,1,2,2,3]=>[2,1,5,3,2,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,5,1,2,3,2]=>[2,1,5,3,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,5,1,3,2,2]=>[2,1,5,4,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,2,3]=>[2,1,6,1,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,5,2,1,3,2]=>[2,1,6,1,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,5,2,2,1,3]=>[2,1,6,2,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,5,2,2,3,1]=>[4,3,1,4,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,2,3,1,2]=>[4,3,1,5,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,5,2,3,2,1]=>[2,1,6,3,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,5,3,1,2,2]=>[3,2,1,1,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,5,3,2,1,2]=>[3,2,1,2,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,5,3,2,2,1]=>[3,2,1,2,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,2,4,4,4]=>[1,2,1,3,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,2,4,2,4,4]=>[1,2,3,6,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,4,4,2,4]=>[1,2,3,1,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,4,4,4,2]=>[1,2,3,1,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,2,2,4,4]=>[1,4,6,1,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,4,2,4,2,4]=>[6,2,4,1,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,4,2,4,4,2]=>[3,6,1,5,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,4,2,2,4]=>[1,4,1,6,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,4,4,2,4,2]=>[3,6,3,1,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,4,4,2,2]=>[1,4,1,1,6,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[2,1,2,4,4,4]=>[2,1,3,4,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,4,2,4,4]=>[3,2,6,1,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,4,4,2,4]=>[3,2,6,3,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,4,4,4,2]=>[3,2,6,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,2,1,4,4,4]=>[2,2,1,5,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[2,2,4,1,4,4]=>[1,1,3,5,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,4,4,1,4]=>[1,1,3,1,5,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,4,4,4,1]=>[1,1,3,1,1,5]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,4,1,2,4,4]=>[1,3,5,2,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,1,4,2,4]=>[6,1,3,2,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,1,4,4,2]=>[1,3,5,4,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,2,1,4,4]=>[3,5,1,2,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,2,4,1,4]=>[6,1,4,1,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,2,4,4,1]=>[1,3,6,3,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,4,1,2,4]=>[1,3,1,5,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,4,1,4,2]=>[1,3,1,5,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,4,2,1,4]=>[3,5,3,1,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,4,2,4,1]=>[1,3,1,6,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,4,4,1,2]=>[1,3,1,1,5,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,4,4,2,1]=>[3,5,3,3,1,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,1,2,2,4,4]=>[1,5,2,1,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,1,2,4,2,4]=>[1,5,2,3,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,2,4,4,2]=>[1,5,2,3,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,4,2,2,4]=>[1,5,4,6,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,4,2,4,2]=>[6,3,2,4,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,4,4,2,2]=>[1,5,4,1,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,2,1,2,4,4]=>[3,1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,4,2,4]=>[3,1,2,6,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,1,4,4,2]=>[3,1,2,6,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,2,2,1,4,4]=>[3,1,3,2,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,2,2,4,1,4]=>[1,6,1,3,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,2,4,4,1]=>[1,6,1,3,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,2,4,1,2,4]=>[1,6,3,5,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,4,1,4,2]=>[6,4,1,3,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,4,2,1,4]=>[3,1,5,1,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,4,2,4,1]=>[6,4,1,4,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,4,4,1,2]=>[1,6,3,1,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,4,4,2,1]=>[3,1,5,3,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,1,2,2,4]=>[1,1,5,2,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,4,1,2,4,2]=>[1,1,5,2,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,4,1,4,2,2]=>[1,1,5,4,6,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,4,2,1,2,4]=>[3,3,1,2,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,4,2,1,4,2]=>[3,3,1,2,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,4,2,2,1,4]=>[3,3,1,3,2,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,4,2,2,4,1]=>[1,1,6,1,3,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,2,4,1,2]=>[1,1,6,3,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,4,2,4,2,1]=>[3,3,1,5,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,4,1,2,2]=>[1,1,1,5,2,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,4,4,2,1,2]=>[3,3,3,1,2,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,4,2,2,1]=>[3,3,3,1,3,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,2,4,4,5]=>[1,2,1,3,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,4,5,4]=>[2,3,2,4,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,2,5,4,4]=>[2,3,2,5,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,4,2,4,5]=>[1,2,3,6,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,4,2,5,4]=>[3,4,5,1,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,4,2,5]=>[1,2,3,1,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,4,4,5,2]=>[1,2,3,1,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,4,5,2,4]=>[1,2,3,2,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,4,5,4,2]=>[3,4,5,4,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,2,5,2,4,4]=>[1,2,4,5,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,5,4,2,4]=>[3,4,6,2,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,4,4,2]=>[3,4,6,2,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,2,4,5]=>[1,4,6,1,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,2,2,5,4]=>[5,1,3,5,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,4,2,4,2,5]=>[6,2,4,1,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,4,2,4,5,2]=>[1,4,6,3,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,5,2,4]=>[6,2,4,2,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,2,5,4,2]=>[5,1,3,1,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,4,2,2,5]=>[1,4,1,6,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,4,4,2,5,2]=>[5,1,5,3,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,4,5,2,2]=>[1,4,1,2,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,5,2,2,4]=>[1,4,2,5,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,5,2,4,2]=>[1,4,2,5,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,4,2,2]=>[3,6,4,2,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,2,2,4,4]=>[1,5,5,1,3,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,5,2,4,2,4]=>[6,3,3,1,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,2,4,4,2]=>[4,1,1,6,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,5,4,2,2,4]=>[4,1,3,2,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,4,2,4,2]=>[4,1,3,2,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,4,4,2,2]=>[4,1,3,4,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,4,4,5]=>[2,1,3,4,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,4,5,4]=>[2,1,3,4,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,2,5,4,4]=>[2,1,3,5,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,4,2,4,5]=>[3,2,6,1,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,2,5,4]=>[5,4,1,3,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,4,2,5]=>[5,4,1,5,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,4,5,2]=>[2,1,5,2,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,5,2,4]=>[2,1,5,3,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,5,4,2]=>[3,2,6,4,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,5,2,4,4]=>[4,3,1,1,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,1,5,4,2,4]=>[4,3,1,3,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,5,4,4,2]=>[4,3,1,3,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,4,4,5]=>[2,2,1,5,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,1,4,5,4]=>[2,2,1,5,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,2,1,5,4,4]=>[2,2,1,6,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,2,4,1,4,5]=>[1,1,3,5,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,4,1,5,4]=>[4,4,6,1,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,4,4,1,5]=>[1,1,3,1,5,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,4,4,5,1]=>[1,1,3,1,2,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,4,5,1,4]=>[1,1,3,2,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,2,4,5,4,1]=>[2,2,4,3,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,2,5,1,4,4]=>[1,1,4,4,4,1]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,5,4,1,4]=>[5,5,1,4,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,2,5,4,4,1]=>[2,2,5,1,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,4,1,2,4,5]=>[1,3,5,2,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,4,1,2,5,4]=>[2,4,6,3,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,4,2,5]=>[6,1,3,2,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,1,4,5,2]=>[1,3,5,4,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,1,5,2,4]=>[6,1,3,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[2,4,1,5,4,2]=>[4,6,1,1,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,2,1,4,5]=>[3,5,1,2,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,1,5,4]=>[4,6,2,3,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,2,4,1,5]=>[6,1,4,1,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,2,4,5,1]=>[1,3,6,3,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,2,5,1,4]=>[6,1,4,2,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,4,2,5,4,1]=>[6,1,4,2,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,4,1,2,5]=>[1,3,1,5,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,4,4,1,5,2]=>[4,6,4,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,4,4,2,1,5]=>[4,6,4,2,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,4,2,5,1]=>[1,3,1,6,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,4,4,5,1,2]=>[1,3,1,2,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,4,4,5,2,1]=>[2,4,2,3,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,5,1,2,4]=>[1,3,2,4,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,4,5,1,4,2]=>[1,3,2,4,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,5,2,1,4]=>[2,4,3,6,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,5,2,4,1]=>[1,3,2,5,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,5,4,1,2]=>[2,4,3,1,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,5,4,2,1]=>[3,5,4,2,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,1,2,4,4]=>[1,4,4,2,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,1,4,2,4]=>[6,2,2,2,4,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,1,4,4,2]=>[5,1,1,1,5,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,5,2,1,4,4]=>[5,1,2,4,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,2,4,1,4]=>[6,2,3,1,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,5,2,4,4,1]=>[1,4,5,3,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,5,4,1,2,4]=>[2,5,1,6,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,1,4,2]=>[5,1,4,2,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,5,4,2,1,4]=>[5,1,4,3,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,5,4,2,4,1]=>[6,2,5,4,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,4,1,2]=>[2,5,1,2,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,4,4,2,1]=>[3,6,2,3,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,2,2,4,5]=>[1,5,2,1,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,2,2,5,4]=>[2,6,3,2,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,4,2,5]=>[1,5,2,3,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,4,5,2]=>[1,5,2,3,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,2,5,2,4]=>[1,5,2,4,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,2,5,4,2]=>[5,2,6,1,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,2,2,5]=>[5,2,1,3,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,4,2,5,2]=>[5,2,1,3,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,4,5,2,2]=>[1,5,4,2,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,5,2,2,4]=>[4,1,1,1,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,1,5,2,4,2]=>[4,1,1,1,6,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,1,5,4,2,2]=>[4,1,1,3,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,2,4,5]=>[3,1,2,4,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,1,2,5,4]=>[3,1,2,4,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,1,4,2,5]=>[5,3,4,1,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,2,1,4,5,2]=>[5,3,4,1,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,5,2,4]=>[4,2,3,1,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,1,5,4,2]=>[4,2,3,1,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,2,1,4,5]=>[3,1,3,2,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,2,1,5,4]=>[4,2,4,3,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,2,2,4,1,5]=>[4,2,4,6,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,2,4,5,1]=>[1,6,1,3,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,2,5,1,4]=>[5,3,5,1,1,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[4,2,2,5,4,1]=>[5,3,5,1,4,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,4,1,2,5]=>[1,6,3,5,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,4,1,5,2]=>[4,2,6,1,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,2,4,2,1,5]=>[4,2,6,2,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,4,2,5,1]=>[6,4,1,4,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,4,5,1,2]=>[1,6,3,2,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,4,5,2,1]=>[4,2,6,5,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,5,1,2,4]=>[1,6,4,4,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,5,1,4,2]=>[5,3,1,1,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[4,2,5,2,1,4]=>[5,3,1,2,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,5,2,4,1]=>[6,4,2,3,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,5,4,1,2]=>[5,3,1,4,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,5,4,2,1]=>[3,1,6,2,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,4,1,2,2,5]=>[1,1,5,2,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,4,1,2,5,2]=>[1,1,5,2,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,4,1,5,2,2]=>[4,4,1,1,1,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,4,2,1,2,5]=>[3,3,1,2,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,4,2,1,5,2]=>[4,4,2,3,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,4,2,2,1,5]=>[4,4,2,4,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,4,2,2,5,1]=>[1,1,6,1,4,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,4,2,5,1,2]=>[1,1,6,4,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,4,2,5,2,1]=>[5,5,3,1,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,5,1,2,2]=>[1,1,2,4,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,4,5,2,1,2]=>[2,2,3,6,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,4,5,2,2,1]=>[2,2,3,6,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,5,1,2,2,4]=>[1,2,4,2,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,5,1,2,4,2]=>[1,2,4,2,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,1,4,2,2]=>[1,2,4,4,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,5,2,1,2,4]=>[2,3,6,1,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,5,2,1,4,2]=>[5,6,2,4,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,2,1,4]=>[2,3,6,2,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,5,2,2,4,1]=>[1,2,5,1,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,5,2,4,1,2]=>[1,2,5,3,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,5,2,4,2,1]=>[4,5,1,6,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,4,1,2,2]=>[2,3,1,6,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,5,4,2,1,2]=>[3,4,2,1,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,5,4,2,2,1]=>[3,4,2,1,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,2,2,4,4]=>[1,4,2,1,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,1,2,4,2,4]=>[1,4,2,3,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,2,4,4,2]=>[1,4,2,3,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,4,2,2,4]=>[1,4,4,6,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,4,2,4,2]=>[6,2,2,4,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,4,4,2,2]=>[1,4,4,1,6,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,2,1,2,4,4]=>[2,6,1,3,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,1,4,2,4]=>[6,3,5,2,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,4,4,2]=>[5,2,4,1,5,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,2,1,4,4]=>[2,6,2,1,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,2,2,4,1,4]=>[1,5,1,3,5,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,2,4,4,1]=>[1,5,1,3,1,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,2,4,1,2,4]=>[1,5,3,5,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,2,4,1,4,2]=>[6,3,1,3,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,2,4,2,1,4]=>[6,3,1,4,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,4,2,4,1]=>[6,3,1,4,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,2,4,4,1,2]=>[1,5,3,1,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,2,4,4,2,1]=>[4,1,6,4,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,1,2,2,4]=>[2,1,6,3,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,4,1,2,4,2]=>[4,3,1,5,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,4,2,2]=>[5,4,2,1,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,2,1,2,4]=>[3,2,1,2,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,4,2,1,4,2]=>[3,2,1,2,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,2,2,1,4]=>[3,2,1,3,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,4,2,2,4,1]=>[4,3,2,4,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,2,4,1,2]=>[4,3,2,6,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,2,4,2,1]=>[3,2,1,5,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,4,4,1,2,2]=>[2,1,2,6,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,4,4,2,1,2]=>[3,2,3,1,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,4,2,2,1]=>[3,2,3,1,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,4,4,6]=>[1,2,1,3,1,3]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,2,2,4,6,4]=>[1,2,1,3,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,2,2,6,4,4]=>[1,2,1,5,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,2,4,2,4,6]=>[1,2,3,6,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,2,4,2,6,4]=>[4,5,6,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,4,4,2,6]=>[1,2,3,1,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,4,4,6,2]=>[1,2,3,1,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,4,6,2,4]=>[1,2,3,3,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,4,6,4,2]=>[3,4,5,5,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,6,2,4,4]=>[1,2,5,4,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,6,4,2,4]=>[4,5,1,2,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,2,6,4,4,2]=>[4,5,1,2,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,2,2,4,6]=>[1,4,6,1,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,4,2,2,6,4]=>[5,1,3,5,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,2,4,2,6]=>[6,2,4,1,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,4,6,2]=>[6,2,4,1,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,4,2,6,2,4]=>[6,2,4,3,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,2,6,4,2]=>[5,1,3,2,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,4,4,2,2,6]=>[1,4,1,6,1,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,4,2,6,2]=>[5,1,5,3,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,4,6,2,2]=>[1,4,1,3,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,4,6,2,2,4]=>[1,4,3,4,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,4,6,2,4,2]=>[6,2,1,2,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,4,6,4,2,2]=>[3,6,5,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,2,2,4,4]=>[1,6,4,1,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,6,2,4,2,4]=>[6,4,2,1,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,6,2,4,4,2]=>[3,1,6,5,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,4,2,2,4]=>[3,1,1,1,3,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,6,4,2,4,2]=>[3,1,1,1,5,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,6,4,4,2,2]=>[3,1,1,3,1,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[2,1,2,4,4,6]=>[2,1,3,4,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,2,4,6,4]=>[3,2,4,5,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,2,6,4,4]=>[4,3,5,1,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,4,2,4,6]=>[6,5,2,4,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,2,6,4]=>[5,4,1,3,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,4,4,2,6]=>[5,4,1,5,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,4,4,6,2]=>[2,1,5,2,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,1,4,6,2,4]=>[6,5,2,1,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,1,4,6,4,2]=>[3,2,6,5,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,6,2,4,4]=>[3,2,1,6,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,6,4,2,4]=>[3,2,1,1,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,6,4,4,2]=>[3,2,1,1,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[2,2,1,4,4,6]=>[2,2,1,5,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,2,1,4,6,4]=>[3,3,2,6,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,2,1,6,4,4]=>[3,3,2,1,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,2,4,1,4,6]=>[1,1,3,5,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,2,4,1,6,4]=>[4,4,6,1,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,2,4,4,1,6]=>[1,1,3,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,2,4,4,6,1]=>[1,1,3,1,3,3]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[2,2,4,6,1,4]=>[1,1,3,3,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,2,4,6,4,1]=>[1,1,3,3,6,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,2,6,1,4,4]=>[1,1,5,3,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,2,6,4,1,4]=>[5,5,2,3,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,6,4,4,1]=>[4,4,1,2,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,4,1,2,4,6]=>[1,3,5,2,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,4,1,2,6,4]=>[4,6,1,5,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,1,4,2,6]=>[6,1,3,2,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,1,4,6,2]=>[6,1,3,2,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,4,1,6,2,4]=>[6,1,3,4,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,1,6,4,2]=>[4,6,1,2,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,4,2,1,4,6]=>[6,1,4,5,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,2,1,6,4]=>[3,5,1,2,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,2,4,1,6]=>[6,1,4,1,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,4,2,4,6,1]=>[6,1,4,1,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[2,4,2,6,1,4]=>[6,1,4,3,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,2,6,4,1]=>[4,6,2,1,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,4,4,1,2,6]=>[1,3,1,5,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,4,1,6,2]=>[1,3,1,5,6,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,4,2,1,6]=>[3,5,3,1,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,4,2,6,1]=>[1,3,1,6,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,4,6,1,2]=>[1,3,1,3,3,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[2,4,4,6,2,1]=>[2,4,2,4,5,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,6,1,2,4]=>[1,3,3,3,2,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,4,6,1,4,2]=>[6,1,1,1,2,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,4,6,2,1,4]=>[6,1,1,2,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,4,6,2,4,1]=>[6,1,1,2,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,4,6,4,1,2]=>[1,3,3,6,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,6,4,2,1]=>[3,5,5,1,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,6,1,2,4,4]=>[1,5,3,2,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,1,4,2,4]=>[6,3,1,2,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,1,4,4,2]=>[1,5,3,4,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,6,2,1,4,4]=>[5,2,1,4,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,6,2,4,1,4]=>[6,3,2,1,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,6,2,4,4,1]=>[1,5,4,3,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,4,1,2,4]=>[4,1,2,1,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,4,1,4,2]=>[5,2,3,2,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,6,4,2,1,4]=>[5,2,3,3,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,6,4,2,4,1]=>[4,1,2,2,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,6,4,4,1,2]=>[4,1,2,4,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,4,4,2,1]=>[4,1,2,4,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,1,2,2,4,6]=>[1,5,2,1,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,1,2,2,6,4]=>[4,1,5,4,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,2,4,2,6]=>[4,1,5,6,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,2,4,6,2]=>[1,5,2,3,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,2,6,2,4]=>[1,5,2,5,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,1,2,6,4,2]=>[4,1,5,1,2,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,4,2,2,6]=>[5,2,1,3,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,4,2,6,2]=>[5,2,1,3,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,4,6,2,2]=>[1,5,4,3,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,6,2,2,4]=>[1,5,6,4,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,6,2,4,2]=>[6,3,4,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,6,4,2,2]=>[4,1,2,2,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[4,2,1,2,4,6]=>[3,1,2,4,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,2,6,4]=>[4,2,3,5,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,4,2,6]=>[5,3,4,1,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,4,6,2]=>[6,4,5,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,2,1,6,2,4]=>[3,1,2,1,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,1,6,4,2]=>[3,1,2,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[4,2,2,1,4,6]=>[3,1,3,2,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,2,1,6,4]=>[3,1,3,2,1,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,2,2,4,1,6]=>[4,2,4,6,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,2,4,6,1]=>[1,6,1,3,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[4,2,2,6,1,4]=>[1,6,1,5,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,2,6,4,1]=>[4,2,4,1,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,2,4,1,2,6]=>[4,2,6,1,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,2,4,1,6,2]=>[6,4,1,3,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,4,2,1,6]=>[3,1,5,1,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,2,4,2,6,1]=>[6,4,1,4,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,4,6,1,2]=>[1,6,3,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,2,4,6,2,1]=>[6,4,1,1,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,2,6,1,2,4]=>[1,6,5,3,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,6,1,4,2]=>[6,4,3,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,6,2,1,4]=>[5,3,2,1,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,6,2,4,1]=>[6,4,3,2,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,6,4,1,2]=>[4,2,1,2,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,2,6,4,2,1]=>[4,2,1,2,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,4,1,2,2,6]=>[1,1,5,2,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[4,4,1,2,6,2]=>[1,1,5,2,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,4,1,6,2,2]=>[1,1,5,6,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,4,2,1,2,6]=>[4,4,2,3,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,4,2,1,6,2]=>[3,3,1,2,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,4,2,2,1,6]=>[3,3,1,3,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,4,2,2,6,1]=>[1,1,6,1,5,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,4,2,6,1,2]=>[1,1,6,5,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,4,2,6,2,1]=>[5,5,3,2,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,4,6,1,2,2]=>[1,1,3,3,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[4,4,6,2,1,2]=>[2,2,4,5,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,4,6,2,2,1]=>[2,2,4,5,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,6,1,2,2,4]=>[1,3,3,2,1,3]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[4,6,1,2,4,2]=>[1,3,3,2,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,6,1,4,2,2]=>[1,3,3,4,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,6,2,1,2,4]=>[2,4,5,1,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,6,2,1,4,2]=>[6,1,2,5,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,6,2,2,1,4]=>[2,4,5,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,6,2,2,4,1]=>[1,3,4,1,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,6,2,4,1,2]=>[1,3,4,3,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,6,2,4,2,1]=>[6,1,2,1,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,6,4,1,2,2]=>[1,3,6,5,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,6,4,2,1,2]=>[3,5,1,1,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,6,4,2,2,1]=>[3,5,1,1,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,1,2,2,4,4]=>[1,3,2,1,3,1]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[6,1,2,4,2,4]=>[1,3,2,3,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[6,1,2,4,4,2]=>[1,3,2,3,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,4,2,2,4]=>[1,3,4,6,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,4,2,4,2]=>[6,1,2,4,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,1,4,4,2,2]=>[1,3,4,1,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[6,2,1,2,4,4]=>[2,5,1,3,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,1,4,2,4]=>[6,2,5,2,4,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,2,1,4,4,2]=>[5,1,4,1,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,2,2,1,4,4]=>[2,5,2,1,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,2,2,4,1,4]=>[1,4,1,3,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,2,2,4,4,1]=>[1,4,1,3,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,2,4,1,2,4]=>[1,4,3,5,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,2,4,1,4,2]=>[6,2,1,3,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,2,4,2,1,4]=>[6,2,1,4,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,2,4,2,4,1]=>[6,2,1,4,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,2,4,4,1,2]=>[1,4,3,1,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,4,4,2,1]=>[3,6,5,3,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,4,1,2,2,4]=>[1,6,5,2,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,4,1,2,4,2]=>[4,2,1,5,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,4,1,4,2,2]=>[5,3,2,1,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,4,2,1,2,4]=>[3,1,1,2,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,4,2,1,4,2]=>[3,1,1,2,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,4,2,2,1,4]=>[3,1,1,3,2,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,4,2,2,4,1]=>[4,2,2,4,6,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,4,2,4,1,2]=>[4,2,2,6,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,4,2,4,2,1]=>[3,1,1,5,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[6,4,4,1,2,2]=>[1,6,1,5,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,4,4,2,1,2]=>[3,1,3,1,2,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,4,2,2,1]=>[3,1,3,1,3,2]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,2,2,4,5,5]=>[1,2,1,3,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,2,5,4,5]=>[2,3,2,5,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,2,5,5,4]=>[2,3,2,5,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,4,2,5,5]=>[1,2,3,6,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,4,5,2,5]=>[1,2,3,2,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,4,5,5,2]=>[1,2,3,2,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,2,5,2,4,5]=>[1,2,4,5,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,5,2,5,4]=>[5,6,1,2,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,5,4,2,5]=>[5,6,1,4,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,5,4,5,2]=>[2,3,5,1,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,5,5,2,4]=>[1,2,4,1,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,5,5,4,2]=>[3,4,6,3,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,2,5,5]=>[1,4,6,1,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,4,2,5,2,5]=>[5,1,3,1,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,2,5,5,2]=>[5,1,3,1,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,5,2,2,5]=>[1,4,2,5,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,5,2,5,2]=>[5,1,6,2,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,5,5,2,2]=>[1,4,2,1,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,5,2,2,4,5]=>[1,5,5,1,3,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,2,2,5,4]=>[5,2,2,5,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,2,4,2,5]=>[6,3,3,1,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,2,4,5,2]=>[4,1,1,6,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,5,2,5,2,4]=>[6,3,3,2,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,5,2,5,4,2]=>[5,2,2,1,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,2,2,5]=>[5,2,4,3,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,4,2,5,2]=>[5,2,4,3,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,5,2,2]=>[4,1,3,5,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,5,5,2,2,4]=>[1,5,1,5,1,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,5,5,2,4,2]=>[4,1,4,1,6,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,5,5,4,2,2]=>[4,1,4,3,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,2,4,5,5]=>[2,1,3,4,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,2,5,4,5]=>[2,1,3,5,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,2,5,5,4]=>[2,1,3,5,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,4,2,5,5]=>[5,4,1,3,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,4,5,2,5]=>[5,4,1,6,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,4,5,5,2]=>[2,1,5,3,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,2,4,5]=>[4,3,1,1,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,5,2,5,4]=>[5,4,2,2,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,1,5,4,2,5]=>[5,4,2,4,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,5,4,5,2]=>[4,3,1,3,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,1,5,5,2,4]=>[4,3,1,4,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,1,5,5,4,2]=>[4,3,1,4,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,2,1,4,5,5]=>[2,2,1,5,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,2,1,5,4,5]=>[2,2,1,6,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,2,1,5,5,4]=>[2,2,1,6,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,2,4,1,5,5]=>[1,1,3,5,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,2,4,5,1,5]=>[1,1,3,2,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,4,5,5,1]=>[1,1,3,2,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,2,5,1,4,5]=>[1,1,4,4,4,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,2,5,1,5,4]=>[5,5,1,1,2,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,2,5,4,1,5]=>[5,5,1,4,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,2,5,4,5,1]=>[2,2,5,1,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,2,5,5,1,4]=>[1,1,4,1,4,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[2,2,5,5,4,1]=>[2,2,5,2,1,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,4,1,2,5,5]=>[1,3,5,2,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,4,1,5,2,5]=>[6,1,3,3,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,4,1,5,5,2]=>[4,6,1,1,4,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[2,4,2,1,5,5]=>[4,6,2,3,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,2,5,1,5]=>[6,1,4,2,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,2,5,5,1]=>[1,3,6,4,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,4,5,1,2,5]=>[1,3,2,4,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,4,5,1,5,2]=>[1,3,2,4,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,5,2,1,5]=>[4,6,5,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,5,2,5,1]=>[1,3,2,5,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,5,5,1,2]=>[1,3,2,1,4,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,4,5,5,2,1]=>[2,4,3,2,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,5,1,2,4,5]=>[1,4,4,2,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,5,1,2,5,4]=>[5,1,1,6,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,5,1,4,2,5]=>[5,1,1,1,3,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[2,5,1,4,5,2]=>[5,1,1,1,6,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,5,1,5,2,4]=>[6,2,2,3,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,5,1,5,4,2]=>[5,1,1,2,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,5,2,1,4,5]=>[5,1,2,4,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,2,1,5,4]=>[5,1,2,4,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,5,2,4,1,5]=>[6,2,3,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,5,2,4,5,1]=>[1,4,5,3,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,2,5,1,4]=>[5,1,2,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[2,5,2,5,4,1]=>[5,1,2,1,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,5,4,1,2,5]=>[5,1,4,2,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,4,1,5,2]=>[5,1,4,2,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,5,4,2,1,5]=>[5,1,4,3,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,4,2,5,1]=>[5,1,4,3,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,5,4,5,1,2]=>[2,5,1,3,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,5,4,5,2,1]=>[2,5,1,3,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,5,1,2,4]=>[1,4,1,4,2,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,5,1,4,2]=>[5,1,5,1,1,3]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[2,5,5,2,1,4]=>[5,1,5,2,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,5,2,4,1]=>[1,4,1,5,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,5,5,4,1,2]=>[2,5,2,1,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,5,4,2,1]=>[3,6,3,2,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,1,2,2,5,5]=>[1,5,2,1,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,2,5,2,5]=>[5,2,6,1,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,2,5,5,2]=>[1,5,2,4,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,5,2,2,5]=>[5,2,2,2,5,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,1,5,2,5,2]=>[5,2,2,2,1,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,1,5,5,2,2]=>[4,1,1,4,1,4]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[4,2,1,2,5,5]=>[3,1,2,4,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,1,5,2,5]=>[5,3,4,2,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,5,5,2]=>[4,2,3,1,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,2,1,5,5]=>[4,2,4,3,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,2,2,5,1,5]=>[5,3,5,1,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,2,5,5,1]=>[1,6,1,4,1,4]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[4,2,5,1,2,5]=>[5,3,1,1,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,2,5,1,5,2]=>[5,3,1,1,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,2,5,2,1,5]=>[5,3,1,2,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,5,2,5,1]=>[5,3,1,2,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,2,5,5,1,2]=>[1,6,4,1,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,5,5,2,1]=>[5,3,1,5,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,5,1,2,2,5]=>[1,2,4,2,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,5,1,2,5,2]=>[1,2,4,2,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,5,1,5,2,2]=>[1,2,4,5,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,5,2,1,2,5]=>[2,3,6,1,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,5,2,1,5,2]=>[4,5,1,3,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,5,2,2,1,5]=>[4,5,1,4,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,5,2,2,5,1]=>[1,2,5,1,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,5,2,5,1,2]=>[1,2,5,4,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,5,2,5,2,1]=>[5,6,2,1,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,5,5,1,2,2]=>[1,2,1,4,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,5,5,2,1,2]=>[2,3,2,6,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,5,5,2,2,1]=>[2,3,2,6,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,2,2,4,5]=>[1,4,2,1,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,1,2,2,5,4]=>[2,5,3,2,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,1,2,4,2,5]=>[1,4,2,3,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,2,4,5,2]=>[1,4,2,3,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,2,5,2,4]=>[1,4,2,4,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,2,5,4,2]=>[5,1,6,1,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,4,2,2,5]=>[5,1,1,3,5,1]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,1,4,2,5,2]=>[5,1,1,3,1,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[5,1,4,5,2,2]=>[1,4,4,2,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,5,2,2,4]=>[1,4,5,5,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,1,5,2,4,2]=>[6,2,3,3,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,5,4,2,2]=>[5,1,2,4,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,2,4,5]=>[2,6,1,3,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,2,1,2,5,4]=>[2,6,1,3,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,1,4,2,5]=>[5,2,4,1,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,1,4,5,2]=>[5,2,4,1,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,5,2,4]=>[4,1,3,1,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,2,1,5,4,2]=>[4,1,3,1,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,2,2,1,4,5]=>[2,6,2,1,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,2,1,5,4]=>[4,1,4,3,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,2,2,4,1,5]=>[4,1,4,6,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,2,2,4,5,1]=>[1,5,1,3,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,2,5,1,4]=>[5,2,5,1,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,2,2,5,4,1]=>[5,2,5,1,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,4,1,2,5]=>[1,5,3,5,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,4,1,5,2]=>[4,1,6,1,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[5,2,4,2,1,5]=>[4,1,6,2,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,4,2,5,1]=>[6,3,1,4,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,4,5,1,2]=>[1,5,3,2,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,2,4,5,2,1]=>[4,1,6,5,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,5,1,2,4]=>[1,5,4,4,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,5,1,4,2]=>[5,2,1,1,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[5,2,5,2,1,4]=>[5,2,1,2,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,5,2,4,1]=>[6,3,2,3,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,2,5,4,1,2]=>[5,2,1,4,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,5,4,2,1]=>[5,2,1,4,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,1,2,2,5]=>[2,1,6,3,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,4,1,2,5,2]=>[5,4,2,6,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,1,5,2,2]=>[4,3,1,1,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,4,2,1,2,5]=>[3,2,1,2,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,4,2,1,5,2]=>[4,3,2,3,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,2,2,1,5]=>[4,3,2,4,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,4,2,2,5,1]=>[5,4,3,5,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,4,2,5,1,2]=>[5,4,3,1,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,2,5,2,1]=>[5,4,3,1,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,5,1,2,2]=>[2,1,3,5,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,4,5,2,1,2]=>[2,1,3,6,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,4,5,2,2,1]=>[2,1,3,6,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,5,1,2,2,4]=>[1,1,4,2,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,5,1,2,4,2]=>[1,1,4,2,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,5,1,4,2,2]=>[1,1,4,4,6,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[5,5,2,1,2,4]=>[2,2,6,1,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,5,2,1,4,2]=>[5,5,2,4,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,5,2,2,1,4]=>[2,2,6,2,1,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,5,2,2,4,1]=>[1,1,5,1,3,5]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[5,5,2,4,1,2]=>[1,1,5,3,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,5,2,4,2,1]=>[4,4,1,6,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,5,4,1,2,2]=>[2,2,1,6,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,5,4,2,1,2]=>[3,3,2,1,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,5,4,2,2,1]=>[3,3,2,1,3,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,2,4,5,6]=>[1,2,1,3,2,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,2,4,6,5]=>[2,3,2,4,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,2,5,4,6]=>[2,3,2,5,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,2,5,6,4]=>[1,2,1,4,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,2,6,4,5]=>[1,2,1,5,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,2,2,6,5,4]=>[2,3,2,6,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,2,5,6]=>[1,2,3,6,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,4,2,6,5]=>[4,5,6,2,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,5,2,6]=>[1,2,3,2,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,2,4,5,6,2]=>[1,2,3,2,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,2,4,6,2,5]=>[1,2,3,3,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,4,6,5,2]=>[2,3,4,4,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,2,4,6]=>[1,2,4,5,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,2,5,2,6,4]=>[5,6,1,2,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,2,5,4,2,6]=>[5,6,1,4,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,4,6,2]=>[2,3,5,1,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,5,6,2,4]=>[1,2,4,2,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,5,6,4,2]=>[3,4,6,4,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,2,6,2,4,5]=>[1,2,5,4,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,6,2,5,4]=>[5,6,2,1,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,6,4,2,5]=>[5,6,2,3,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,2,6,4,5,2]=>[4,5,1,2,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,2,6,5,2,4]=>[4,5,1,3,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,6,5,4,2]=>[4,5,1,3,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,2,2,5,6]=>[1,4,6,1,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,4,2,2,6,5]=>[5,1,3,5,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,2,5,2,6]=>[5,1,3,1,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,2,5,6,2]=>[5,1,3,1,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,2,6,2,5]=>[5,1,3,2,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,2,6,5,2]=>[5,1,3,2,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,5,2,2,6]=>[1,4,2,5,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,4,5,2,6,2]=>[5,1,6,2,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,5,6,2,2]=>[1,4,2,2,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,4,6,2,2,5]=>[1,4,3,4,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,4,6,2,5,2]=>[6,2,1,2,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,4,6,5,2,2]=>[2,5,4,1,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,2,2,4,6]=>[1,5,5,1,3,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,5,2,2,6,4]=>[4,1,1,4,1,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,5,2,4,2,6]=>[4,1,1,6,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,5,2,4,6,2]=>[6,3,3,1,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,5,2,6,2,4]=>[6,3,3,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,5,2,6,4,2]=>[4,1,1,1,2,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,5,4,2,2,6]=>[4,1,3,2,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,5,4,2,6,2]=>[5,2,4,3,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,4,6,2,2]=>[2,6,1,4,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,6,2,2,4]=>[1,5,2,4,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,5,6,2,4,2]=>[1,5,2,4,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,6,4,2,2]=>[4,1,5,2,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,2,2,4,5]=>[1,6,4,1,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,2,2,5,4]=>[5,3,1,5,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,6,2,4,2,5]=>[6,4,2,1,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,6,2,4,5,2]=>[1,6,4,3,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,5,2,4]=>[6,4,2,2,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,2,5,4,2]=>[5,3,1,1,4,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,6,4,2,2,5]=>[3,1,1,1,3,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,6,4,2,5,2]=>[5,3,3,3,1,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,6,4,5,2,2]=>[4,2,2,5,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,5,2,2,4]=>[4,2,3,1,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,5,2,4,2]=>[4,2,3,1,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,5,4,2,2]=>[3,1,2,2,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,2,4,5,6]=>[2,1,3,4,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,1,2,4,6,5]=>[2,1,3,4,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,2,5,4,6]=>[2,1,3,5,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,2,5,6,4]=>[3,2,4,6,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,2,6,4,5]=>[4,3,5,1,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,2,6,5,4]=>[2,1,3,6,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,1,4,2,5,6]=>[5,4,1,3,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,4,2,6,5]=>[5,4,1,3,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,4,5,2,6]=>[5,4,1,6,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,4,5,6,2]=>[2,1,5,3,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,4,6,2,5]=>[6,5,2,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,1,4,6,5,2]=>[2,1,5,4,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,5,2,4,6]=>[6,5,3,3,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,1,5,2,6,4]=>[4,3,1,1,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,5,4,2,6]=>[4,3,1,3,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,5,4,6,2]=>[2,1,6,1,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,5,6,2,4]=>[2,1,6,3,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,6,4,2]=>[4,3,1,5,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,6,2,4,5]=>[3,2,1,6,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,6,2,5,4]=>[5,4,3,1,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,6,4,2,5]=>[3,2,1,1,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,1,6,4,5,2]=>[4,3,2,2,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,6,5,2,4]=>[4,3,2,3,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,6,5,4,2]=>[3,2,1,2,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[2,2,1,4,5,6]=>[2,2,1,5,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,2,1,4,6,5]=>[2,2,1,5,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,2,1,5,4,6]=>[2,2,1,6,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,2,1,5,6,4]=>[4,4,3,1,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,2,1,6,4,5]=>[3,3,2,1,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,2,1,6,5,4]=>[3,3,2,1,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,2,4,1,5,6]=>[1,1,3,5,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,2,4,1,6,5]=>[4,4,6,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,2,4,5,1,6]=>[1,1,3,2,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,2,4,5,6,1]=>[1,1,3,2,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,2,4,6,1,5]=>[1,1,3,3,3,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,2,4,6,5,1]=>[2,2,4,4,1,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,5,1,4,6]=>[1,1,4,4,4,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,2,5,1,6,4]=>[5,5,1,1,3,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,2,5,4,1,6]=>[5,5,1,4,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,2,5,4,6,1]=>[2,2,5,1,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,2,5,6,1,4]=>[1,1,4,2,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,2,5,6,4,1]=>[1,1,4,2,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,6,1,4,5]=>[1,1,5,3,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,2,6,1,5,4]=>[4,4,1,6,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,2,6,4,1,5]=>[4,4,1,2,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,2,6,4,5,1]=>[1,1,5,6,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,2,6,5,1,4]=>[5,5,2,4,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,2,6,5,4,1]=>[4,4,1,3,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,4,1,2,5,6]=>[1,3,5,2,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,1,2,6,5]=>[4,6,1,5,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,1,5,2,6]=>[4,6,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[2,4,1,5,6,2]=>[1,3,5,5,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,1,6,2,5]=>[6,1,3,4,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,1,6,5,2]=>[4,6,1,2,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,2,1,5,6]=>[4,6,2,3,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,2,1,6,5]=>[3,5,1,2,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,4,2,5,1,6]=>[6,1,4,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,4,2,5,6,1]=>[1,3,6,4,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,2,6,1,5]=>[6,1,4,3,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,2,6,5,1]=>[6,1,4,3,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,5,1,2,6]=>[1,3,2,4,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,5,1,6,2]=>[1,3,2,4,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,5,2,1,6]=>[4,6,5,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,5,2,6,1]=>[1,3,2,5,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,5,6,1,2]=>[1,3,2,2,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[2,4,5,6,2,1]=>[2,4,3,3,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,6,1,2,5]=>[1,3,3,3,2,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,4,6,1,5,2]=>[6,1,1,1,3,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,4,6,2,1,5]=>[6,1,1,2,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,6,2,5,1]=>[6,1,1,2,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[2,4,6,5,1,2]=>[2,4,4,1,5,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,4,6,5,2,1]=>[2,4,4,1,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,5,1,2,4,6]=>[1,4,4,2,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,5,1,2,6,4]=>[5,1,1,6,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,1,4,2,6]=>[5,1,1,1,3,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,5,1,4,6,2]=>[6,2,2,2,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[2,5,1,6,2,4]=>[6,2,2,4,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,1,6,4,2]=>[5,1,1,3,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,5,2,1,4,6]=>[6,2,3,5,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,2,1,6,4]=>[5,1,2,4,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,5,2,4,1,6]=>[6,2,3,1,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,5,2,4,6,1]=>[6,2,3,1,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,5,2,6,1,4]=>[6,2,3,3,1,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,5,2,6,4,1]=>[5,1,2,2,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,5,4,1,2,6]=>[5,1,4,2,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,4,1,6,2]=>[5,1,4,2,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,5,4,2,1,6]=>[3,6,2,1,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,5,4,2,6,1]=>[6,2,5,4,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,6,1,2]=>[2,5,1,4,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,4,6,2,1]=>[2,5,1,4,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,6,1,2,4]=>[1,4,2,3,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,5,6,1,4,2]=>[1,4,2,3,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,5,6,2,1,4]=>[5,1,6,1,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,5,6,2,4,1]=>[1,4,2,4,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,6,4,1,2]=>[1,4,2,6,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,6,4,2,1]=>[3,6,4,1,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,1,2,4,5]=>[1,5,3,2,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,6,1,2,5,4]=>[2,6,4,3,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,1,4,2,5]=>[6,3,1,2,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,6,1,4,5,2]=>[1,5,3,4,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,6,1,5,2,4]=>[6,3,1,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[2,6,1,5,4,2]=>[4,1,6,1,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,2,1,4,5]=>[5,2,1,4,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,2,1,5,4]=>[5,2,1,4,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,6,2,4,1,5]=>[6,3,2,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,6,2,4,5,1]=>[1,5,4,3,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,6,2,5,1,4]=>[5,2,1,1,1,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[2,6,2,5,4,1]=>[5,2,1,1,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,6,4,1,2,5]=>[5,2,3,2,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,4,1,5,2]=>[4,1,2,1,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[2,6,4,2,1,5]=>[4,1,2,2,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,6,4,2,5,1]=>[5,2,3,3,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,4,5,1,2]=>[1,5,6,2,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,4,5,2,1]=>[4,1,2,5,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,5,1,2,4]=>[2,6,1,5,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,5,1,4,2]=>[5,2,4,1,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,5,2,1,4]=>[5,2,4,2,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,6,5,2,4,1]=>[4,1,3,1,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,5,4,1,2]=>[4,1,3,3,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,6,5,4,2,1]=>[4,1,3,3,2,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,2,2,5,6]=>[1,5,2,1,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,2,2,6,5]=>[4,1,5,4,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,2,5,2,6]=>[5,2,6,1,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,2,5,6,2]=>[1,5,2,4,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,1,2,6,2,5]=>[5,2,6,2,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,1,2,6,5,2]=>[4,1,5,1,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,5,2,2,6]=>[4,1,1,1,4,1]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[4,1,5,2,6,2]=>[5,2,2,2,2,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,1,5,6,2,2]=>[1,5,5,2,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,1,6,2,2,5]=>[5,2,3,1,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,1,6,2,5,2]=>[5,2,3,1,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,6,5,2,2]=>[4,1,2,3,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,2,5,6]=>[3,1,2,4,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,1,2,6,5]=>[4,2,3,5,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,5,2,6]=>[4,2,3,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,2,1,5,6,2]=>[5,3,4,2,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,6,2,5]=>[5,3,4,3,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,2,1,6,5,2]=>[4,2,3,2,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,2,1,5,6]=>[4,2,4,3,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,2,1,6,5]=>[3,1,3,2,1,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,2,2,5,1,6]=>[5,3,5,1,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,2,2,5,6,1]=>[1,6,1,4,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,2,6,1,5]=>[4,2,4,1,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,2,2,6,5,1]=>[5,3,5,2,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,5,1,2,6]=>[5,3,1,1,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,5,1,6,2]=>[5,3,1,1,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[4,2,5,2,1,6]=>[5,3,1,2,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,5,2,6,1]=>[6,4,2,3,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,5,6,1,2]=>[1,6,4,2,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,5,6,2,1]=>[5,3,1,6,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,6,1,2,5]=>[1,6,5,3,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,6,1,5,2]=>[4,2,1,6,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,2,6,2,1,5]=>[5,3,2,1,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,6,2,5,1]=>[5,3,2,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,2,6,5,1,2]=>[5,3,2,4,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,6,5,2,1]=>[4,2,1,3,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,5,1,2,2,6]=>[1,2,4,2,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,5,1,2,6,2]=>[1,2,4,2,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,5,1,6,2,2]=>[1,2,4,6,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,5,2,1,2,6]=>[4,5,1,3,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,5,2,1,6,2]=>[5,6,2,4,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,2,1,6]=>[4,5,1,4,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,5,2,2,6,1]=>[1,2,5,1,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,5,2,6,1,2]=>[1,2,5,5,3,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,5,2,6,2,1]=>[5,6,2,2,1,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,5,6,1,2,2]=>[1,2,2,3,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[4,5,6,2,1,2]=>[2,3,3,5,1,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,5,6,2,2,1]=>[2,3,3,5,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,6,1,2,2,5]=>[1,3,3,2,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,6,1,2,5,2]=>[1,3,3,2,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,6,1,5,2,2]=>[1,3,3,5,5,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,6,2,1,2,5]=>[2,4,5,1,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,6,2,1,5,2]=>[6,1,2,5,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,6,2,2,1,5]=>[2,4,5,2,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,6,2,2,5,1]=>[1,3,4,1,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,6,2,5,1,2]=>[1,3,4,4,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,6,2,5,2,1]=>[6,1,2,2,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,6,5,1,2,2]=>[2,4,1,5,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,6,5,2,1,2]=>[2,4,1,6,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,6,5,2,2,1]=>[2,4,1,6,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,1,2,2,4,6]=>[1,4,2,1,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,1,2,2,6,4]=>[1,4,2,1,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,2,4,2,6]=>[1,4,2,3,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,2,4,6,2]=>[1,4,2,3,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,1,2,6,2,4]=>[1,4,2,5,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,2,6,4,2]=>[5,1,6,2,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,4,2,2,6]=>[5,1,1,3,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,1,4,2,6,2]=>[5,1,1,3,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[5,1,4,6,2,2]=>[1,4,4,3,4,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,1,6,2,2,4]=>[1,4,6,4,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,1,6,2,4,2]=>[6,2,4,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,6,4,2,2]=>[3,6,1,1,1,3]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,2,1,2,4,6]=>[2,6,1,3,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,1,2,6,4]=>[4,1,3,5,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,1,4,2,6]=>[5,2,4,1,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,2,1,4,6,2]=>[6,3,5,2,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,1,6,2,4]=>[6,3,5,4,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,6,4,2]=>[4,1,3,2,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,2,2,1,4,6]=>[2,6,2,1,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,2,1,6,4]=>[4,1,4,3,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,2,2,4,1,6]=>[4,1,4,6,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,2,2,4,6,1]=>[1,5,1,3,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,2,2,6,1,4]=>[1,5,1,5,3,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,2,2,6,4,1]=>[4,1,4,1,2,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,2,4,1,2,6]=>[4,1,6,1,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[5,2,4,1,6,2]=>[6,3,1,3,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,2,4,2,1,6]=>[4,1,6,2,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,4,2,6,1]=>[6,3,1,4,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,2,4,6,1,2]=>[1,5,3,3,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,2,4,6,2,1]=>[6,3,1,1,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,6,1,2,4]=>[1,5,5,3,2,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,2,6,1,4,2]=>[6,3,3,1,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,2,6,2,1,4]=>[5,2,2,1,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,6,2,4,1]=>[6,3,3,2,1,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,2,6,4,1,2]=>[4,1,1,2,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,2,6,4,2,1]=>[4,1,1,2,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,4,1,2,2,6]=>[4,3,1,5,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,4,1,2,6,2]=>[5,4,2,6,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,1,6,2,2]=>[5,4,2,3,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,2,1,2,6]=>[4,3,2,3,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,4,2,1,6,2]=>[3,2,1,2,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,2,2,1,6]=>[3,2,1,3,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,4,2,2,6,1]=>[4,3,2,4,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,4,2,6,1,2]=>[4,3,2,1,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,2,6,2,1]=>[5,4,3,2,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,4,6,1,2,2]=>[2,1,4,4,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,4,6,2,1,2]=>[2,1,4,5,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,4,6,2,2,1]=>[2,1,4,5,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,6,1,2,2,4]=>[1,2,3,2,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,6,1,2,4,2]=>[1,2,3,2,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,6,1,4,2,2]=>[1,2,3,4,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,6,2,1,2,4]=>[2,3,5,1,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,6,2,1,4,2]=>[5,6,1,4,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,6,2,2,1,4]=>[2,3,5,2,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,6,2,2,4,1]=>[1,2,4,1,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,6,2,4,1,2]=>[1,2,4,3,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,6,2,4,2,1]=>[3,4,6,5,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,4,1,2,2]=>[1,2,6,5,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,6,4,2,1,2]=>[3,4,1,1,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,6,4,2,2,1]=>[3,4,1,1,3,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,1,2,2,4,5]=>[1,3,2,1,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[6,1,2,2,5,4]=>[2,4,3,2,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,2,4,2,5]=>[1,3,2,3,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,1,2,4,5,2]=>[1,3,2,3,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,1,2,5,2,4]=>[1,3,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,1,2,5,4,2]=>[3,5,4,6,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,2,2,5]=>[1,3,4,6,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,1,4,2,5,2]=>[6,1,2,4,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,4,5,2,2]=>[1,3,4,2,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,5,2,2,4]=>[1,3,5,5,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[6,1,5,2,4,2]=>[6,1,3,3,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,1,5,4,2,2]=>[4,6,1,3,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,1,2,4,5]=>[2,5,1,3,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,2,1,2,5,4]=>[2,5,1,3,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,2,1,4,2,5]=>[5,1,4,1,3,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,2,1,4,5,2]=>[5,1,4,1,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,1,5,2,4]=>[6,2,5,3,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,1,5,4,2]=>[5,1,4,2,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,2,2,1,4,5]=>[2,5,2,1,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,2,2,1,5,4]=>[2,5,2,1,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,2,2,4,1,5]=>[1,4,1,3,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,2,2,4,5,1]=>[1,4,1,3,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,2,2,5,1,4]=>[5,1,5,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[6,2,2,5,4,1]=>[5,1,5,1,4,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,4,1,2,5]=>[1,4,3,5,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,2,4,1,5,2]=>[6,2,1,3,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[6,2,4,2,1,5]=>[6,2,1,4,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,4,2,5,1]=>[6,2,1,4,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[6,2,4,5,1,2]=>[1,4,3,2,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,2,4,5,2,1]=>[2,5,4,3,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,5,1,2,4]=>[1,4,4,4,2,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,2,5,1,4,2]=>[5,1,1,1,1,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[6,2,5,2,1,4]=>[5,1,1,2,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,2,5,2,4,1]=>[6,2,2,3,1,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,2,5,4,1,2]=>[5,1,1,4,2,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,5,4,2,1]=>[5,1,1,4,3,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,4,1,2,2,5]=>[1,6,5,2,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,4,1,2,5,2]=>[5,3,2,6,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,4,1,5,2,2]=>[4,2,1,1,1,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[6,4,2,1,2,5]=>[3,1,1,2,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,4,2,1,5,2]=>[4,2,2,3,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,2,2,1,5]=>[4,2,2,4,3,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,4,2,2,5,1]=>[5,3,3,5,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[6,4,2,5,1,2]=>[5,3,3,1,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,4,2,5,2,1]=>[5,3,3,1,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,4,5,1,2,2]=>[1,6,2,4,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,4,5,2,1,2]=>[4,2,5,1,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,4,5,2,2,1]=>[4,2,5,1,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,1,2,2,4]=>[2,1,5,3,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,5,1,2,4,2]=>[3,2,6,4,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,1,4,2,2]=>[5,4,1,1,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,5,2,1,2,4]=>[2,1,6,1,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,5,2,1,4,2]=>[5,4,2,4,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,2,2,1,4]=>[2,1,6,2,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,5,2,2,4,1]=>[4,3,1,4,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,5,2,4,1,2]=>[4,3,1,6,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,5,2,4,2,1]=>[4,3,1,6,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,4,1,2,2]=>[2,1,1,6,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,5,4,2,1,2]=>[3,2,2,1,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,5,4,2,2,1]=>[3,2,2,1,3,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,3,3,3]=>[1,2,2,1,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,3,2,3,3,3]=>[2,4,1,3,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,3,2,3,3]=>[2,4,2,1,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,3,3,2,3]=>[2,4,2,2,1,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,3,3,3,2]=>[2,4,2,2,2,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,1,3,3,3,3]=>[2,1,4,2,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[2,3,1,3,3,3]=>[1,2,6,3,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,3,1,3,3]=>[1,2,1,6,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,3,3,1,3]=>[1,2,1,1,6,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,3,3,3,3,1]=>[1,2,1,1,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,1,2,3,3,3]=>[1,6,2,2,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,1,3,2,3,3]=>[3,1,5,2,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,3,3,2,3]=>[3,1,5,3,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,3,3,3,2]=>[3,1,5,3,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,2,1,3,3,3]=>[2,1,1,4,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,2,3,1,3,3]=>[3,2,4,1,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,3,3,1,3]=>[3,2,4,3,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,3,3,3,1]=>[3,2,4,3,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,1,2,3,3]=>[1,1,6,2,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,3,1,3,2,3]=>[3,3,1,5,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,3,1,3,3,2]=>[3,3,1,5,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,3,2,1,3,3]=>[2,2,1,1,4,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,3,2,3,1,3]=>[3,3,2,4,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,3,2,3,3,1]=>[3,3,2,4,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,3,1,2,3]=>[1,1,1,6,2,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,3,3,1,3,2]=>[3,3,3,1,5,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,3,3,2,1,3]=>[2,2,2,1,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,3,3,2,3,1]=>[3,3,3,2,4,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,3,3,1,2]=>[1,1,1,1,6,2]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,3,3,3,2,1]=>[2,2,2,2,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,3,3,3,4]=>[1,2,2,1,1,2]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,3,3,4,3]=>[2,3,3,2,3,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,4,3,3]=>[2,3,3,3,1,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,4,3,3,3]=>[2,3,4,1,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,2,3,3,4]=>[2,4,1,3,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,2,3,4,3]=>[2,4,1,3,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,2,4,3,3]=>[2,4,1,4,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,3,2,3,4]=>[2,4,2,1,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,3,2,4,3]=>[2,4,2,1,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,3,3,2,4]=>[2,4,2,2,1,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,3,3,4,2]=>[1,3,1,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,3,4,2,3]=>[1,3,1,2,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,3,4,3,2]=>[2,4,2,3,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,3,4,2,3,3]=>[1,3,2,6,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,4,3,2,3]=>[2,4,3,1,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,4,3,3,2]=>[2,4,3,1,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,4,2,3,3,3]=>[1,4,6,2,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,3,2,3,3]=>[2,5,1,1,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,3,3,2,3]=>[2,5,1,2,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,3,3,3,2]=>[2,5,1,2,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,3,3,3,4]=>[2,1,4,2,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,3,3,4,3]=>[2,1,4,2,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,3,4,3,3]=>[2,1,4,3,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,4,3,3,3]=>[2,1,5,1,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,1,3,3,4]=>[1,2,6,3,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,1,3,4,3]=>[3,4,1,5,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,1,4,3,3]=>[3,4,1,6,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,3,1,3,4]=>[1,2,1,6,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,3,1,4,3]=>[3,4,3,1,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,3,3,1,4]=>[1,2,1,1,6,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,3,3,3,4,1]=>[1,2,1,1,2,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,3,3,4,1,3]=>[1,2,1,2,5,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,3,4,3,1]=>[3,4,3,4,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,4,1,3,3]=>[1,2,2,5,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,4,3,1,3]=>[3,4,4,2,1,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,4,3,3,1]=>[3,4,4,2,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,1,3,3,3]=>[1,3,5,3,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,3,1,3,3]=>[3,5,2,1,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,3,3,1,3]=>[3,5,2,3,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,3,3,3,1]=>[3,5,2,3,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,2,3,3,4]=>[1,6,2,2,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,1,2,3,4,3]=>[3,1,4,4,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,1,2,4,3,3]=>[3,1,4,5,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,3,2,3,4]=>[3,1,5,2,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,3,2,4,3]=>[3,1,5,2,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,1,3,3,2,4]=>[3,1,5,3,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,3,3,4,2]=>[3,1,5,3,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,3,4,2,3]=>[3,1,5,4,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,3,4,3,2]=>[3,1,5,4,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,4,2,3,3]=>[3,1,6,1,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,4,3,2,3]=>[3,1,6,2,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,4,3,3,2]=>[3,1,6,2,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,1,3,3,4]=>[2,1,1,4,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,3,4,3]=>[2,1,1,4,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,1,4,3,3]=>[2,1,1,5,1,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,2,3,1,3,4]=>[3,2,4,1,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,3,1,4,3]=>[3,2,4,1,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,3,3,1,4]=>[3,2,4,3,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,3,3,4,1]=>[2,1,3,2,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,3,4,1,3]=>[2,1,3,3,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,3,4,3,1]=>[3,2,4,4,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,4,1,3,3]=>[2,1,4,6,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,4,3,1,3]=>[3,2,5,2,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,4,3,3,1]=>[3,2,5,2,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,1,2,3,4]=>[1,1,6,2,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,3,1,2,4,3]=>[3,3,1,4,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,3,1,3,2,4]=>[3,3,1,5,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,3,1,3,4,2]=>[3,3,1,5,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,3,1,4,2,3]=>[3,3,1,6,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,1,4,3,2]=>[3,3,1,6,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,3,2,1,3,4]=>[2,2,1,1,4,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,3,2,1,4,3]=>[2,2,1,1,5,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,3,2,3,1,4]=>[3,3,2,4,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,3,2,3,4,1]=>[2,2,1,3,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,3,2,4,1,3]=>[2,2,1,4,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,3,2,4,3,1]=>[3,3,2,5,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,3,1,2,4]=>[1,1,1,6,2,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,3,3,1,4,2]=>[3,3,3,1,6,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,3,3,2,1,4]=>[2,2,2,1,1,5]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,3,3,2,4,1]=>[2,2,2,1,4,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,3,4,1,2]=>[1,1,1,2,5,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,3,3,4,2,1]=>[3,3,3,4,1,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,3,4,1,2,3]=>[1,1,2,5,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,3,4,1,3,2]=>[2,2,3,6,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,3,4,2,1,3]=>[3,3,4,1,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,3,4,2,3,1]=>[3,3,4,1,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,3,4,3,1,2]=>[3,3,4,2,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,3,4,3,2,1]=>[2,2,3,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,4,1,2,3,3]=>[1,2,5,2,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,4,1,3,2,3]=>[2,3,6,4,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,1,3,3,2]=>[2,3,6,4,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,2,1,3,3]=>[3,4,1,2,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,2,3,1,3]=>[3,4,1,4,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,4,2,3,3,1]=>[3,4,1,4,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,4,3,1,2,3]=>[3,4,2,1,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,4,3,1,3,2]=>[3,4,2,1,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,4,3,2,1,3]=>[2,3,1,1,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,4,3,2,3,1]=>[3,4,2,2,4,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,4,3,3,1,2]=>[3,4,2,3,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,3,3,2,1]=>[2,3,1,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,1,2,3,3,3]=>[1,5,2,2,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,1,3,2,3,3]=>[2,6,4,1,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,3,3,2,3]=>[2,6,4,2,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,3,3,3,2]=>[2,6,4,2,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,2,1,3,3,3]=>[3,1,2,5,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,2,3,1,3,3]=>[3,1,4,1,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,2,3,3,1,3]=>[3,1,4,3,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,2,3,3,3,1]=>[3,1,4,3,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,3,1,2,3,3]=>[3,2,1,4,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,1,3,2,3]=>[3,2,1,5,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,1,3,3,2]=>[3,2,1,5,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,3,2,1,3,3]=>[2,1,1,1,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,3,2,3,1,3]=>[3,2,2,4,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,2,3,3,1]=>[3,2,2,4,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,1,2,3]=>[3,2,3,1,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,3,1,3,2]=>[3,2,3,1,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,3,3,2,1,3]=>[2,1,2,1,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,3,3,2,3,1]=>[3,2,3,2,4,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,3,3,1,2]=>[3,2,3,3,1,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,3,3,2,1]=>[2,1,2,2,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,3,3,3,5]=>[1,2,2,1,1,3]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,3,5,3]=>[1,2,2,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,3,5,3,3]=>[1,2,2,3,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,5,3,3,3]=>[1,2,4,6,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,2,3,3,5]=>[2,4,1,3,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,2,3,5,3]=>[3,5,2,4,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,2,5,3,3]=>[3,5,2,6,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,3,2,3,5]=>[2,4,2,1,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,3,2,5,3]=>[3,5,3,2,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,3,3,2,5]=>[2,4,2,2,1,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,3,3,3,5,2]=>[1,3,1,1,3,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,3,5,2,3]=>[1,3,1,3,5,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,3,5,3,2]=>[3,5,3,5,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,5,2,3,3]=>[1,3,3,5,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,5,3,2,3]=>[3,5,5,1,2,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,5,3,3,2]=>[3,5,5,1,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,2,3,3,3]=>[1,5,5,2,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,5,3,2,3,3]=>[4,1,2,3,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,3,3,2,3]=>[4,1,2,4,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,3,3,3,2]=>[4,1,2,4,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,3,3,5]=>[2,1,4,2,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,3,3,5,3]=>[3,2,5,3,5,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,3,5,3,3]=>[3,2,5,5,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,5,3,3,3]=>[4,3,1,2,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,1,3,3,5]=>[1,2,6,3,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,1,3,5,3]=>[3,4,1,5,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,1,5,3,3]=>[4,5,2,1,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,3,3,1,3,5]=>[1,2,1,6,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,3,1,5,3]=>[4,5,4,2,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,3,3,3,1,5]=>[1,2,1,1,6,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,3,3,3,5,1]=>[1,2,1,1,3,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,3,5,1,3]=>[1,2,1,3,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,3,5,3,1]=>[3,4,3,5,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,3,5,1,3,3]=>[1,2,3,4,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,5,3,1,3]=>[3,4,5,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,5,3,3,1]=>[3,4,5,1,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,1,3,3,3]=>[1,4,4,3,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,5,3,1,3,3]=>[3,6,1,1,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,5,3,3,1,3]=>[3,6,1,3,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,5,3,3,3,1]=>[3,6,1,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,2,3,3,5]=>[1,6,2,2,1,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,2,3,5,3]=>[3,1,4,4,5,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,2,5,3,3]=>[3,1,4,6,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,3,2,3,5]=>[3,1,5,2,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,3,2,5,3]=>[3,1,5,2,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,3,3,2,5]=>[3,1,5,3,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,3,3,5,2]=>[1,6,3,1,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,3,5,2,3]=>[1,6,3,3,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,3,5,3,2]=>[3,1,5,5,1,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,5,2,3,3]=>[4,2,1,1,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,5,3,2,3]=>[4,2,1,2,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,5,3,3,2]=>[4,2,1,2,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,3,3,5]=>[2,1,1,4,2,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[3,2,1,3,5,3]=>[3,2,2,5,5,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,2,1,5,3,3]=>[4,3,3,1,2,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,1,3,5]=>[3,2,4,1,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,3,1,5,3]=>[4,3,5,2,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,3,3,1,5]=>[4,3,5,4,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,3,3,5,1]=>[2,1,3,2,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,3,5,1,3]=>[2,1,3,4,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,3,5,3,1]=>[3,2,4,5,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,5,1,3,3]=>[2,1,5,5,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,2,5,3,1,3]=>[3,2,6,1,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,5,3,3,1]=>[3,2,6,1,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,1,2,3,5]=>[1,1,6,2,2,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,3,1,2,5,3]=>[3,3,1,4,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,1,3,2,5]=>[3,3,1,5,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,3,1,3,5,2]=>[1,1,6,3,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,3,1,5,2,3]=>[4,4,2,1,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,3,1,5,3,2]=>[4,4,2,1,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,3,2,1,3,5]=>[2,2,1,1,4,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[3,3,2,1,5,3]=>[4,4,3,3,1,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,3,2,3,1,5]=>[4,4,3,5,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,3,2,3,5,1]=>[2,2,1,3,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,2,5,1,3]=>[2,2,1,5,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,3,2,5,3,1]=>[3,3,2,6,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,3,1,2,5]=>[1,1,1,6,2,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,3,3,1,5,2]=>[4,4,4,2,1,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,3,3,2,1,5]=>[2,2,2,1,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,3,3,2,5,1]=>[2,2,2,1,5,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,3,3,5,1,2]=>[1,1,1,3,4,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,3,5,2,1]=>[2,2,2,4,6,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,5,1,2,3]=>[1,1,3,4,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,3,5,1,3,2]=>[2,2,4,5,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,3,5,2,1,3]=>[2,2,4,6,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,3,5,2,3,1]=>[1,1,3,5,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,5,3,1,2]=>[3,3,5,1,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,3,5,3,2,1]=>[3,3,5,1,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,5,1,2,3,3]=>[1,3,4,2,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,5,1,3,2,3]=>[2,4,5,4,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,3,3,2]=>[2,4,5,4,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,5,2,1,3,3]=>[2,4,6,1,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,5,2,3,1,3]=>[1,3,5,2,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,2,3,3,1]=>[1,3,5,2,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,3,1,2,3]=>[3,5,1,1,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,5,3,1,3,2]=>[3,5,1,1,5,2]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,5,3,2,1,3]=>[3,5,1,2,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,5,3,2,3,1]=>[3,5,1,2,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,5,3,3,1,2]=>[3,5,1,3,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,5,3,3,2,1]=>[3,5,1,3,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,2,3,3,3]=>[1,4,2,2,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,1,3,2,3,3]=>[2,5,4,1,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,3,3,2,3]=>[2,5,4,2,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,3,3,3,2]=>[2,5,4,2,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,2,1,3,3,3]=>[2,6,1,4,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,2,3,1,3,3]=>[1,5,2,6,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,3,3,1,3]=>[1,5,2,1,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,3,3,3,1]=>[1,5,2,1,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,3,1,2,3,3]=>[3,1,1,4,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,3,1,3,2,3]=>[3,1,1,5,2,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,3,1,3,3,2]=>[3,1,1,5,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,3,2,1,3,3]=>[3,1,2,2,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,3,2,3,1,3]=>[3,1,2,4,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,3,2,3,3,1]=>[3,1,2,4,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,3,1,2,3]=>[3,1,3,1,4,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,3,3,1,3,2]=>[3,1,3,1,5,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,3,3,2,1,3]=>[3,1,3,2,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,3,3,2,3,1]=>[3,1,3,2,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,3,3,1,2]=>[3,1,3,3,1,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,3,3,3,2,1]=>[3,1,3,3,2,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,3,3,6]=>[1,2,2,1,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,2,3,3,6,3]=>[1,2,2,1,4,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,3,6,3,3]=>[1,2,2,4,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,6,3,3,3]=>[1,2,5,5,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,3,2,3,3,6]=>[2,4,1,3,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,2,3,6,3]=>[2,4,1,3,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,6,3,3]=>[4,6,3,1,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,3,2,3,6]=>[2,4,2,1,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,3,2,6,3]=>[4,6,4,3,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,3,3,3,2,6]=>[2,4,2,2,1,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,3,3,3,6,2]=>[1,3,1,1,4,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,3,3,6,2,3]=>[1,3,1,4,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,3,6,3,2]=>[2,4,2,5,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,6,2,3,3]=>[1,3,4,4,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,6,3,2,3]=>[2,4,5,6,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,6,3,3,2]=>[2,4,5,6,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,2,3,3,3]=>[1,6,4,2,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,6,3,2,3,3]=>[4,2,1,3,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,3,3,2,3]=>[4,2,1,4,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,3,3,3,2]=>[4,2,1,4,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,3,3,6]=>[2,1,4,2,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,1,3,3,6,3]=>[2,1,4,2,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,3,6,3,3]=>[2,1,4,5,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,6,3,3,3]=>[4,3,2,1,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,1,3,3,6]=>[1,2,6,3,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,1,3,6,3]=>[1,2,6,3,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,6,3,3]=>[4,5,2,2,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,3,3,1,3,6]=>[1,2,1,6,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,3,1,6,3]=>[4,5,4,2,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,3,3,3,1,6]=>[3,4,3,3,1,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[2,3,3,3,6,1]=>[1,2,1,1,4,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,3,6,1,3]=>[1,2,1,4,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,3,6,3,1]=>[1,2,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,6,1,3,3]=>[1,2,4,3,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,6,3,1,3]=>[1,2,4,5,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,6,3,3,1]=>[1,2,4,5,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,1,3,3,3]=>[1,5,3,3,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,6,3,1,3,3]=>[4,1,1,2,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,3,3,1,3]=>[4,1,1,4,2,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,3,3,3,1]=>[4,1,1,4,4,2]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,1,2,3,3,6]=>[1,6,2,2,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,2,3,6,3]=>[1,6,2,2,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,2,6,3,3]=>[4,2,5,1,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,3,2,3,6]=>[3,1,5,2,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,3,2,6,3]=>[4,2,6,3,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,3,3,2,6]=>[4,2,6,4,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,3,3,6,2]=>[1,6,3,1,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,3,6,2,3]=>[1,6,3,4,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,3,6,3,2]=>[6,4,1,2,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,6,2,3,3]=>[3,1,1,6,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,6,3,2,3]=>[4,2,2,1,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,6,3,3,2]=>[4,2,2,1,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,3,3,6]=>[2,1,1,4,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,2,1,3,6,3]=>[2,1,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,6,3,3]=>[4,3,3,2,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,1,3,6]=>[3,2,4,1,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,3,1,6,3]=>[4,3,5,2,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,3,3,1,6]=>[3,2,4,3,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,3,3,6,1]=>[2,1,3,2,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,3,6,1,3]=>[2,1,3,5,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,3,6,3,1]=>[5,4,6,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,1,3,3]=>[2,1,6,4,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,6,3,1,3]=>[4,3,1,1,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,6,3,3,1]=>[4,3,1,1,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,1,2,3,6]=>[1,1,6,2,2,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,3,1,2,6,3]=>[4,4,2,5,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,3,1,3,2,6]=>[4,4,2,6,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,3,1,3,6,2]=>[1,1,6,3,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,1,6,2,3]=>[3,3,1,1,6,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,3,1,6,3,2]=>[4,4,2,2,1,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,3,2,1,3,6]=>[2,2,1,1,4,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,3,2,1,6,3]=>[4,4,3,3,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,3,2,3,1,6]=>[3,3,2,4,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,2,3,6,1]=>[2,2,1,3,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,2,6,1,3]=>[2,2,1,6,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,3,2,6,3,1]=>[4,4,3,1,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,3,1,2,6]=>[1,1,1,6,2,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,3,3,1,6,2]=>[3,3,3,1,1,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,3,3,2,1,6]=>[3,3,3,2,2,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,3,3,2,6,1]=>[2,2,2,1,6,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,3,6,1,2]=>[1,1,1,4,3,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,3,6,2,1]=>[2,2,2,5,5,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,3,6,1,2,3]=>[1,1,4,3,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,3,6,1,3,2]=>[2,2,5,4,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,3,6,2,1,3]=>[2,2,5,5,1,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,3,6,2,3,1]=>[1,1,4,4,2,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,3,6,3,1,2]=>[1,1,4,5,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,6,3,2,1]=>[2,2,5,6,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,6,1,2,3,3]=>[1,4,3,2,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,6,1,3,2,3]=>[2,5,4,4,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,1,3,3,2]=>[2,5,4,4,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,6,2,1,3,3]=>[2,5,5,1,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,6,2,3,1,3]=>[1,4,4,2,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,6,2,3,3,1]=>[1,4,4,2,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,6,3,1,2,3]=>[1,4,5,6,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,3,1,3,2]=>[6,2,3,4,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,3,2,1,3]=>[2,5,6,1,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,3,2,3,1]=>[5,1,2,4,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,3,3,1,2]=>[1,4,5,1,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,3,3,2,1]=>[2,5,6,2,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,1,2,3,3,3]=>[1,3,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[6,1,3,2,3,3]=>[2,4,4,1,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,3,3,2,3]=>[2,4,4,2,1,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,3,3,3,2]=>[2,4,4,2,2,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[6,2,1,3,3,3]=>[2,5,1,4,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,2,3,1,3,3]=>[1,4,2,6,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,2,3,3,1,3]=>[1,4,2,1,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,2,3,3,3,1]=>[1,4,2,1,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,3,1,2,3,3]=>[1,5,6,2,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,1,3,2,3]=>[4,1,2,6,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,1,3,3,2]=>[4,1,2,6,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,3,2,1,3,3]=>[2,6,1,1,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,3,2,3,1,3]=>[4,1,3,5,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,2,3,3,1]=>[4,1,3,5,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,3,1,2,3]=>[1,5,1,6,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,3,1,3,2]=>[4,1,4,2,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,3,3,2,1,3]=>[2,6,2,1,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,3,3,2,3,1]=>[4,1,4,3,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,3,3,1,2]=>[1,5,1,1,6,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,3,3,3,2,1]=>[2,6,2,2,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,2,3,3,4,4]=>[1,2,2,1,2,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,3,4,3,4]=>[2,3,3,3,1,3]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,3,4,4,3]=>[2,3,3,3,2,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,4,3,3,4]=>[2,3,4,1,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,3,4,3]=>[2,3,4,1,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,4,4,3,3]=>[2,3,4,2,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,2,3,4,4]=>[2,4,1,3,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,2,4,3,4]=>[2,4,1,4,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,2,4,4,3]=>[2,4,1,4,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,3,3,2,4,4]=>[2,4,2,1,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,3,4,2,4]=>[1,3,1,2,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,3,4,4,2]=>[1,3,1,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,4,2,3,4]=>[1,3,2,6,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,3,4,2,4,3]=>[3,5,4,1,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,3,2,4]=>[2,4,3,1,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,4,3,4,2]=>[3,5,4,2,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,4,4,2,3]=>[1,3,2,1,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,3,4,4,3,2]=>[2,4,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,4,2,3,3,4]=>[1,4,6,2,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,4,2,3,4,3]=>[3,6,1,4,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,2,4,3,3]=>[3,6,1,5,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,2,3,4]=>[2,5,1,1,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,4,3,2,4,3]=>[2,5,1,1,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,4,3,3,2,4]=>[2,5,1,2,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,3,3,4,2]=>[3,6,2,3,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,3,4,2,3]=>[3,6,2,4,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,3,4,3,2]=>[2,5,1,3,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,4,4,2,3,3]=>[1,4,1,6,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,4,3,2,3]=>[2,5,2,1,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,4,4,3,3,2]=>[2,5,2,1,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,3,3,4,4]=>[2,1,4,2,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,3,4,3,4]=>[2,1,4,3,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,3,4,4,3]=>[2,1,4,3,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,4,3,3,4]=>[2,1,5,1,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,4,3,4,3]=>[2,1,5,1,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,4,4,3,3]=>[2,1,5,2,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,1,3,4,4]=>[1,2,6,3,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,3,1,4,3,4]=>[3,4,1,6,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,1,4,4,3]=>[3,4,1,6,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,3,1,4,4]=>[1,2,1,6,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,3,3,4,1,4]=>[1,2,1,2,5,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,3,3,4,4,1]=>[1,2,1,2,1,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,3,4,1,3,4]=>[1,2,2,5,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[2,3,4,1,4,3]=>[2,3,3,6,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,3,4,3,1,4]=>[3,4,4,2,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,4,3,4,1]=>[2,3,3,1,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,3,4,4,1,3]=>[1,2,2,1,5,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,3,4,4,3,1]=>[3,4,4,3,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,1,3,3,4]=>[1,3,5,3,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,1,3,4,3]=>[2,4,6,4,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,1,4,3,3]=>[2,4,6,5,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,4,3,1,3,4]=>[3,5,2,1,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,3,1,4,3]=>[3,5,2,1,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,3,3,1,4]=>[3,5,2,3,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,3,3,4,1]=>[2,4,1,2,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,3,4,1,3]=>[2,4,1,3,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,3,4,3,1]=>[3,5,2,4,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,4,1,3,3]=>[1,3,1,5,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,4,3,1,3]=>[3,5,3,2,1,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,4,3,3,1]=>[3,5,3,2,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,2,3,4,4]=>[1,6,2,2,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,1,2,4,3,4]=>[3,1,4,5,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,4,4,3]=>[3,1,4,5,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,3,2,4,4]=>[3,1,5,2,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,3,4,2,4]=>[3,1,5,4,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,3,4,4,2]=>[3,1,5,4,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,4,2,3,4]=>[3,1,6,1,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,4,2,4,3]=>[3,1,6,1,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,3,2,4]=>[3,1,6,2,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,4,3,4,2]=>[3,1,6,2,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,4,4,2,3]=>[3,1,6,3,1,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,4,4,3,2]=>[3,1,6,3,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,1,3,4,4]=>[2,1,1,4,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,4,3,4]=>[2,1,1,5,1,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,2,1,4,4,3]=>[2,1,1,5,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,2,3,1,4,4]=>[3,2,4,1,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,3,4,1,4]=>[2,1,3,3,6,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,3,4,4,1]=>[2,1,3,3,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,2,4,1,3,4]=>[2,1,4,6,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,4,1,4,3]=>[2,1,4,6,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,4,3,1,4]=>[3,2,5,2,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,4,3,4,1]=>[2,1,4,1,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,4,4,1,3]=>[2,1,4,2,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,2,4,4,3,1]=>[3,2,5,3,2,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,3,1,2,4,4]=>[1,1,6,2,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,3,1,4,2,4]=>[3,3,1,6,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,3,1,4,4,2]=>[3,3,1,6,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,3,2,1,4,4]=>[2,2,1,1,5,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,3,2,4,1,4]=>[2,2,1,4,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,3,2,4,4,1]=>[2,2,1,4,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,3,4,1,2,4]=>[1,1,2,5,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,3,4,1,4,2]=>[1,1,2,5,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,4,2,1,4]=>[3,3,4,1,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,3,4,2,4,1]=>[1,1,2,6,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,4,4,1,2]=>[1,1,2,1,5,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,3,4,4,2,1]=>[3,3,4,3,1,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,4,1,2,3,4]=>[1,2,5,2,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[3,4,1,2,4,3]=>[2,3,6,3,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,1,3,2,4]=>[2,3,6,4,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,4,1,3,4,2]=>[1,2,5,3,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,4,2,3]=>[1,2,5,4,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,4,1,4,3,2]=>[2,3,6,5,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,2,1,3,4]=>[3,4,1,2,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,2,1,4,3]=>[3,4,1,2,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,2,3,1,4]=>[3,4,1,4,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,4,2,3,4,1]=>[1,2,6,2,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,2,4,1,3]=>[1,2,6,3,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,4,2,4,3,1]=>[3,4,1,5,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,3,1,2,4]=>[3,4,2,1,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,3,1,4,2]=>[3,4,2,1,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,3,2,1,4]=>[2,3,1,1,1,5]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,4,3,2,4,1]=>[2,3,1,1,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,3,4,1,2]=>[2,3,1,3,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,3,4,2,1]=>[3,4,2,4,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,4,4,1,2,3]=>[1,2,1,5,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,4,4,1,3,2]=>[2,3,2,6,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,4,2,1,3]=>[3,4,3,1,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,4,2,3,1]=>[3,4,3,1,4,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[3,4,4,3,1,2]=>[3,4,3,2,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,4,4,3,2,1]=>[2,3,2,1,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,1,2,3,3,4]=>[1,5,2,2,1,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,2,3,4,3]=>[2,6,3,3,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,1,2,4,3,3]=>[2,6,3,4,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,3,2,3,4]=>[2,6,4,1,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,3,2,4,3]=>[2,6,4,1,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,1,3,3,2,4]=>[2,6,4,2,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,3,3,4,2]=>[1,5,3,1,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,3,4,2,3]=>[1,5,3,2,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,3,4,3,2]=>[2,6,4,3,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,4,2,3,3]=>[1,5,4,6,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,4,3,2,3]=>[2,6,5,1,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,4,3,3,2]=>[2,6,5,1,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,2,1,3,3,4]=>[3,1,2,5,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,3,4,3]=>[3,1,2,5,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,4,3,3]=>[3,1,2,6,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,2,3,1,3,4]=>[3,1,4,1,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,2,3,1,4,3]=>[3,1,4,1,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,3,3,1,4]=>[3,1,4,3,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,2,3,3,4,1]=>[1,6,2,1,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,2,3,4,1,3]=>[1,6,2,2,5,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,2,3,4,3,1]=>[3,1,4,4,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,4,1,3,3]=>[1,6,3,5,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,4,3,1,3]=>[3,1,5,2,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,4,3,3,1]=>[3,1,5,2,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,1,2,3,4]=>[3,2,1,4,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,3,1,2,4,3]=>[3,2,1,4,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,1,3,2,4]=>[3,2,1,5,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,3,1,3,4,2]=>[3,2,1,5,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,4,2,3]=>[3,2,1,6,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,1,4,3,2]=>[3,2,1,6,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,3,2,1,3,4]=>[2,1,1,1,4,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,3,2,1,4,3]=>[2,1,1,1,5,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[4,3,2,3,1,4]=>[3,2,2,4,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,3,2,3,4,1]=>[2,1,1,3,3,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,2,4,1,3]=>[2,1,1,4,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,3,2,4,3,1]=>[3,2,2,5,2,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,3,3,1,2,4]=>[3,2,3,1,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,3,1,4,2]=>[3,2,3,1,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,3,2,1,4]=>[2,1,2,1,1,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,3,3,2,4,1]=>[2,1,2,1,4,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,3,4,1,2]=>[2,1,2,3,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,3,3,4,2,1]=>[3,2,3,4,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,4,1,2,3]=>[2,1,3,6,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,3,4,1,3,2]=>[2,1,3,6,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,4,2,1,3]=>[3,2,4,1,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,4,2,3,1]=>[3,2,4,1,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,3,4,3,1,2]=>[3,2,4,2,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,3,4,3,2,1]=>[2,1,3,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[4,4,1,2,3,3]=>[1,1,5,2,2,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,4,1,3,2,3]=>[2,2,6,4,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,4,1,3,3,2]=>[2,2,6,4,2,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,4,2,1,3,3]=>[3,3,1,2,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,4,2,3,1,3]=>[3,3,1,4,1,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,4,2,3,3,1]=>[3,3,1,4,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,4,3,1,2,3]=>[3,3,2,1,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,4,3,1,3,2]=>[3,3,2,1,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,4,3,2,1,3]=>[2,2,1,1,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,4,3,2,3,1]=>[3,3,2,2,4,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,3,3,1,2]=>[3,3,2,3,1,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,3,3,2,1]=>[2,2,1,2,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,3,3,4,5]=>[1,2,2,1,2,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,3,3,5,4]=>[2,3,3,2,4,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,3,4,3,5]=>[2,3,3,3,1,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,3,4,5,3]=>[1,2,2,2,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,2,3,5,3,4]=>[1,2,2,3,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,5,4,3]=>[2,3,3,4,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,4,3,3,5]=>[2,3,4,1,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,4,3,5,3]=>[3,4,5,2,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,4,5,3,3]=>[1,2,3,2,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,5,3,3,4]=>[1,2,4,6,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,5,3,4,3]=>[3,4,6,1,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,4,3,3]=>[2,3,5,1,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,2,3,4,5]=>[2,4,1,3,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,2,3,5,4]=>[2,4,1,3,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,2,4,3,5]=>[2,4,1,4,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,3,2,4,5,3]=>[3,5,2,5,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,2,5,3,4]=>[3,5,2,6,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,5,4,3]=>[2,4,1,5,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,3,3,2,4,5]=>[2,4,2,1,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,3,2,5,4]=>[2,4,2,1,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,3,4,2,5]=>[1,3,1,2,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,3,4,5,2]=>[1,3,1,2,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,3,5,2,4]=>[1,3,1,3,5,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,3,3,5,4,2]=>[3,5,3,5,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,3,4,2,3,5]=>[1,3,2,6,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,3,4,2,5,3]=>[3,5,4,1,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,4,3,2,5]=>[2,4,3,1,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,4,3,5,2]=>[2,4,3,1,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,5,2,3]=>[1,3,2,2,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,3,4,5,3,2]=>[3,5,4,4,1,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,5,2,3,4]=>[1,3,3,5,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,5,2,4,3]=>[6,1,1,3,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,5,3,2,4]=>[6,1,1,4,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,5,3,4,2]=>[3,5,5,1,4,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,5,4,2,3]=>[3,5,5,2,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,5,4,3,2]=>[2,4,4,1,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,4,2,3,3,5]=>[1,4,6,2,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,2,3,5,3]=>[3,6,1,4,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,5,3,3]=>[5,1,3,1,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,4,3,2,3,5]=>[2,5,1,1,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,3,2,5,3]=>[5,1,4,4,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,3,3,2,5]=>[2,5,1,2,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,3,3,5,2]=>[2,5,1,2,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,3,5,2,3]=>[2,5,1,4,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,5,3,2]=>[3,6,2,5,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,5,2,3,3]=>[1,4,2,5,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,5,3,2,3]=>[3,6,4,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,5,3,3,2]=>[3,6,4,1,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,2,3,3,4]=>[1,5,5,2,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,2,3,4,3]=>[4,1,1,5,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,5,2,4,3,3]=>[4,1,1,6,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,3,2,3,4]=>[4,1,2,3,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,3,2,4,3]=>[4,1,2,3,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,3,3,2,4]=>[4,1,2,4,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,3,3,4,2]=>[4,1,2,4,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,3,4,2,3]=>[4,1,2,5,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,3,4,3,2]=>[4,1,2,5,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,4,2,3,3]=>[4,1,3,2,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,4,3,2,3]=>[2,6,1,1,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,5,4,3,3,2]=>[2,6,1,1,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,1,3,3,4,5]=>[2,1,4,2,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,3,3,5,4]=>[2,1,4,2,4,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,3,4,3,5]=>[2,1,4,3,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,3,4,5,3]=>[3,2,5,4,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,3,5,3,4]=>[3,2,5,5,1,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,3,5,4,3]=>[2,1,4,4,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,1,4,3,3,5]=>[2,1,5,1,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,4,3,5,3]=>[3,2,6,2,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,5,3,3]=>[3,2,6,4,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,5,3,3,4]=>[4,3,1,2,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,5,3,4,3]=>[4,3,1,2,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,5,4,3,3]=>[2,1,6,1,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,1,3,4,5]=>[1,2,6,3,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,3,1,3,5,4]=>[3,4,1,5,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,1,4,3,5]=>[3,4,1,6,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,4,5,3]=>[3,4,1,6,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,3,1,5,3,4]=>[4,5,2,1,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,1,5,4,3]=>[4,5,2,1,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,3,1,4,5]=>[1,2,1,6,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,3,1,5,4]=>[4,5,4,2,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,3,4,1,5]=>[1,2,1,2,5,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,3,3,4,5,1]=>[1,2,1,2,2,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,3,3,5,1,4]=>[1,2,1,3,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,3,5,4,1]=>[2,3,2,4,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,3,4,1,3,5]=>[1,2,2,5,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,3,4,1,5,3]=>[4,5,5,1,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,3,4,3,1,5]=>[4,5,5,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,3,5,1]=>[2,3,3,1,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,4,5,1,3]=>[1,2,2,2,4,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,3,4,5,3,1]=>[3,4,4,4,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,3,5,1,3,4]=>[1,2,3,4,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,5,1,4,3]=>[2,3,4,5,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,5,3,1,4]=>[3,4,5,1,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,5,3,4,1]=>[1,2,3,6,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,5,4,1,3]=>[2,3,4,1,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,5,4,3,1]=>[3,4,5,2,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,4,1,3,3,5]=>[1,3,5,3,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,4,1,3,5,3]=>[6,1,3,1,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,1,5,3,3]=>[4,6,1,1,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,3,1,3,5]=>[6,1,5,4,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,4,3,1,5,3]=>[4,6,3,2,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,3,3,1,5]=>[4,6,3,4,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,3,3,5,1]=>[2,4,1,2,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,3,5,1,3]=>[6,1,5,1,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,4,3,5,3,1]=>[3,5,2,5,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,4,5,1,3,3]=>[1,3,2,4,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,4,5,3,1,3]=>[3,5,4,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,4,5,3,3,1]=>[3,5,4,1,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,1,3,3,4]=>[1,4,4,3,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,1,3,4,3]=>[2,5,5,4,3,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,1,4,3,3]=>[5,1,1,1,4,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[2,5,3,1,3,4]=>[3,6,1,1,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,5,3,1,4,3]=>[5,1,3,3,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,3,3,1,4]=>[5,1,3,5,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,5,3,3,4,1]=>[1,4,6,1,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,3,4,1,3]=>[1,4,6,2,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,3,4,3,1]=>[3,6,1,4,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,5,4,1,3,3]=>[2,5,1,6,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,4,3,1,3]=>[3,6,2,2,1,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,4,3,3,1]=>[3,6,2,2,3,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,2,3,4,5]=>[1,6,2,2,2,2]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[3,1,2,3,5,4]=>[3,1,4,4,5,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,4,3,5]=>[3,1,4,5,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,2,4,5,3]=>[3,1,4,5,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,2,5,3,4]=>[3,1,4,6,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,2,5,4,3]=>[3,1,4,6,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,3,2,4,5]=>[3,1,5,2,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,3,2,5,4]=>[3,1,5,2,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,3,4,2,5]=>[3,1,5,4,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,3,4,5,2]=>[1,6,3,2,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,3,5,2,4]=>[6,4,1,1,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,1,3,5,4,2]=>[3,1,5,5,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,1,4,2,3,5]=>[3,1,6,1,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,2,5,3]=>[5,3,1,3,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,4,3,2,5]=>[5,3,1,4,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,1,4,3,5,2]=>[6,4,2,5,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,5,2,3]=>[1,6,4,2,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,4,5,3,2]=>[3,1,6,4,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,5,2,3,4]=>[4,2,1,1,5,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,1,5,2,4,3]=>[4,2,1,1,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,5,3,2,4]=>[4,2,1,2,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,5,3,4,2]=>[4,2,1,2,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,5,4,2,3]=>[4,2,1,3,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,5,4,3,2]=>[4,2,1,3,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,2,1,3,4,5]=>[2,1,1,4,3,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,2,1,3,5,4]=>[2,1,1,4,4,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[3,2,1,4,3,5]=>[2,1,1,5,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,1,4,5,3]=>[3,2,2,6,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,1,5,3,4]=>[4,3,3,1,2,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,1,5,4,3]=>[2,1,1,6,1,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[3,2,3,1,4,5]=>[3,2,4,1,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,3,1,5,4]=>[4,3,5,2,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,3,4,1,5]=>[4,3,5,5,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,2,3,4,5,1]=>[2,1,3,3,3,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,2,3,5,1,4]=>[2,1,3,4,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,3,5,4,1]=>[2,1,3,4,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,4,1,3,5]=>[6,5,1,3,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,2,4,1,5,3]=>[4,3,6,1,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,4,3,1,5]=>[4,3,6,3,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,4,3,5,1]=>[2,1,4,1,4,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,4,5,1,3]=>[2,1,4,3,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,4,5,3,1]=>[3,2,5,4,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,5,1,3,4]=>[2,1,5,5,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,5,1,4,3]=>[5,4,1,1,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,2,5,3,1,4]=>[5,4,1,3,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,2,5,3,4,1]=>[5,4,1,3,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,5,4,1,3]=>[2,1,5,1,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,5,4,3,1]=>[3,2,6,2,2,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,3,1,2,4,5]=>[1,1,6,2,3,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,3,1,2,5,4]=>[3,3,1,4,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,3,1,4,2,5]=>[5,5,3,1,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,3,1,4,5,2]=>[1,1,6,4,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,1,5,2,4]=>[4,4,2,1,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,3,1,5,4,2]=>[4,4,2,1,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,3,2,1,4,5]=>[2,2,1,1,5,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,3,2,1,5,4]=>[2,2,1,1,6,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,3,2,4,1,5]=>[4,4,3,6,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,2,4,5,1]=>[2,2,1,4,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,2,5,1,4]=>[5,5,4,1,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,3,2,5,4,1]=>[2,2,1,5,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,3,4,1,2,5]=>[1,1,2,5,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,3,4,1,5,2]=>[4,4,5,1,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,3,4,2,1,5]=>[4,4,5,2,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,3,4,2,5,1]=>[1,1,2,6,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,3,4,5,1,2]=>[1,1,2,2,4,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,3,4,5,2,1]=>[2,2,3,3,6,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,3,5,1,2,4]=>[1,1,3,4,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,5,1,4,2]=>[1,1,3,4,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,5,2,1,4]=>[2,2,4,6,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,3,5,2,4,1]=>[1,1,3,5,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,3,5,4,1,2]=>[2,2,4,1,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,3,5,4,2,1]=>[3,3,5,2,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,4,1,2,3,5]=>[1,2,5,2,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,4,1,2,5,3]=>[1,2,5,2,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,4,1,3,2,5]=>[2,3,6,4,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,1,3,5,2]=>[1,2,5,3,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,4,1,5,2,3]=>[4,5,1,1,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,4,1,5,3,2]=>[4,5,1,1,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,2,1,3,5]=>[3,4,1,2,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,2,1,5,3]=>[4,5,2,3,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,4,2,3,1,5]=>[4,5,2,5,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,2,3,5,1]=>[1,2,6,2,3,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,2,5,1,3]=>[1,2,6,4,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,4,2,5,3,1]=>[3,4,1,6,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,4,3,1,2,5]=>[3,4,2,1,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,4,3,1,5,2]=>[4,5,3,2,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,3,2,1,5]=>[2,3,1,1,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,4,3,2,5,1]=>[2,3,1,1,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,4,3,5,1,2]=>[2,3,1,4,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,3,5,2,1]=>[2,3,1,4,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,5,1,2,3]=>[1,2,2,4,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[3,4,5,1,3,2]=>[2,3,3,5,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,5,2,1,3]=>[2,3,3,6,1,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,5,2,3,1]=>[1,2,2,5,2,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,5,3,1,2]=>[3,4,4,1,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[3,4,5,3,2,1]=>[3,4,4,1,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,5,1,2,3,4]=>[1,3,4,2,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[3,5,1,2,4,3]=>[2,4,5,3,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,3,2,4]=>[6,1,2,1,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,5,1,3,4,2]=>[1,3,4,3,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,1,4,2,3]=>[1,3,4,4,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,1,4,3,2]=>[2,4,5,5,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,5,2,1,3,4]=>[2,4,6,1,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,2,1,4,3]=>[2,4,6,1,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,5,2,3,1,4]=>[1,3,5,2,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,3,4,1]=>[1,3,5,2,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,5,2,4,1,3]=>[6,1,3,1,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[3,5,2,4,3,1]=>[6,1,3,1,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,3,1,2,4]=>[3,5,1,1,4,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,5,3,1,4,2]=>[3,5,1,1,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,5,3,2,1,4]=>[3,5,1,2,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,5,3,2,4,1]=>[6,1,4,5,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,3,4,1,2]=>[1,3,6,2,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,5,3,4,2,1]=>[3,5,1,4,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,5,4,1,2,3]=>[2,4,1,6,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,4,1,3,2]=>[2,4,1,6,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,5,4,2,1,3]=>[3,5,2,1,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,5,4,2,3,1]=>[3,5,2,1,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,5,4,3,1,2]=>[3,5,2,2,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,5,4,3,2,1]=>[2,4,1,1,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[4,1,2,3,3,5]=>[1,5,2,2,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,2,3,5,3]=>[1,5,2,2,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,5,3,3]=>[1,5,2,4,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,2,3,5]=>[2,6,4,1,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,3,2,5,3]=>[6,3,1,5,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,3,2,5]=>[2,6,4,2,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,3,3,5,2]=>[1,5,3,1,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,3,5,2,3]=>[1,5,3,3,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,1,3,5,3,2]=>[6,3,1,1,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,5,2,3,3]=>[4,1,1,1,5,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,5,3,2,3]=>[4,1,1,2,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,5,3,3,2]=>[4,1,1,2,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,3,3,5]=>[3,1,2,5,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,2,1,3,5,3]=>[3,1,2,5,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,2,1,5,3,3]=>[4,2,3,1,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,3,1,3,5]=>[3,1,4,1,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,2,3,1,5,3]=>[4,2,5,2,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,2,3,3,1,5]=>[4,2,5,4,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,2,3,3,5,1]=>[1,6,2,1,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,3,5,1,3]=>[1,6,2,3,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,3,5,3,1]=>[3,1,4,5,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,2,5,1,3,3]=>[1,6,4,4,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,5,3,1,3]=>[3,1,6,1,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,2,5,3,3,1]=>[3,1,6,1,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[4,3,1,2,3,5]=>[3,2,1,4,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,1,2,5,3]=>[3,2,1,4,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,1,3,2,5]=>[3,2,1,5,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,1,3,5,2]=>[6,5,4,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,3,1,5,2,3]=>[4,3,2,1,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,5,3,2]=>[4,3,2,1,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,2,1,3,5]=>[2,1,1,1,4,4]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[4,3,2,1,5,3]=>[4,3,3,3,1,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,2,3,1,5]=>[4,3,3,5,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,2,3,5,1]=>[2,1,1,3,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,2,5,1,3]=>[2,1,1,5,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,3,2,5,3,1]=>[3,2,2,6,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,3,3,1,2,5]=>[3,2,3,1,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,3,1,5,2]=>[4,3,4,2,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,3,3,2,1,5]=>[2,1,2,1,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[4,3,3,2,5,1]=>[2,1,2,1,5,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,3,3,5,1,2]=>[2,1,2,4,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,3,5,2,1]=>[2,1,2,4,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,5,1,2,3]=>[2,1,4,5,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,5,1,3,2]=>[2,1,4,5,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,3,5,2,1,3]=>[2,1,4,6,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,3,5,2,3,1]=>[4,3,6,1,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,5,3,1,2]=>[3,2,5,1,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,5,3,2,1]=>[3,2,5,1,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,5,1,2,3,3]=>[1,2,4,2,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[4,5,1,3,2,3]=>[2,3,5,4,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,5,1,3,3,2]=>[2,3,5,4,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,2,1,3,3]=>[2,3,6,1,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,2,3,1,3]=>[1,2,5,2,6,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,5,2,3,3,1]=>[1,2,5,2,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,5,3,1,2,3]=>[3,4,1,1,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[4,5,3,1,3,2]=>[3,4,1,1,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,5,3,2,1,3]=>[3,4,1,2,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,3,2,3,1]=>[3,4,1,2,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,5,3,3,1,2]=>[3,4,1,3,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,5,3,3,2,1]=>[3,4,1,3,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,2,3,3,4]=>[1,4,2,2,1,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[5,1,2,3,4,3]=>[2,5,3,3,3,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,1,2,4,3,3]=>[2,5,3,4,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,3,2,3,4]=>[2,5,4,1,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,3,2,4,3]=>[2,5,4,1,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,3,3,2,4]=>[2,5,4,2,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,3,3,4,2]=>[1,4,3,1,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,3,4,2,3]=>[1,4,3,2,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,3,4,3,2]=>[2,5,4,3,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,1,4,2,3,3]=>[1,4,4,6,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,4,3,2,3]=>[2,5,5,1,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,1,4,3,3,2]=>[2,5,5,1,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,2,1,3,3,4]=>[2,6,1,4,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,1,3,4,3]=>[2,6,1,4,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,1,4,3,3]=>[2,6,1,5,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,3,1,3,4]=>[1,5,2,6,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,3,1,4,3]=>[5,2,6,3,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,3,3,1,4]=>[1,5,2,1,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,3,3,4,1]=>[1,5,2,1,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,2,3,4,1,3]=>[1,5,2,2,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,2,3,4,3,1]=>[4,1,5,5,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,4,1,3,3]=>[1,5,3,5,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,4,3,1,3]=>[6,3,1,5,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,4,3,3,1]=>[4,1,6,3,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,1,2,3,4]=>[3,1,1,4,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,3,1,2,4,3]=>[3,1,1,4,5,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,3,1,3,2,4]=>[3,1,1,5,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,3,1,3,4,2]=>[3,1,1,5,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,3,1,4,2,3]=>[3,1,1,6,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,1,4,3,2]=>[3,1,1,6,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,3,2,1,3,4]=>[3,1,2,2,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,3,2,1,4,3]=>[3,1,2,2,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,3,2,3,1,4]=>[3,1,2,4,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,2,3,4,1]=>[4,2,3,5,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,3,2,4,1,3]=>[6,4,5,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,3,2,4,3,1]=>[3,1,2,5,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,3,3,1,2,4]=>[3,1,3,1,4,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,3,3,1,4,2]=>[3,1,3,1,6,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,1,4]=>[3,1,3,2,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,3,3,2,4,1]=>[4,2,4,3,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,3,4,1,2]=>[1,6,1,2,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,3,3,4,2,1]=>[3,1,3,4,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,3,4,1,2,3]=>[1,6,2,5,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,3,4,1,3,2]=>[4,2,5,1,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,4,2,1,3]=>[3,1,4,1,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,3,4,2,3,1]=>[3,1,4,1,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,3,4,3,1,2]=>[3,1,4,2,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,3,4,3,2,1]=>[3,1,4,2,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,4,1,2,3,3]=>[2,1,6,3,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,4,1,3,2,3]=>[2,1,6,4,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,4,1,3,3,2]=>[2,1,6,4,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,4,2,1,3,3]=>[3,2,1,2,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,4,2,3,1,3]=>[3,2,1,4,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,4,2,3,3,1]=>[3,2,1,4,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,3,1,2,3]=>[3,2,2,1,4,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,4,3,1,3,2]=>[3,2,2,1,5,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,4,3,2,1,3]=>[2,1,1,1,1,4]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[5,4,3,2,3,1]=>[3,2,2,2,4,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,4,3,3,1,2]=>[3,2,2,3,1,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,3,3,2,1]=>[2,1,1,2,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,3,3,4,6]=>[1,2,2,1,2,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,3,6,4]=>[1,2,2,1,4,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,3,4,3,6]=>[2,3,3,3,1,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,3,4,6,3]=>[1,2,2,2,3,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,3,6,3,4]=>[1,2,2,4,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,2,3,6,4,3]=>[3,4,4,6,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,4,3,3,6]=>[2,3,4,1,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,4,3,6,3]=>[2,3,4,1,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,6,3,3]=>[1,2,3,3,5,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,6,3,3,4]=>[1,2,5,5,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,2,6,3,4,3]=>[4,5,1,1,5,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,2,6,4,3,3]=>[4,5,1,2,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,3,4,6]=>[2,4,1,3,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,2,3,6,4]=>[3,5,2,4,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,4,3,6]=>[2,4,1,4,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,2,4,6,3]=>[6,1,5,1,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,3,2,6,3,4]=>[4,6,3,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,2,6,4,3]=>[4,6,3,1,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,3,2,4,6]=>[2,4,2,1,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,3,2,6,4]=>[4,6,4,3,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,3,4,2,6]=>[1,3,1,2,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,3,4,6,2]=>[1,3,1,2,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,3,6,2,4]=>[1,3,1,4,4,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,3,6,4,2]=>[3,5,3,6,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,4,2,3,6]=>[1,3,2,6,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,4,2,6,3]=>[4,6,5,2,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,4,3,2,6]=>[2,4,3,1,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,4,3,6,2]=>[2,4,3,1,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,3,4,6,2,3]=>[1,3,2,3,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,4,6,3,2]=>[2,4,3,4,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,6,2,3,4]=>[1,3,4,4,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,6,2,4,3]=>[6,1,2,2,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,3,6,3,2,4]=>[6,1,2,3,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,6,3,4,2]=>[1,3,4,5,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,6,4,2,3]=>[3,5,6,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,6,4,3,2]=>[3,5,6,1,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,2,3,3,6]=>[1,4,6,2,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,4,2,3,6,3]=>[5,1,3,6,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,2,6,3,3]=>[5,1,3,2,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,3,2,3,6]=>[2,5,1,1,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,3,2,6,3]=>[5,1,4,4,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,3,3,2,6]=>[2,5,1,2,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,3,3,6,2]=>[5,1,4,5,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,3,6,2,3]=>[5,1,4,1,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,4,3,6,3,2]=>[5,1,4,1,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,6,2,3,3]=>[1,4,3,4,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,6,3,2,3]=>[2,5,4,6,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,6,3,3,2]=>[2,5,4,6,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,2,3,3,4]=>[1,6,4,2,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,6,2,3,4,3]=>[3,1,6,4,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,2,4,3,3]=>[3,1,6,5,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,3,2,3,4]=>[4,2,1,3,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,3,2,4,3]=>[4,2,1,3,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,3,3,2,4]=>[4,2,1,4,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,3,3,4,2]=>[4,2,1,4,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,3,4,2,3]=>[4,2,1,5,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,3,4,3,2]=>[4,2,1,5,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,4,2,3,3]=>[3,1,1,1,4,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,6,4,3,2,3]=>[3,1,1,2,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,6,4,3,3,2]=>[3,1,1,2,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,3,4,6]=>[2,1,4,2,3,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,3,3,6,4]=>[3,2,5,3,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,3,4,3,6]=>[2,1,4,3,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,3,4,6,3]=>[2,1,4,3,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,3,6,3,4]=>[2,1,4,5,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,6,4,3]=>[3,2,5,6,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,4,3,3,6]=>[2,1,5,1,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,1,4,3,6,3]=>[5,4,1,4,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,1,4,6,3,3]=>[2,1,5,4,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,6,3,3,4]=>[4,3,2,1,4,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,6,3,4,3]=>[4,3,2,1,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,4,3,3]=>[3,2,1,1,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,1,3,4,6]=>[1,2,6,3,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,3,6,4]=>[3,4,1,5,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,4,3,6]=>[5,6,3,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,4,6,3]=>[1,2,6,4,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,6,3,4]=>[4,5,2,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,1,6,4,3]=>[3,4,1,1,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,3,1,4,6]=>[1,2,1,6,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,3,1,6,4]=>[3,4,3,1,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[2,3,3,4,1,6]=>[1,2,1,2,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,3,4,6,1]=>[1,2,1,2,3,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,3,6,1,4]=>[1,2,1,4,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,3,6,4,1]=>[1,2,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,3,4,1,3,6]=>[1,2,2,5,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,4,1,6,3]=>[4,5,5,1,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,3,4,3,1,6]=>[3,4,4,2,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,4,3,6,1]=>[2,3,3,1,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,4,6,1,3]=>[1,2,2,3,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,3,4,6,3,1]=>[1,2,2,3,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,6,1,3,4]=>[1,2,4,3,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,6,1,4,3]=>[2,3,5,4,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,6,3,1,4]=>[5,6,1,2,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,6,3,4,1]=>[1,2,4,5,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,6,4,1,3]=>[1,2,4,6,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,6,4,3,1]=>[3,4,6,1,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,1,3,3,6]=>[1,3,5,3,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,1,3,6,3]=>[6,1,3,1,2,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,4,1,6,3,3]=>[4,6,1,2,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,3,1,3,6]=>[6,1,5,4,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,3,1,6,3]=>[4,6,3,2,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,3,3,1,6]=>[3,5,2,3,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,3,3,6,1]=>[2,4,1,2,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,3,6,1,3]=>[6,1,5,2,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,4,3,6,3,1]=>[6,1,5,2,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,6,1,3,3]=>[1,3,3,3,3,1]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[2,4,6,3,1,3]=>[6,1,1,3,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,6,3,3,1]=>[1,3,3,5,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,6,1,3,3,4]=>[1,5,3,3,1,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,1,3,4,3]=>[2,6,4,4,3,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,6,1,4,3,3]=>[2,6,4,5,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,3,1,3,4]=>[4,1,1,2,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,3,1,4,3]=>[5,2,2,3,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,6,3,3,1,4]=>[5,2,2,5,3,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,3,3,4,1]=>[4,1,1,4,5,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,6,3,4,1,3]=>[4,1,1,5,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,6,3,4,3,1]=>[4,1,1,5,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,4,1,3,3]=>[4,1,2,1,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,4,3,1,3]=>[4,1,2,3,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,6,4,3,3,1]=>[4,1,2,3,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,3,4,6]=>[1,6,2,2,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,1,2,3,6,4]=>[3,1,4,4,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,2,4,3,6]=>[3,1,4,5,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,4,6,3]=>[1,6,2,3,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,2,6,3,4]=>[4,2,5,1,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,1,2,6,4,3]=>[4,2,5,1,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,3,2,4,6]=>[6,4,1,5,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,1,3,2,6,4]=>[4,2,6,3,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,3,4,2,6]=>[4,2,6,5,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,3,4,6,2]=>[1,6,3,2,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,3,6,2,4]=>[6,4,1,2,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,3,6,4,2]=>[3,1,5,6,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,4,2,3,6]=>[5,3,1,3,6,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,4,2,6,3]=>[5,3,1,3,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,1,4,3,2,6]=>[5,3,1,4,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,4,3,6,2]=>[5,3,1,4,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,1,4,6,2,3]=>[1,6,4,3,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,4,6,3,2]=>[6,4,2,1,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,6,2,3,4]=>[3,1,1,6,4,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,6,2,4,3]=>[3,1,1,6,5,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,6,3,2,4]=>[4,2,2,1,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,6,3,4,2]=>[4,2,2,1,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,6,4,2,3]=>[3,1,1,1,1,4]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[3,1,6,4,3,2]=>[3,1,1,1,2,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,1,3,4,6]=>[2,1,1,4,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,1,3,6,4]=>[3,2,2,5,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,1,4,3,6]=>[2,1,1,5,1,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[3,2,1,4,6,3]=>[2,1,1,5,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,1,6,3,4]=>[4,3,3,2,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,1,6,4,3]=>[3,2,2,1,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,3,1,4,6]=>[3,2,4,1,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,3,1,6,4]=>[3,2,4,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,3,4,1,6]=>[4,3,5,5,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,3,4,6,1]=>[2,1,3,3,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,6,1,4]=>[2,1,3,5,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,3,6,4,1]=>[5,4,6,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,4,1,3,6]=>[6,5,1,3,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,4,1,6,3]=>[4,3,6,1,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,4,3,1,6]=>[3,2,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,4,3,6,1]=>[2,1,4,1,5,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,4,6,1,3]=>[6,5,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[3,2,4,6,3,1]=>[6,5,1,1,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,6,1,3,4]=>[2,1,6,4,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,6,1,4,3]=>[2,1,6,4,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,6,3,1,4]=>[5,4,2,2,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,6,3,4,1]=>[4,3,1,1,5,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,2,6,4,1,3]=>[4,3,1,2,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,6,4,3,1]=>[4,3,1,2,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,3,1,2,4,6]=>[1,1,6,2,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,1,2,6,4]=>[4,4,2,5,1,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,3,1,4,2,6]=>[5,5,3,1,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,3,1,4,6,2]=>[1,1,6,4,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,1,6,2,4]=>[3,3,1,1,6,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,3,1,6,4,2]=>[3,3,1,1,1,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[3,3,2,1,4,6]=>[2,2,1,1,5,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,3,2,1,6,4]=>[3,3,2,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,2,4,1,6]=>[4,4,3,6,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,3,2,4,6,1]=>[2,2,1,4,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,3,2,6,1,4]=>[2,2,1,6,4,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,3,2,6,4,1]=>[4,4,3,1,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,4,1,2,6]=>[1,1,2,5,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[3,3,4,1,6,2]=>[1,1,2,5,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,4,2,1,6]=>[3,3,4,1,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,4,2,6,1]=>[1,1,2,6,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,3,4,6,1,2]=>[1,1,2,3,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,4,6,2,1]=>[2,2,3,4,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,6,1,2,4]=>[1,1,4,3,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,3,6,1,4,2]=>[1,1,4,3,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,6,2,1,4]=>[5,5,1,1,4,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,3,6,2,4,1]=>[1,1,4,4,3,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,3,6,4,1,2]=>[1,1,4,6,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,6,4,2,1]=>[3,3,6,1,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,4,1,2,3,6]=>[1,2,5,2,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,4,1,2,6,3]=>[4,5,1,5,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,4,1,3,2,6]=>[4,5,1,6,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,4,1,3,6,2]=>[1,2,5,3,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,1,6,2,3]=>[1,2,5,6,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,4,1,6,3,2]=>[4,5,1,2,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,2,1,3,6]=>[3,4,1,2,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,1,6,3]=>[4,5,2,3,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,4,2,3,1,6]=>[3,4,1,4,1,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[3,4,2,3,6,1]=>[1,2,6,2,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,2,6,1,3]=>[1,2,6,5,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,4,2,6,3,1]=>[4,5,2,1,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,3,1,2,6]=>[4,5,3,2,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,3,1,6,2]=>[3,4,2,1,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,3,2,1,6]=>[3,4,2,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[3,4,3,2,6,1]=>[2,3,1,1,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,4,3,6,1,2]=>[2,3,1,5,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,3,6,2,1]=>[2,3,1,5,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,4,6,1,2,3]=>[1,2,3,3,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[3,4,6,1,3,2]=>[2,3,4,4,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,4,6,2,1,3]=>[2,3,4,5,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,6,2,3,1]=>[1,2,3,4,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,6,3,1,2]=>[1,2,3,5,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,6,3,2,1]=>[2,3,4,6,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,6,1,2,3,4]=>[1,4,3,2,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[3,6,1,2,4,3]=>[2,5,4,3,4,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,1,3,2,4]=>[6,2,1,1,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,6,1,3,4,2]=>[1,4,3,3,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,6,1,4,2,3]=>[1,4,3,4,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,6,1,4,3,2]=>[2,5,4,5,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,6,2,1,3,4]=>[2,5,5,1,4,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,6,2,1,4,3]=>[5,1,1,4,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,6,2,3,1,4]=>[5,1,1,6,3,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,6,2,3,4,1]=>[1,4,4,2,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,6,2,4,1,3]=>[6,2,2,1,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,6,2,4,3,1]=>[6,2,2,1,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,3,1,2,4]=>[1,4,5,6,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,3,1,4,2]=>[5,1,2,3,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,6,3,2,1,4]=>[5,1,2,4,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,6,3,2,4,1]=>[6,2,3,5,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,6,3,4,1,2]=>[1,4,5,2,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,6,3,4,2,1]=>[5,1,2,6,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,4,1,2,3]=>[1,4,6,5,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,6,4,1,3,2]=>[6,2,4,3,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,4,2,1,3]=>[3,6,1,1,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,4,2,3,1]=>[3,6,1,1,4,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,6,4,3,1,2]=>[3,6,1,2,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,6,4,3,2,1]=>[3,6,1,2,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,2,3,3,6]=>[1,5,2,2,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,2,3,6,3]=>[1,5,2,2,4,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,2,6,3,3]=>[4,1,5,1,1,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,3,2,3,6]=>[2,6,4,1,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,2,6,3]=>[4,1,6,3,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,1,3,3,2,6]=>[4,1,6,4,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,1,3,3,6,2]=>[1,5,3,1,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,1,3,6,2,3]=>[1,5,3,4,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,1,3,6,3,2]=>[6,3,1,2,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,6,2,3,3]=>[1,5,6,4,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,6,3,2,3]=>[4,1,2,1,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,6,3,3,2]=>[4,1,2,1,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,3,3,6]=>[3,1,2,5,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,1,3,6,3]=>[6,4,5,1,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,6,3,3]=>[4,2,3,2,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,3,1,3,6]=>[3,1,4,1,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,3,1,6,3]=>[4,2,5,2,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,2,3,3,1,6]=>[3,1,4,3,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[4,2,3,3,6,1]=>[1,6,2,1,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,3,6,1,3]=>[1,6,2,4,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,3,6,3,1]=>[5,3,6,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,6,1,3,3]=>[1,6,5,3,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,6,3,1,3]=>[4,2,1,1,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,6,3,3,1]=>[4,2,1,1,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,3,1,2,3,6]=>[3,2,1,4,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,3,1,2,6,3]=>[4,3,2,5,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,1,3,2,6]=>[4,3,2,6,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,1,3,6,2]=>[6,5,4,1,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,1,6,2,3]=>[3,2,1,1,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,1,6,3,2]=>[4,3,2,2,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,2,1,3,6]=>[2,1,1,1,4,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,3,2,1,6,3]=>[4,3,3,3,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,3,2,3,1,6]=>[3,2,2,4,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,3,2,3,6,1]=>[2,1,1,3,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,2,6,1,3]=>[2,1,1,6,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,3,2,6,3,1]=>[4,3,3,1,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,3,3,1,2,6]=>[4,3,4,2,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,3,1,6,2]=>[3,2,3,1,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,3,2,1,6]=>[3,2,3,2,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[4,3,3,2,6,1]=>[2,1,2,1,6,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,3,6,1,2]=>[2,1,2,5,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,3,6,2,1]=>[2,1,2,5,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,3,6,1,2,3]=>[2,1,5,4,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,6,1,3,2]=>[2,1,5,4,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,3,6,2,1,3]=>[2,1,5,5,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,3,6,2,3,1]=>[5,4,1,1,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,3,6,3,1,2]=>[5,4,1,2,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,6,3,2,1]=>[2,1,5,6,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,6,1,2,3,3]=>[1,3,3,2,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,6,1,3,2,3]=>[2,4,4,4,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,6,1,3,3,2]=>[2,4,4,4,2,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,6,2,1,3,3]=>[2,4,5,1,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,6,2,3,1,3]=>[1,3,4,2,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,6,2,3,3,1]=>[1,3,4,2,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,6,3,1,2,3]=>[1,3,5,6,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,6,3,1,3,2]=>[6,1,3,4,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,6,3,2,1,3]=>[2,4,6,1,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,6,3,2,3,1]=>[4,6,1,3,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,3,3,1,2]=>[1,3,5,1,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,6,3,3,2,1]=>[2,4,6,2,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,1,2,3,3,4]=>[1,3,2,2,1,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[6,1,2,3,4,3]=>[2,4,3,3,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[6,1,2,4,3,3]=>[2,4,3,4,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,3,2,3,4]=>[2,4,4,1,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,3,2,4,3]=>[2,4,4,1,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[6,1,3,3,2,4]=>[2,4,4,2,1,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[6,1,3,3,4,2]=>[1,3,3,1,2,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,3,4,2,3]=>[1,3,3,2,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,3,4,3,2]=>[2,4,4,3,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,1,4,2,3,3]=>[1,3,4,6,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,4,3,2,3]=>[2,4,5,1,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,4,3,3,2]=>[2,4,5,1,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,1,3,3,4]=>[2,5,1,4,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,1,3,4,3]=>[2,5,1,4,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,2,1,4,3,3]=>[2,5,1,5,1,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,2,3,1,3,4]=>[1,4,2,6,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,2,3,1,4,3]=>[5,1,6,3,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,3,3,1,4]=>[1,4,2,1,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,2,3,3,4,1]=>[1,4,2,1,2,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,3,4,1,3]=>[1,4,2,2,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,3,4,3,1]=>[3,6,4,4,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,4,1,3,3]=>[1,4,3,5,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,2,4,3,1,3]=>[6,2,1,5,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,4,3,3,1]=>[3,6,5,2,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,2,3,4]=>[1,5,6,2,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,3,1,2,4,3]=>[4,1,2,5,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,1,3,2,4]=>[6,3,4,1,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,3,1,3,4,2]=>[4,1,2,6,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,3,1,4,2,3]=>[5,2,3,1,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,4,3,2]=>[5,2,3,1,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,2,1,3,4]=>[2,6,1,1,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,3,2,1,4,3]=>[2,6,1,1,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,3,2,3,1,4]=>[5,2,4,6,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,2,3,4,1]=>[4,1,3,5,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,3,2,4,1,3]=>[6,3,5,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,3,2,4,3,1]=>[4,1,3,6,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,3,3,1,2,4]=>[1,5,1,6,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,3,1,4,2]=>[5,2,5,3,1,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,3,3,2,1,4]=>[2,6,2,1,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,3,2,4,1]=>[4,1,4,3,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,3,3,4,1,2]=>[1,5,1,2,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,3,3,4,2,1]=>[4,1,4,5,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,3,4,1,2,3]=>[1,5,2,5,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[6,3,4,1,3,2]=>[4,1,5,1,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,3,4,2,1,3]=>[4,1,5,2,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,4,2,3,1]=>[4,1,5,2,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,3,4,3,1,2]=>[4,1,5,3,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,3,4,3,2,1]=>[2,6,3,1,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,4,1,2,3,3]=>[1,6,5,2,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,4,1,3,2,3]=>[4,2,1,6,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,1,3,3,2]=>[4,2,1,6,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,2,1,3,3]=>[3,1,1,2,5,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,4,2,3,1,3]=>[3,1,1,4,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[6,4,2,3,3,1]=>[3,1,1,4,3,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[6,4,3,1,2,3]=>[3,1,2,1,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,4,3,1,3,2]=>[3,1,2,1,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,4,3,2,1,3]=>[3,1,2,2,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,4,3,2,3,1]=>[3,1,2,2,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,3,3,1,2]=>[3,1,2,3,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,3,3,2,1]=>[3,1,2,3,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,3,5,5]=>[1,2,2,1,3,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,2,3,5,3,5]=>[1,2,2,3,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,3,5,5,3]=>[1,2,2,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,5,3,3,5]=>[1,2,4,6,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,2,5,3,5,3]=>[3,4,6,1,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,5,5,3,3]=>[1,2,4,1,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,2,3,5,5]=>[2,4,1,3,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,2,5,3,5]=>[6,1,5,2,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,2,5,5,3]=>[3,5,2,6,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,3,3,2,5,5]=>[2,4,2,1,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,3,3,5,2,5]=>[1,3,1,3,5,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,3,3,5,5,2]=>[1,3,1,3,1,5]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,3,5,2,3,5]=>[1,3,3,5,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,3,5,2,5,3]=>[6,1,1,3,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,5,3,2,5]=>[6,1,1,4,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,5,3,5,2]=>[6,1,1,4,1,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,3,5,5,2,3]=>[1,3,3,1,5,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,3,5,5,3,2]=>[3,5,5,3,1,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,5,2,3,3,5]=>[1,5,5,2,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,2,3,5,3]=>[4,1,1,5,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,2,5,3,3]=>[5,2,2,1,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,3,2,3,5]=>[4,1,2,3,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,3,2,5,3]=>[5,2,3,4,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,3,3,2,5]=>[5,2,3,5,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,3,3,5,2]=>[4,1,2,4,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,5,3,5,2,3]=>[4,1,2,6,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,3,5,3,2]=>[4,1,2,6,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,5,2,3,3]=>[1,5,1,5,2,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,5,5,3,2,3]=>[4,1,4,2,3,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,5,3,3,2]=>[4,1,4,2,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,1,3,3,5,5]=>[2,1,4,2,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,1,3,5,3,5]=>[6,5,1,1,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,1,3,5,5,3]=>[3,2,5,5,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,1,5,3,3,5]=>[4,3,1,2,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,5,3,5,3]=>[4,3,1,2,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,5,5,3,3]=>[4,3,1,4,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,1,3,5,5]=>[1,2,6,3,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,3,1,5,3,5]=>[4,5,2,1,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,5,5,3]=>[4,5,2,1,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,3,3,1,5,5]=>[1,2,1,6,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,3,3,5,1,5]=>[1,2,1,3,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,3,5,5,1]=>[1,2,1,3,1,4]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,5,1,3,5]=>[1,2,3,4,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,3,5,1,5,3]=>[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,3,1,5]=>[4,5,6,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,5,3,5,1]=>[1,2,3,6,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,5,5,1,3]=>[1,2,3,1,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,5,5,3,1]=>[3,4,5,3,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,1,3,3,5]=>[1,4,4,3,1,3]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[2,5,1,3,5,3]=>[6,2,2,1,1,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,5,1,5,3,3]=>[5,1,1,2,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,5,3,1,3,5]=>[6,2,4,4,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,5,3,1,5,3]=>[5,1,3,3,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,5,3,3,1,5]=>[5,1,3,5,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,5,3,3,5,1]=>[1,4,6,1,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,3,5,1,3]=>[6,2,4,1,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,5,3,5,3,1]=>[3,6,1,5,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,5,5,1,3,3]=>[1,4,1,4,3,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,5,5,3,1,3]=>[3,6,3,1,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,5,5,3,3,1]=>[3,6,3,1,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,1,2,3,5,5]=>[1,6,2,2,3,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,2,5,3,5]=>[3,1,4,6,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,2,5,5,3]=>[3,1,4,6,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,3,2,5,5]=>[3,1,5,2,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,1,3,5,2,5]=>[6,4,1,1,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,3,5,5,2]=>[1,6,3,3,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,5,2,3,5]=>[4,2,1,1,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,5,3]=>[5,3,2,2,1,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,1,5,3,2,5]=>[5,3,2,3,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,5,3,5,2]=>[4,2,1,2,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,5,5,2,3]=>[4,2,1,4,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,1,5,5,3,2]=>[4,2,1,4,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,3,5,5]=>[2,1,1,4,4,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[3,2,1,5,3,5]=>[4,3,3,1,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,1,5,5,3]=>[4,3,3,1,4,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,1,5,5]=>[4,3,5,2,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,3,5,1,5]=>[2,1,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,3,5,5,1]=>[2,1,3,4,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,5,1,3,5]=>[6,5,2,2,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,2,5,1,5,3]=>[5,4,1,1,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,5,3,1,5]=>[5,4,1,3,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,5,3,5,1]=>[6,5,2,4,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,5,5,1,3]=>[2,1,5,2,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,2,5,5,3,1]=>[3,2,6,3,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,3,1,2,5,5]=>[1,1,6,2,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,3,1,5,2,5]=>[5,5,3,2,2,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,3,1,5,5,2]=>[4,4,2,1,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[3,3,2,1,5,5]=>[2,2,1,1,6,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,3,2,5,1,5]=>[5,5,4,1,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,3,2,5,5,1]=>[2,2,1,5,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[3,3,5,1,2,5]=>[1,1,3,4,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,5,1,5,2]=>[1,1,3,4,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,3,5,2,1,5]=>[4,4,6,1,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,5,2,5,1]=>[1,1,3,5,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,3,5,5,1,2]=>[1,1,3,1,4,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,3,5,5,2,1]=>[2,2,4,2,6,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,5,1,2,3,5]=>[1,3,4,2,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,5,1,2,5,3]=>[1,3,4,2,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,1,3,2,5]=>[6,1,2,1,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,5,1,3,5,2]=>[6,1,2,1,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,5,1,5,2,3]=>[1,3,4,5,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,5,1,5,3,2]=>[6,1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,1,3,5]=>[6,1,3,5,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,5,2,1,5,3]=>[4,6,1,3,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,2,3,1,5]=>[4,6,1,5,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,5,2,3,5,1]=>[1,3,5,2,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,2,5,1,3]=>[6,1,3,2,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,5,2,5,3,1]=>[6,1,3,2,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,3,1,2,5]=>[3,5,1,1,4,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,3,1,5,2]=>[4,6,2,2,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,5,3,2,1,5]=>[4,6,2,3,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,3,2,5,1]=>[6,1,4,5,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,3,5,1,2]=>[1,3,6,3,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,3,5,2,1]=>[6,1,4,1,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,5,1,2,3]=>[1,3,1,4,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,5,5,1,3,2]=>[2,4,2,5,4,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,5,5,2,1,3]=>[2,4,2,6,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,5,5,2,3,1]=>[1,3,1,5,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,5,3,1,2]=>[3,5,3,1,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,5,5,3,2,1]=>[3,5,3,1,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,1,2,3,3,5]=>[1,4,2,2,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,1,2,3,5,3]=>[1,4,2,2,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,2,5,3,3]=>[1,4,2,4,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,3,2,3,5]=>[2,5,4,1,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,3,2,5,3]=>[6,2,1,5,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,3,3,2,5]=>[2,5,4,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,3,3,5,2]=>[1,4,3,1,3,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,1,3,5,2,3]=>[1,4,3,3,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,3,5,3,2]=>[6,2,1,1,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,5,2,3,3]=>[1,4,5,5,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,5,3,2,3]=>[5,1,2,3,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,5,3,3,2]=>[5,1,2,3,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,3,3,5]=>[2,6,1,4,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,2,1,3,5,3]=>[6,3,5,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,1,5,3,3]=>[4,1,3,1,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,2,3,1,3,5]=>[1,5,2,6,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,3,1,5,3]=>[4,1,5,2,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,3,3,1,5]=>[4,1,5,4,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,2,3,3,5,1]=>[1,5,2,1,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,3,5,1,3]=>[1,5,2,3,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,2,3,5,3,1]=>[4,1,5,6,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,5,1,3,3]=>[1,5,4,4,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,2,5,3,1,3]=>[6,3,2,4,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,5,3,3,1]=>[5,2,1,3,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,3,1,2,3,5]=>[3,1,1,4,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,3,1,2,5,3]=>[3,1,1,4,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,1,3,2,5]=>[3,1,1,5,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,3,1,3,5,2]=>[6,4,4,1,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,3,1,5,2,3]=>[4,2,2,1,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,3,1,5,3,2]=>[4,2,2,1,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,3,2,1,3,5]=>[3,1,2,2,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,3,2,1,5,3]=>[4,2,3,3,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,3,2,3,1,5]=>[4,2,3,5,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,3,2,3,5,1]=>[3,1,2,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,2,5,1,3]=>[6,4,5,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,2,5,3,1]=>[3,1,2,6,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,3,3,1,2,5]=>[3,1,3,1,4,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,3,1,5,2]=>[4,2,4,2,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[5,3,3,2,1,5]=>[4,2,4,3,3,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,3,3,2,5,1]=>[5,3,5,4,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,3,5,1,2]=>[1,6,1,3,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,3,5,2,1]=>[4,2,4,6,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,5,1,2,3]=>[1,6,3,4,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,5,1,3,2]=>[6,4,1,2,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,3,5,2,1,3]=>[6,4,1,3,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,3,5,2,3,1]=>[4,2,6,1,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,5,3,1,2]=>[3,1,5,1,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,3,5,3,2,1]=>[3,1,5,1,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,5,1,2,3,3]=>[1,1,4,2,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[5,5,1,3,2,3]=>[2,2,5,4,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,5,1,3,3,2]=>[2,2,5,4,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,5,2,1,3,3]=>[2,2,6,1,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,5,2,3,1,3]=>[1,1,5,2,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,5,2,3,3,1]=>[1,1,5,2,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,5,3,1,2,3]=>[3,3,1,1,4,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[5,5,3,1,3,2]=>[3,3,1,1,5,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,5,3,2,1,3]=>[3,3,1,2,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,5,3,2,3,1]=>[3,3,1,2,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,5,3,3,1,2]=>[3,3,1,3,1,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,5,3,3,2,1]=>[3,3,1,3,2,2]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,2,3,3,5,6]=>[1,2,2,1,3,2]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,3,6,5]=>[2,3,3,2,5,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,3,5,3,6]=>[1,2,2,3,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,3,5,6,3]=>[1,2,2,3,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,3,6,3,5]=>[1,2,2,4,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,3,6,5,3]=>[3,4,4,6,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,3,3,6]=>[1,2,4,6,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,2,5,3,6,3]=>[5,6,1,3,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,2,5,6,3,3]=>[1,2,4,2,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,2,6,3,3,5]=>[1,2,5,5,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,6,3,5,3]=>[4,5,1,1,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,2,6,5,3,3]=>[4,5,1,3,2,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,3,5,6]=>[2,4,1,3,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,2,3,6,5]=>[2,4,1,3,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,5,3,6]=>[6,1,5,2,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,2,5,6,3]=>[2,4,1,5,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,6,3,5]=>[6,1,5,3,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,3,2,6,5,3]=>[4,6,3,1,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,3,3,2,5,6]=>[2,4,2,1,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,3,2,6,5]=>[2,4,2,1,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,3,5,2,6]=>[1,3,1,3,5,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,3,3,5,6,2]=>[1,3,1,3,2,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,3,6,2,5]=>[1,3,1,4,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,3,3,6,5,2]=>[2,4,2,5,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,5,2,3,6]=>[1,3,3,5,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,3,5,2,6,3]=>[6,1,1,3,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,3,5,3,2,6]=>[6,1,1,4,5,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,5,3,6,2]=>[6,1,1,4,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,3,5,6,2,3]=>[1,3,3,2,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,3,5,6,3,2]=>[2,4,4,3,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,6,2,3,5]=>[1,3,4,4,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,6,2,5,3]=>[6,1,2,2,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,3,6,3,2,5]=>[6,1,2,3,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,3,6,3,5,2]=>[6,1,2,3,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,6,5,2,3]=>[2,4,5,1,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,6,5,3,2]=>[3,5,6,2,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,2,3,3,6]=>[1,5,5,2,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,2,3,6,3]=>[5,2,2,6,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,5,2,6,3,3]=>[4,1,1,1,1,4]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,5,3,2,3,6]=>[5,2,3,4,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,3,2,6,3]=>[4,1,2,3,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,5,3,3,2,6]=>[4,1,2,4,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,5,3,3,6,2]=>[5,2,3,5,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,5,3,6,2,3]=>[5,2,3,1,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,5,3,6,3,2]=>[5,2,3,1,2,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,5,6,2,3,3]=>[1,5,2,4,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,6,3,2,3]=>[4,1,5,1,3,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,5,6,3,3,2]=>[4,1,5,1,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,6,2,3,3,5]=>[1,6,4,2,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,6,2,3,5,3]=>[3,1,6,4,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,5,3,3]=>[5,3,1,1,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,6,3,2,3,5]=>[4,2,1,3,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,3,2,5,3]=>[5,3,2,4,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,3,3,2,5]=>[5,3,2,5,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,3,3,5,2]=>[4,2,1,4,6,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,6,3,5,2,3]=>[4,2,1,6,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,3,5,3,2]=>[4,2,1,6,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,5,2,3,3]=>[4,2,3,1,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,5,3,2,3]=>[3,1,2,1,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,6,5,3,3,2]=>[3,1,2,1,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,3,5,6]=>[2,1,4,2,4,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,3,3,6,5]=>[2,1,4,2,5,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,3,5,3,6]=>[6,5,1,1,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,1,3,5,6,3]=>[2,1,4,4,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,3,6,3,5]=>[6,5,1,2,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,3,6,5,3]=>[3,2,5,6,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,3,3,6]=>[5,4,2,3,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,5,3,6,3]=>[5,4,2,3,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,1,5,6,3,3]=>[4,3,1,5,1,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,6,3,3,5]=>[4,3,2,1,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,6,3,5,3]=>[4,3,2,1,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,1,6,5,3,3]=>[3,2,1,2,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,1,3,5,6]=>[1,2,6,3,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,3,1,3,6,5]=>[3,4,1,5,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,5,3,6]=>[5,6,3,2,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,3,1,5,6,3]=>[4,5,2,1,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,3,1,6,3,5]=>[4,5,2,2,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,3,1,6,5,3]=>[3,4,1,1,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,3,3,1,5,6]=>[1,2,1,6,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,3,1,6,5]=>[3,4,3,1,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,3,3,5,1,6]=>[1,2,1,3,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,3,5,6,1]=>[1,2,1,3,2,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,3,6,1,5]=>[1,2,1,4,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,3,3,6,5,1]=>[2,3,2,5,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,3,5,1,3,6]=>[1,2,3,4,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,5,1,6,3]=>[1,2,3,4,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,3,1,6]=>[3,4,5,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,3,5,3,6,1]=>[1,2,3,6,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,3,5,6,1,3]=>[1,2,3,2,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,3,5,6,3,1]=>[1,2,3,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,6,1,3,5]=>[1,2,4,3,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,3,6,1,5,3]=>[1,2,4,3,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,6,3,1,5]=>[5,6,1,2,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,6,3,5,1]=>[1,2,4,5,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,6,5,1,3]=>[2,3,5,1,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,6,5,3,1]=>[3,4,6,2,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,5,1,3,3,6]=>[1,4,4,3,1,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[2,5,1,3,6,3]=>[6,2,2,1,2,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,5,1,6,3,3]=>[5,1,1,3,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,5,3,1,3,6]=>[6,2,4,4,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,5,3,1,6,3]=>[5,1,3,3,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,5,3,3,1,6]=>[3,6,1,3,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[2,5,3,3,6,1]=>[1,4,6,1,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[2,5,3,6,1,3]=>[6,2,4,2,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,5,3,6,3,1]=>[5,1,3,1,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,6,1,3,3]=>[1,4,2,3,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,5,6,3,1,3]=>[1,4,2,5,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,6,3,3,1]=>[1,4,2,5,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,1,3,3,5]=>[1,5,3,3,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,6,1,3,5,3]=>[6,3,1,1,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,1,5,3,3]=>[4,1,6,1,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,3,1,3,5]=>[6,3,3,4,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,6,3,1,5,3]=>[4,1,1,2,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,6,3,3,1,5]=>[4,1,1,4,2,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[2,6,3,3,5,1]=>[1,5,5,1,3,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,6,3,5,1,3]=>[6,3,3,1,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,6,3,5,3,1]=>[4,1,1,6,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,6,5,1,3,3]=>[2,6,1,5,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,5,3,1,3]=>[4,1,3,2,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,6,5,3,3,1]=>[4,1,3,2,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,3,5,6]=>[1,6,2,2,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,1,2,3,6,5]=>[3,1,4,4,6,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,2,5,3,6]=>[5,3,6,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,2,5,6,3]=>[1,6,2,4,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,2,6,3,5]=>[4,2,5,1,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,2,6,5,3]=>[4,2,5,1,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,3,2,5,6]=>[3,1,5,2,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,3,2,6,5]=>[4,2,6,3,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,3,5,2,6]=>[6,4,1,1,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,3,5,6,2]=>[1,6,3,3,2,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,3,6,2,5]=>[6,4,1,2,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,3,6,5,2]=>[6,4,1,2,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,2,3,6]=>[5,3,2,2,6,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,5,2,6,3]=>[4,2,1,1,1,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[3,1,5,3,2,6]=>[4,2,1,2,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,1,5,3,6,2]=>[5,3,2,3,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,1,5,6,2,3]=>[1,6,5,2,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,1,5,6,3,2]=>[4,2,1,5,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,6,2,3,5]=>[3,1,1,6,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,6,2,5,3]=>[5,3,3,1,1,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[3,1,6,3,2,5]=>[5,3,3,2,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,6,3,5,2]=>[4,2,2,1,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,6,5,2,3]=>[4,2,2,3,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,6,5,3,2]=>[3,1,1,2,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,1,3,5,6]=>[2,1,1,4,4,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,2,1,3,6,5]=>[2,1,1,4,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,1,5,3,6]=>[5,4,4,2,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,1,5,6,3]=>[4,3,3,1,5,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,2,1,6,3,5]=>[4,3,3,2,1,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,1,6,5,3]=>[3,2,2,1,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[3,2,3,1,5,6]=>[4,3,5,2,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,3,1,6,5]=>[3,2,4,1,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,3,5,1,6]=>[3,2,4,5,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,3,5,6,1]=>[2,1,3,4,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,3,6,1,5]=>[2,1,3,5,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,3,6,5,1]=>[2,1,3,5,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,5,1,3,6]=>[6,5,2,2,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,2,5,1,6,3]=>[5,4,1,1,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,2,5,3,1,6]=>[3,2,6,1,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,2,5,3,6,1]=>[6,5,2,4,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,5,6,1,3]=>[2,1,5,3,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,5,6,3,1]=>[5,4,1,6,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,1,3,5]=>[6,5,3,1,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,2,6,1,5,3]=>[4,3,1,6,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,6,3,1,5]=>[4,3,1,1,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,6,3,5,1]=>[6,5,3,3,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,2,6,5,1,3]=>[2,1,6,1,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,2,6,5,3,1]=>[4,3,1,3,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,3,1,2,5,6]=>[1,1,6,2,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,3,1,2,6,5]=>[4,4,2,5,1,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,3,1,5,2,6]=>[4,4,2,1,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[3,3,1,5,6,2]=>[1,1,6,5,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,3,1,6,2,5]=>[5,5,3,3,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,3,1,6,5,2]=>[4,4,2,2,3,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,3,2,1,5,6]=>[2,2,1,1,6,3]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,3,2,1,6,5]=>[3,3,2,2,1,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[3,3,2,5,1,6]=>[5,5,4,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,3,2,5,6,1]=>[2,2,1,5,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,2,6,1,5]=>[4,4,3,1,6,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,2,6,5,1]=>[2,2,1,6,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,3,5,1,2,6]=>[1,1,3,4,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,3,5,1,6,2]=>[1,1,3,4,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,3,5,2,1,6]=>[4,4,6,1,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,3,5,2,6,1]=>[1,1,3,5,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,3,5,6,1,2]=>[1,1,3,2,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,3,5,6,2,1]=>[2,2,4,3,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,3,6,1,2,5]=>[1,1,4,3,2,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,3,6,1,5,2]=>[1,1,4,3,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,3,6,2,1,5]=>[5,5,1,1,4,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,3,6,2,5,1]=>[5,5,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[3,3,6,5,1,2]=>[2,2,5,1,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,3,6,5,2,1]=>[2,2,5,1,6,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,5,1,2,3,6]=>[1,3,4,2,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,5,1,2,6,3]=>[1,3,4,2,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,5,1,3,2,6]=>[6,1,2,1,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,1,3,6,2]=>[6,1,2,1,2,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,1,6,2,3]=>[1,3,4,6,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,1,6,3,2]=>[6,1,2,4,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,1,3,6]=>[6,1,3,5,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,2,1,6,3]=>[4,6,1,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,2,3,1,6]=>[4,6,1,5,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,2,3,6,1]=>[1,3,5,2,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,2,6,1,3]=>[6,1,3,3,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[3,5,2,6,3,1]=>[4,6,1,1,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,5,3,1,2,6]=>[4,6,2,2,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,3,1,6,2]=>[3,5,1,1,1,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,5,3,2,1,6]=>[3,5,1,2,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,5,3,2,6,1]=>[6,1,4,5,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,3,6,1,2]=>[1,3,6,4,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,3,6,2,1]=>[6,1,4,2,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,6,1,2,3]=>[1,3,2,3,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[3,5,6,1,3,2]=>[2,4,3,4,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,5,6,2,1,3]=>[2,4,3,5,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,6,2,3,1]=>[1,3,2,4,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,6,3,1,2]=>[1,3,2,5,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,5,6,3,2,1]=>[2,4,3,6,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,6,1,2,3,5]=>[1,4,3,2,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,6,1,2,5,3]=>[1,4,3,2,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,6,1,3,2,5]=>[6,2,1,1,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,6,1,3,5,2]=>[6,2,1,1,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,6,1,5,2,3]=>[1,4,3,5,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,6,1,5,3,2]=>[6,2,1,3,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,2,1,3,5]=>[6,2,2,5,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,6,2,1,5,3]=>[5,1,1,4,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,6,2,3,1,5]=>[5,1,1,6,3,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,2,3,5,1]=>[1,4,4,2,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,6,2,5,1,3]=>[6,2,2,2,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[3,6,2,5,3,1]=>[5,1,1,1,3,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,6,3,1,2,5]=>[5,1,2,3,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,3,1,5,2]=>[5,1,2,3,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,6,3,2,1,5]=>[5,1,2,4,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,6,3,2,5,1]=>[5,1,2,4,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,6,3,5,1,2]=>[1,4,5,3,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,3,5,2,1]=>[6,2,3,1,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,6,5,1,2,3]=>[2,5,1,5,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,6,5,1,3,2]=>[2,5,1,5,4,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,6,5,2,1,3]=>[2,5,1,6,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,5,2,3,1]=>[5,1,4,2,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,5,3,1,2]=>[3,6,2,1,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,6,5,3,2,1]=>[3,6,2,1,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,1,2,3,3,6]=>[1,4,2,2,1,4]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[5,1,2,3,6,3]=>[1,4,2,2,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,2,6,3,3]=>[1,4,2,5,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,3,2,3,6]=>[2,5,4,1,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,3,2,6,3]=>[6,2,1,5,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,3,3,2,6]=>[2,5,4,2,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,3,3,6,2]=>[1,4,3,1,4,4]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[5,1,3,6,2,3]=>[1,4,3,4,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,1,3,6,3,2]=>[6,2,1,2,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,6,2,3,3]=>[1,4,6,4,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,6,3,2,3]=>[5,1,3,2,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,6,3,3,2]=>[5,1,3,2,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,2,1,3,3,6]=>[2,6,1,4,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,1,3,6,3]=>[6,3,5,1,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,1,6,3,3]=>[4,1,3,2,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,2,3,1,3,6]=>[1,5,2,6,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,3,1,6,3]=>[4,1,5,2,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,2,3,3,1,6]=>[4,1,5,4,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,2,3,3,6,1]=>[1,5,2,1,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,3,6,1,3]=>[1,5,2,4,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,2,3,6,3,1]=>[5,2,6,1,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,6,1,3,3]=>[1,5,5,3,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,6,3,1,3]=>[4,1,1,1,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,2,6,3,3,1]=>[4,1,1,1,4,2]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[5,3,1,2,3,6]=>[3,1,1,4,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[5,3,1,2,6,3]=>[4,2,2,5,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[5,3,1,3,2,6]=>[4,2,2,6,3,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,1,3,6,2]=>[6,4,4,1,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,3,1,6,2,3]=>[3,1,1,1,6,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,3,1,6,3,2]=>[4,2,2,2,1,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,3,2,1,3,6]=>[3,1,2,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,3,2,1,6,3]=>[4,2,3,3,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,3,2,3,1,6]=>[3,1,2,4,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,3,2,3,6,1]=>[3,1,2,4,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,2,6,1,3]=>[6,4,5,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,3,2,6,3,1]=>[4,2,3,1,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,3,3,1,2,6]=>[4,2,4,2,5,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,3,3,1,6,2]=>[3,1,3,1,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,3,2,1,6]=>[3,1,3,2,2,1]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[5,3,3,2,6,1]=>[4,2,4,3,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,3,6,1,2]=>[1,6,1,4,3,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,3,6,2,1]=>[5,3,5,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,6,1,2,3]=>[1,6,4,3,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,6,1,3,2]=>[6,4,2,1,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,3,6,2,1,3]=>[6,4,2,2,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,6,2,3,1]=>[5,3,1,1,6,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,3,6,3,1,2]=>[5,3,1,2,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,6,3,2,1]=>[5,3,1,2,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,6,1,2,3,3]=>[1,2,3,2,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[5,6,1,3,2,3]=>[2,3,4,4,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,6,1,3,3,2]=>[2,3,4,4,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[5,6,2,1,3,3]=>[2,3,5,1,4,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,6,2,3,1,3]=>[1,2,4,2,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,6,2,3,3,1]=>[1,2,4,2,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,6,3,1,2,3]=>[1,2,5,6,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,6,3,1,3,2]=>[4,5,1,2,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,3,2,1,3]=>[2,3,6,1,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,6,3,2,3,1]=>[4,5,1,3,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,6,3,3,1,2]=>[1,2,5,1,6,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,6,3,3,2,1]=>[2,3,6,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,1,2,3,3,5]=>[1,3,2,2,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[6,1,2,3,5,3]=>[1,3,2,2,3,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,2,5,3,3]=>[1,3,2,4,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,3,2,3,5]=>[2,4,4,1,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,1,3,2,5,3]=>[6,1,1,5,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,1,3,3,2,5]=>[2,4,4,2,1,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,1,3,3,5,2]=>[1,3,3,1,3,5]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[6,1,3,5,2,3]=>[1,3,3,3,5,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[6,1,3,5,3,2]=>[6,1,1,1,4,5]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,1,5,2,3,3]=>[1,3,5,5,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,1,5,3,2,3]=>[4,6,1,2,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,5,3,3,2]=>[4,6,1,2,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,2,1,3,3,5]=>[2,5,1,4,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,2,1,3,5,3]=>[6,2,5,1,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,1,5,3,3]=>[5,1,4,2,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,2,3,1,3,5]=>[1,4,2,6,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,2,3,1,5,3]=>[5,1,6,3,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,2,3,3,1,5]=>[1,4,2,1,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,2,3,3,5,1]=>[1,4,2,1,3,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,2,3,5,1,3]=>[1,4,2,3,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,2,3,5,3,1]=>[3,6,4,5,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,5,1,3,3]=>[1,4,4,4,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[6,2,5,3,1,3]=>[6,2,2,4,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,2,5,3,3,1]=>[5,1,1,3,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[6,3,1,2,3,5]=>[1,5,6,2,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,1,2,5,3]=>[5,2,3,6,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,3,2,5]=>[6,3,4,1,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,1,3,5,2]=>[6,3,4,1,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,3,1,5,2,3]=>[4,1,2,1,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,3,1,5,3,2]=>[4,1,2,1,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,3,2,1,3,5]=>[2,6,1,1,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,3,2,1,5,3]=>[4,1,3,3,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,3,2,3,1,5]=>[4,1,3,5,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,3,2,3,5,1]=>[2,6,1,3,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,2,5,1,3]=>[6,3,5,2,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,2,5,3,1]=>[5,2,4,1,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,3,3,1,2,5]=>[1,5,1,6,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,3,1,5,2]=>[4,1,4,2,1,1]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[6,3,3,2,1,5]=>[4,1,4,3,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[6,3,3,2,5,1]=>[5,2,5,4,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,3,3,5,1,2]=>[1,5,1,3,4,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,3,3,5,2,1]=>[4,1,4,6,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,3,5,1,2,3]=>[1,5,3,4,2,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,3,5,1,3,2]=>[6,3,1,2,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,5,2,1,3]=>[6,3,1,3,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,3,5,2,3,1]=>[4,1,6,1,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,5,3,1,2]=>[4,1,6,2,2,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,3,5,3,2,1]=>[4,1,6,2,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,1,2,3,3]=>[2,1,5,3,3,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,5,1,3,2,3]=>[2,1,5,4,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,5,1,3,3,2]=>[2,1,5,4,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,5,2,1,3,3]=>[2,1,6,1,4,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[6,5,2,3,1,3]=>[4,3,1,5,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,2,3,3,1]=>[4,3,1,5,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,5,3,1,2,3]=>[3,2,1,1,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[6,5,3,1,3,2]=>[3,2,1,1,5,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[6,5,3,2,1,3]=>[3,2,1,2,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,5,3,2,3,1]=>[3,2,1,2,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,5,3,3,1,2]=>[3,2,1,3,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,5,3,3,2,1]=>[3,2,1,3,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,4,4,4]=>[1,2,2,2,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,4,3,4,4]=>[2,3,4,1,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,4,3,4]=>[2,3,4,2,1,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,4,4,3]=>[2,3,4,2,2,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,2,4,4,4]=>[2,4,1,4,2,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,3,4,2,4,4]=>[1,3,2,6,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,4,4,2,4]=>[1,3,2,1,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,3,4,4,4,2]=>[1,3,2,1,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,4,2,3,4,4]=>[1,4,6,2,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,4,2,4,3,4]=>[3,6,1,5,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,4,4,3]=>[3,6,1,5,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,2,4,4]=>[2,5,1,1,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,3,4,2,4]=>[3,6,2,4,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,4,4,2]=>[3,6,2,4,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,4,2,3,4]=>[1,4,1,6,2,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,4,4,2,4,3]=>[3,6,3,1,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,4,3,2,4]=>[2,5,2,1,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,4,3,4,2]=>[3,6,3,2,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,4,4,2,3]=>[1,4,1,1,6,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,4,4,4,3,2]=>[2,5,2,2,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,1,3,4,4,4]=>[2,1,4,3,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[2,1,4,3,4,4]=>[2,1,5,1,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,4,4,3,4]=>[2,1,5,2,1,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,4,4,4,3]=>[2,1,5,2,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[2,3,1,4,4,4]=>[1,2,6,4,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,3,4,1,4,4]=>[1,2,2,5,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,3,4,4,1,4]=>[1,2,2,1,5,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,3,4,4,4,1]=>[1,2,2,1,1,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[2,4,1,3,4,4]=>[1,3,5,3,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,1,4,3,4]=>[2,4,6,5,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,4,4,3]=>[2,4,6,5,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,4,3,1,4,4]=>[3,5,2,1,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,3,4,1,4]=>[2,4,1,3,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,4,4,1]=>[2,4,1,3,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,4,1,3,4]=>[1,3,1,5,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,4,1,4,3]=>[2,4,2,6,5,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,4,4,3,1,4]=>[3,5,3,2,1,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,4,4,3,4,1]=>[2,4,2,1,3,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,4,4,1,3]=>[1,3,1,1,5,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[2,4,4,4,3,1]=>[3,5,3,3,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,2,4,4,4]=>[1,6,2,3,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,1,4,2,4,4]=>[3,1,6,1,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,4,4,2,4]=>[3,1,6,3,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,4,4,4,2]=>[3,1,6,3,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,2,1,4,4,4]=>[2,1,1,5,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[3,2,4,1,4,4]=>[2,1,4,6,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,4,4,1,4]=>[2,1,4,2,6,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,4,4,4,1]=>[2,1,4,2,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,4,1,2,4,4]=>[1,2,5,2,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,4,1,4,2,4]=>[1,2,5,4,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,1,4,4,2]=>[1,2,5,4,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,2,1,4,4]=>[3,4,1,2,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,2,4,1,4]=>[1,2,6,3,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,4,4,1]=>[1,2,6,3,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,4,1,2,4]=>[1,2,1,5,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,4,4,1,4,2]=>[1,2,1,5,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,4,2,1,4]=>[3,4,3,1,2,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,4,2,4,1]=>[1,2,1,6,3,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,4,4,1,2]=>[1,2,1,1,5,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[3,4,4,4,2,1]=>[3,4,3,3,1,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,1,2,3,4,4]=>[1,5,2,2,2,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,1,2,4,3,4]=>[2,6,3,4,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,2,4,4,3]=>[2,6,3,4,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,1,3,2,4,4]=>[2,6,4,1,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,1,3,4,2,4]=>[1,5,3,2,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,3,4,4,2]=>[1,5,3,2,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,4,2,3,4]=>[1,5,4,6,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,4,2,4,3]=>[6,3,2,4,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,3,2,4]=>[2,6,5,1,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,4,3,4,2]=>[5,2,1,4,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,4,2,3]=>[1,5,4,1,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,4,4,3,2]=>[2,6,5,2,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,2,1,3,4,4]=>[3,1,2,5,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,4,3,4]=>[3,1,2,6,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,1,4,4,3]=>[3,1,2,6,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,2,3,1,4,4]=>[3,1,4,1,6,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,2,3,4,1,4]=>[1,6,2,2,5,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,2,3,4,4,1]=>[1,6,2,2,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,2,4,1,3,4]=>[1,6,3,5,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,4,1,4,3]=>[6,4,1,3,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,4,3,1,4]=>[3,1,5,2,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,4,3,4,1]=>[4,2,6,3,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,4,4,1,3]=>[1,6,3,1,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,2,4,4,3,1]=>[3,1,5,3,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,3,1,2,4,4]=>[3,2,1,4,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,4,2,4]=>[3,2,1,6,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,3,1,4,4,2]=>[3,2,1,6,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,2,1,4,4]=>[2,1,1,1,5,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,3,2,4,1,4]=>[2,1,1,4,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,2,4,4,1]=>[2,1,1,4,2,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,3,4,1,2,4]=>[2,1,3,6,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,4,1,4,2]=>[5,4,6,2,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,4,2,1,4]=>[3,2,4,1,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,3,4,2,4,1]=>[4,3,5,2,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,4,4,1,2]=>[2,1,3,2,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,3,4,4,2,1]=>[3,2,4,3,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,1,2,3,4]=>[1,1,5,2,2,2]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[4,4,1,2,4,3]=>[2,2,6,3,4,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,4,1,3,2,4]=>[2,2,6,4,1,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,4,1,3,4,2]=>[1,1,5,3,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,4,1,4,2,3]=>[1,1,5,4,6,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,4,1,4,3,2]=>[2,2,6,5,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,4,2,1,3,4]=>[3,3,1,2,5,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,4,2,1,4,3]=>[3,3,1,2,6,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,4,2,3,1,4]=>[3,3,1,4,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,4,2,3,4,1]=>[1,1,6,2,2,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,4,2,4,1,3]=>[1,1,6,3,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,4,2,4,3,1]=>[3,3,1,5,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,4,3,1,2,4]=>[3,3,2,1,4,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,4,3,1,4,2]=>[3,3,2,1,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,4,3,2,1,4]=>[2,2,1,1,1,5]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,4,3,2,4,1]=>[2,2,1,1,4,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,4,3,4,1,2]=>[2,2,1,3,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,4,3,4,2,1]=>[3,3,2,4,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,4,4,1,2,3]=>[1,1,1,5,2,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[4,4,4,1,3,2]=>[2,2,2,6,4,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,4,4,2,1,3]=>[3,3,3,1,2,5]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,4,4,2,3,1]=>[3,3,3,1,4,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,4,4,3,1,2]=>[3,3,3,2,1,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,4,4,3,2,1]=>[2,2,2,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,2,3,4,4,5]=>[1,2,2,2,1,2]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,3,4,5,4]=>[2,3,3,3,3,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,2,3,5,4,4]=>[2,3,3,4,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,3,4,5]=>[2,3,4,1,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,4,3,5,4]=>[2,3,4,1,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,2,4,4,3,5]=>[2,3,4,2,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,4,4,5,3]=>[1,2,3,1,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,4,5,3,4]=>[1,2,3,2,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,4,5,4,3]=>[2,3,4,3,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,2,5,3,4,4]=>[1,2,4,6,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,5,4,3,4]=>[2,3,5,1,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,5,4,4,3]=>[2,3,5,1,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,2,4,4,5]=>[2,4,1,4,2,3]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,2,4,5,4]=>[2,4,1,4,3,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,3,2,5,4,4]=>[2,4,1,5,1,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,4,2,4,5]=>[1,3,2,6,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,3,4,2,5,4]=>[3,5,4,1,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,4,2,5]=>[1,3,2,1,6,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,4,4,5,2]=>[1,3,2,1,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,4,5,2,4]=>[1,3,2,2,5,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,3,4,5,4,2]=>[3,5,4,4,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,5,2,4,4]=>[1,3,3,5,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,3,5,4,2,4]=>[6,1,1,5,4,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,5,4,4,2]=>[3,5,5,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,2,3,4,5]=>[1,4,6,2,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,4,2,3,5,4]=>[3,6,1,4,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,2,4,3,5]=>[6,2,4,1,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,4,2,4,5,3]=>[3,6,1,5,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,5,3,4]=>[5,1,3,1,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,2,5,4,3]=>[5,1,3,1,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,4,3,2,4,5]=>[2,5,1,1,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,4,3,2,5,4]=>[2,5,1,1,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,4,3,4,2,5]=>[5,1,4,6,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,3,4,5,2]=>[2,5,1,3,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,5,2,4]=>[6,2,5,1,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,3,5,4,2]=>[3,6,2,5,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,4,2,3,5]=>[1,4,1,6,2,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,4,2,5,3]=>[5,1,5,3,1,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,4,4,3,2,5]=>[2,5,2,1,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,4,3,5,2]=>[2,5,2,1,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,4,5,2,3]=>[1,4,1,2,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,4,5,3,2]=>[3,6,3,4,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,5,2,3,4]=>[1,4,2,5,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,4,5,2,4,3]=>[2,5,3,6,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,3,2,4]=>[3,6,4,1,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,3,4,2]=>[3,6,4,1,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,4,5,4,2,3]=>[3,6,4,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,4,5,4,3,2]=>[2,5,3,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,5,2,3,4,4]=>[1,5,5,2,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,2,4,3,4]=>[4,1,1,6,3,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,2,4,4,3]=>[4,1,1,6,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,3,2,4,4]=>[4,1,2,3,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,3,4,2,4]=>[4,1,2,5,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,5,3,4,4,2]=>[4,1,2,5,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,4,2,3,4]=>[4,1,3,2,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,5,4,2,4,3]=>[4,1,3,2,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,4,3,2,4]=>[2,6,1,1,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,5,4,3,4,2]=>[4,1,3,3,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,4,4,2,3]=>[4,1,3,4,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,4,4,3,2]=>[2,6,1,2,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,1,3,4,4,5]=>[2,1,4,3,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,3,4,5,4]=>[2,1,4,3,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,1,3,5,4,4]=>[2,1,4,4,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,4,5]=>[2,1,5,1,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,1,4,3,5,4]=>[2,1,5,1,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,4,4,3,5]=>[2,1,5,2,1,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,4,4,5,3]=>[3,2,6,3,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,4,5,3,4]=>[3,2,6,4,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,1,4,5,4,3]=>[2,1,5,3,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,1,5,3,4,4]=>[4,3,1,2,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,5,4,3,4]=>[2,1,6,1,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,1,5,4,4,3]=>[2,1,6,1,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,1,4,4,5]=>[1,2,6,4,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,1,4,5,4]=>[3,4,1,6,4,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,3,1,5,4,4]=>[4,5,2,1,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,4,1,4,5]=>[1,2,2,5,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,3,4,1,5,4]=>[4,5,5,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,3,4,4,1,5]=>[1,2,2,1,5,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,3,4,4,5,1]=>[1,2,2,1,2,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,3,4,5,1,4]=>[1,2,2,2,4,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[2,3,4,5,4,1]=>[2,3,3,3,1,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[2,3,5,1,4,4]=>[1,2,3,4,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,5,4,1,4]=>[2,3,4,1,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,4,4,1]=>[2,3,4,1,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,1,3,4,5]=>[1,3,5,3,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,4,1,3,5,4]=>[6,1,3,1,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,4,1,4,3,5]=>[6,1,3,2,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,1,4,5,3]=>[1,3,5,4,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,1,5,3,4]=>[4,6,1,1,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,1,5,4,3]=>[4,6,1,1,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,3,1,4,5]=>[3,5,2,1,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,1,5,4]=>[4,6,3,2,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,3,4,1,5]=>[4,6,3,5,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,3,4,5,1]=>[2,4,1,3,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,4,3,5,1,4]=>[6,1,5,1,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,4,3,5,4,1]=>[2,4,1,4,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,4,1,3,5]=>[1,3,1,5,3,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,4,4,1,5,3]=>[4,6,4,1,1,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,4,3,1,5]=>[4,6,4,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,4,3,5,1]=>[2,4,2,1,4,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,4,5,1,3]=>[1,3,1,2,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,4,4,5,3,1]=>[3,5,3,4,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,5,1,3,4]=>[1,3,2,4,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,4,5,1,4,3]=>[2,4,3,5,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,4,5,3,1,4]=>[3,5,4,1,1,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,4,5,3,4,1]=>[1,3,2,6,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,5,4,1,3]=>[2,4,3,1,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,5,4,3,1]=>[3,5,4,2,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,1,3,4,4]=>[1,4,4,3,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,1,4,3,4]=>[5,1,1,1,4,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,5,1,4,4,3]=>[5,1,1,1,5,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[2,5,3,1,4,4]=>[5,1,3,3,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,5,3,4,1,4]=>[5,1,3,6,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,3,4,4,1]=>[1,4,6,2,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,4,1,3,4]=>[2,5,1,6,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,1,4,3]=>[5,1,4,2,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,5,4,3,1,4]=>[5,1,4,4,3,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,5,4,3,4,1]=>[2,5,1,1,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,4,4,1,3]=>[2,5,1,2,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,4,4,3,1]=>[3,6,2,3,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,2,4,4,5]=>[1,6,2,3,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,2,4,5,4]=>[3,1,4,5,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,1,2,5,4,4]=>[3,1,4,6,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,4,2,4,5]=>[3,1,6,1,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,4,2,5,4]=>[5,3,1,3,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,4,4,2,5]=>[5,3,1,5,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,4,4,5,2]=>[1,6,4,1,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,4,5,2,4]=>[1,6,4,2,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,4,5,4,2]=>[3,1,6,4,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,1,5,2,4,4]=>[4,2,1,1,6,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,5,4,2,4]=>[4,2,1,3,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,5,4,4,2]=>[4,2,1,3,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,4,4,5]=>[2,1,1,5,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,4,5,4]=>[2,1,1,5,3,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[3,2,1,5,4,4]=>[2,1,1,6,1,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,2,4,1,4,5]=>[2,1,4,6,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,4,1,5,4]=>[4,3,6,1,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,2,4,4,1,5]=>[4,3,6,4,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,2,4,4,5,1]=>[2,1,4,2,3,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,4,5,1,4]=>[2,1,4,3,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,4,5,4,1]=>[2,1,4,3,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,2,5,1,4,4]=>[5,4,1,1,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,2,5,4,1,4]=>[5,4,1,4,2,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,5,4,4,1]=>[2,1,5,1,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,4,1,2,4,5]=>[1,2,5,2,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,4,1,2,5,4]=>[2,3,6,3,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,4,1,4,2,5]=>[5,6,2,1,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,1,4,5,2]=>[1,2,5,4,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,1,5,2,4]=>[4,5,1,1,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,4,1,5,4,2]=>[4,5,1,1,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,2,1,4,5]=>[3,4,1,2,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,4,2,1,5,4]=>[4,5,2,3,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,2,4,1,5]=>[4,5,2,6,1,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,2,4,5,1]=>[1,2,6,3,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,2,5,1,4]=>[5,6,3,1,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,4,2,5,4,1]=>[5,6,3,1,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,4,1,2,5]=>[1,2,1,5,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,4,1,5,2]=>[4,5,4,1,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,4,4,2,1,5]=>[4,5,4,2,3,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,4,2,5,1]=>[1,2,1,6,4,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,4,4,5,1,2]=>[1,2,1,2,4,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,4,4,5,2,1]=>[2,3,2,3,6,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,4,5,1,2,4]=>[1,2,2,4,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[3,4,5,1,4,2]=>[1,2,2,4,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,4,5,2,1,4]=>[2,3,3,6,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,4,5,2,4,1]=>[1,2,2,5,3,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,4,5,4,1,2]=>[2,3,3,1,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,5,4,2,1]=>[3,4,4,2,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,5,1,2,4,4]=>[1,3,4,2,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,5,1,4,2,4]=>[6,1,2,2,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,5,1,4,4,2]=>[1,3,4,4,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,2,1,4,4]=>[2,4,6,1,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,2,4,1,4]=>[6,1,3,1,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,5,2,4,4,1]=>[1,3,5,3,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,4,1,2,4]=>[2,4,1,6,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,5,4,1,4,2]=>[6,1,5,3,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,4,2,1,4]=>[3,5,2,1,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,5,4,2,4,1]=>[6,1,5,4,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,4,4,1,2]=>[2,4,1,2,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,4,4,2,1]=>[3,5,2,3,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,2,3,4,5]=>[1,5,2,2,2,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[4,1,2,3,5,4]=>[2,6,3,3,4,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,1,2,4,3,5]=>[2,6,3,4,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,2,4,5,3]=>[1,5,2,3,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,1,2,5,3,4]=>[1,5,2,4,6,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,2,5,4,3]=>[2,6,3,5,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,3,2,4,5]=>[2,6,4,1,4,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,3,2,5,4]=>[2,6,4,1,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,4,2,5]=>[1,5,3,2,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,4,5,2]=>[1,5,3,2,2,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,1,3,5,2,4]=>[6,3,1,1,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[4,1,3,5,4,2]=>[6,3,1,1,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,1,4,2,3,5]=>[1,5,4,6,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,4,2,5,3]=>[5,2,1,3,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,1,4,3,2,5]=>[5,2,1,4,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,1,4,3,5,2]=>[6,3,2,5,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,4,5,2,3]=>[1,5,4,2,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,4,5,3,2]=>[5,2,1,6,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,5,2,3,4]=>[4,1,1,1,5,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,5,2,4,3]=>[4,1,1,1,6,3]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,1,5,3,2,4]=>[4,1,1,2,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,5,3,4,2]=>[4,1,1,2,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,5,4,2,3]=>[4,1,1,3,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,5,4,3,2]=>[4,1,1,3,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[4,2,1,3,4,5]=>[3,1,2,5,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,2,1,3,5,4]=>[3,1,2,5,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,2,1,4,3,5]=>[3,1,2,6,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,2,1,4,5,3]=>[3,1,2,6,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,1,5,3,4]=>[4,2,3,1,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,5,4,3]=>[4,2,3,1,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[4,2,3,1,4,5]=>[3,1,4,1,6,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,3,1,5,4]=>[4,2,5,2,1,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,3,4,1,5]=>[4,2,5,5,1,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,2,3,4,5,1]=>[1,6,2,2,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,2,3,5,1,4]=>[1,6,2,3,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,3,5,4,1]=>[4,2,5,6,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,4,1,3,5]=>[6,4,1,3,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,2,4,1,5,3]=>[4,2,6,1,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,4,3,1,5]=>[4,2,6,3,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,4,3,5,1]=>[6,4,1,5,1,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,2,4,5,1,3]=>[1,6,3,2,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,4,5,3,1]=>[3,1,5,4,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,2,5,1,3,4]=>[1,6,4,4,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,5,1,4,3]=>[5,3,1,1,1,4]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,2,5,3,1,4]=>[5,3,1,3,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[4,2,5,3,4,1]=>[5,3,1,3,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,5,4,1,3]=>[6,4,2,5,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,5,4,3,1]=>[3,1,6,2,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,3,1,2,4,5]=>[3,2,1,4,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,1,2,5,4]=>[3,2,1,4,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,3,1,4,2,5]=>[5,4,3,1,3,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,3,1,4,5,2]=>[5,4,3,1,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,5,2,4]=>[4,3,2,1,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,1,5,4,2]=>[4,3,2,1,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,2,1,4,5]=>[2,1,1,1,5,3]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,3,2,1,5,4]=>[2,1,1,1,6,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[4,3,2,4,1,5]=>[4,3,3,6,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,3,2,4,5,1]=>[2,1,1,4,3,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,2,5,1,4]=>[5,4,4,1,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,3,2,5,4,1]=>[2,1,1,5,1,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,3,4,1,2,5]=>[2,1,3,6,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,3,4,1,5,2]=>[4,3,5,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,3,4,2,1,5]=>[4,3,5,2,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,4,2,5,1]=>[5,4,6,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,3,4,5,1,2]=>[2,1,3,3,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,3,4,5,2,1]=>[2,1,3,3,6,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,3,5,1,2,4]=>[2,1,4,5,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,5,1,4,2]=>[6,5,1,2,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,5,2,1,4]=>[2,1,4,6,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,5,2,4,1]=>[6,5,1,3,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,3,5,4,1,2]=>[2,1,4,1,6,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,3,5,4,2,1]=>[3,2,5,2,1,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,4,1,2,3,5]=>[1,1,5,2,2,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,4,1,2,5,3]=>[1,1,5,2,4,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,4,1,3,2,5]=>[2,2,6,4,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,4,1,3,5,2]=>[1,1,5,3,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,4,1,5,2,3]=>[4,4,1,1,1,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,4,1,5,3,2]=>[4,4,1,1,2,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,4,2,1,3,5]=>[3,3,1,2,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,4,2,1,5,3]=>[4,4,2,3,1,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,4,2,3,1,5]=>[4,4,2,5,2,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,4,2,3,5,1]=>[1,1,6,2,3,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,4,2,5,1,3]=>[1,1,6,4,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,4,2,5,3,1]=>[3,3,1,6,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[4,4,3,1,2,5]=>[3,3,2,1,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,4,3,1,5,2]=>[4,4,3,2,1,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,4,3,2,1,5]=>[2,2,1,1,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[4,4,3,2,5,1]=>[2,2,1,1,5,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,4,3,5,1,2]=>[2,2,1,4,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,4,3,5,2,1]=>[2,2,1,4,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,4,5,1,2,3]=>[1,1,2,4,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[4,4,5,1,3,2]=>[2,2,3,5,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,4,5,2,1,3]=>[2,2,3,6,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,4,5,2,3,1]=>[1,1,2,5,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,4,5,3,1,2]=>[3,3,4,1,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,4,5,3,2,1]=>[3,3,4,1,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,5,1,2,3,4]=>[1,2,4,2,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[4,5,1,2,4,3]=>[2,3,5,3,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,5,1,3,2,4]=>[2,3,5,4,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,5,1,3,4,2]=>[1,2,4,3,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,1,4,2,3]=>[1,2,4,4,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,5,1,4,3,2]=>[2,3,5,5,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,5,2,1,3,4]=>[2,3,6,1,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,5,2,1,4,3]=>[2,3,6,1,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,5,2,3,1,4]=>[1,2,5,2,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,5,2,3,4,1]=>[1,2,5,2,2,5]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[4,5,2,4,1,3]=>[1,2,5,3,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,5,2,4,3,1]=>[4,5,1,6,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,3,1,2,4]=>[3,4,1,1,4,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,5,3,1,4,2]=>[3,4,1,1,6,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,5,3,2,1,4]=>[3,4,1,2,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,3,2,4,1]=>[4,5,2,3,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,3,4,1,2]=>[1,2,6,2,5,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,5,3,4,2,1]=>[3,4,1,4,1,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,5,4,1,2,3]=>[2,3,1,6,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,5,4,1,3,2]=>[2,3,1,6,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,5,4,2,1,3]=>[3,4,2,1,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,4,2,3,1]=>[3,4,2,1,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,5,4,3,1,2]=>[3,4,2,2,1,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,5,4,3,2,1]=>[2,3,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[5,1,2,3,4,4]=>[1,4,2,2,2,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[5,1,2,4,3,4]=>[2,5,3,4,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,4,4,3]=>[2,5,3,4,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,3,2,4,4]=>[2,5,4,1,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,3,4,2,4]=>[1,4,3,2,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,1,3,4,4,2]=>[1,4,3,2,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,1,4,2,3,4]=>[1,4,4,6,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,4,2,4,3]=>[6,2,2,4,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,4,3,2,4]=>[2,5,5,1,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,4,3,4,2]=>[5,1,1,4,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,4,4,2,3]=>[1,4,4,1,6,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,1,4,4,3,2]=>[2,5,5,2,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,2,1,3,4,4]=>[2,6,1,4,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,1,4,3,4]=>[2,6,1,5,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,1,4,4,3]=>[2,6,1,5,2,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,2,3,1,4,4]=>[1,5,2,6,4,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,3,4,1,4]=>[1,5,2,2,5,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,2,3,4,4,1]=>[1,5,2,2,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,2,4,1,3,4]=>[1,5,3,5,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,2,4,1,4,3]=>[6,3,1,3,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,4,3,1,4]=>[6,3,1,5,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,4,3,4,1]=>[4,1,6,3,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,4,4,1,3]=>[1,5,3,1,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,2,4,4,3,1]=>[4,1,6,4,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,1,2,4,4]=>[3,1,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,3,1,4,2,4]=>[3,1,1,6,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[5,3,1,4,4,2]=>[3,1,1,6,3,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,3,2,1,4,4]=>[3,1,2,2,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,3,2,4,1,4]=>[6,4,5,1,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,2,4,4,1]=>[4,2,3,6,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,3,4,1,2,4]=>[1,6,2,5,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,3,4,1,4,2]=>[5,3,6,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,4,2,1,4]=>[3,1,4,1,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,4,2,4,1]=>[4,2,5,2,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,4,4,1,2]=>[1,6,2,1,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,3,4,4,2,1]=>[3,1,4,3,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,1,2,3,4]=>[2,1,6,3,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[5,4,1,2,4,3]=>[2,1,6,3,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,4,1,3,2,4]=>[2,1,6,4,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,4,1,3,4,2]=>[4,3,1,6,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,4,2,3]=>[5,4,2,1,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,4,3,2]=>[2,1,6,5,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,4,2,1,3,4]=>[3,2,1,2,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,4,2,1,4,3]=>[3,2,1,2,6,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[5,4,2,3,1,4]=>[3,2,1,4,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,4,2,3,4,1]=>[4,3,2,5,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,2,4,1,3]=>[6,5,4,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,2,4,3,1]=>[3,2,1,5,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,4,3,1,2,4]=>[3,2,2,1,4,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,4,3,1,4,2]=>[3,2,2,1,6,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,3,2,1,4]=>[2,1,1,1,1,5]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[5,4,3,2,4,1]=>[2,1,1,1,4,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,4,3,4,1,2]=>[2,1,1,3,6,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,4,3,4,2,1]=>[3,2,2,4,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,4,4,1,2,3]=>[2,1,2,6,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,4,4,1,3,2]=>[2,1,2,6,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,4,4,2,1,3]=>[3,2,3,1,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,4,4,2,3,1]=>[3,2,3,1,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,4,3,1,2]=>[3,2,3,2,1,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,4,3,2,1]=>[2,1,2,1,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,3,4,4,6]=>[1,2,2,2,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,2,3,4,6,4]=>[1,2,2,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,6,4,4]=>[1,2,2,4,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,4,3,4,6]=>[2,3,4,1,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,4,3,6,4]=>[3,4,5,2,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,4,4,3,6]=>[2,3,4,2,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,2,4,4,6,3]=>[1,2,3,1,3,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,4,6,3,4]=>[1,2,3,3,5,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,2,4,6,4,3]=>[3,4,5,5,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,6,3,4,4]=>[1,2,5,5,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,2,6,4,3,4]=>[4,5,1,2,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,6,4,4,3]=>[4,5,1,2,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,3,2,4,4,6]=>[2,4,1,4,2,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,3,2,4,6,4]=>[6,1,5,1,1,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,3,2,6,4,4]=>[4,6,3,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,4,2,4,6]=>[1,3,2,6,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,3,4,2,6,4]=>[4,6,5,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,3,4,4,2,6]=>[1,3,2,1,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,4,4,6,2]=>[1,3,2,1,3,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,3,4,6,2,4]=>[1,3,2,3,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,4,6,4,2]=>[3,5,4,5,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,6,2,4,4]=>[1,3,4,4,3,1]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,3,6,4,2,4]=>[6,1,2,4,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,3,6,4,4,2]=>[3,5,6,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,2,3,4,6]=>[1,4,6,2,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,2,3,6,4]=>[5,1,3,6,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,4,2,4,3,6]=>[6,2,4,1,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,2,4,6,3]=>[6,2,4,1,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,2,6,3,4]=>[5,1,3,2,2,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,2,6,4,3]=>[5,1,3,2,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,3,2,4,6]=>[2,5,1,1,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,3,2,6,4]=>[5,1,4,4,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,4,3,4,2,6]=>[5,1,4,6,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,3,4,6,2]=>[2,5,1,3,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,3,6,2,4]=>[6,2,5,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,3,6,4,2]=>[5,1,4,1,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,4,4,2,3,6]=>[1,4,1,6,2,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,4,4,2,6,3]=>[5,1,5,3,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,4,4,3,2,6]=>[2,5,2,1,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,4,3,6,2]=>[5,1,5,4,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,4,4,6,2,3]=>[1,4,1,3,4,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,4,4,6,3,2]=>[2,5,2,4,6,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,6,2,3,4]=>[1,4,3,4,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,4,6,2,4,3]=>[6,2,1,2,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,4,6,3,2,4]=>[6,2,1,3,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,6,3,4,2]=>[1,4,3,5,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,6,4,2,3]=>[3,6,5,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,6,4,3,2]=>[3,6,5,1,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,6,2,3,4,4]=>[1,6,4,2,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,6,2,4,3,4]=>[3,1,6,5,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,4,4,3]=>[3,1,6,5,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,3,2,4,4]=>[4,2,1,3,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,6,3,4,2,4]=>[4,2,1,5,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,6,3,4,4,2]=>[4,2,1,5,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,6,4,2,3,4]=>[3,1,1,1,4,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,6,4,2,4,3]=>[3,1,1,1,5,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,6,4,3,2,4]=>[3,1,1,2,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,6,4,3,4,2]=>[3,1,1,2,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,6,4,4,2,3]=>[3,1,1,3,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,6,4,4,3,2]=>[3,1,1,3,2,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,1,3,4,4,6]=>[2,1,4,3,2,4]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,1,3,4,6,4]=>[3,2,5,4,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,3,6,4,4]=>[3,2,5,6,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,4,3,4,6]=>[2,1,5,1,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,4,3,6,4]=>[5,4,1,4,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[2,1,4,4,3,6]=>[2,1,5,2,1,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,1,4,4,6,3]=>[2,1,5,2,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,1,4,6,3,4]=>[2,1,5,4,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,6,4,3]=>[3,2,6,5,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,6,3,4,4]=>[4,3,2,1,5,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,6,4,3,4]=>[3,2,1,1,2,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,6,4,4,3]=>[3,2,1,1,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,1,4,4,6]=>[1,2,6,4,1,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,3,1,4,6,4]=>[3,4,1,6,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,1,6,4,4]=>[3,4,1,1,1,3]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[2,3,4,1,4,6]=>[1,2,2,5,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,3,4,1,6,4]=>[4,5,5,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,4,4,1,6]=>[1,2,2,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,3,4,4,6,1]=>[1,2,2,1,3,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[2,3,4,6,1,4]=>[1,2,2,3,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,4,6,4,1]=>[1,2,2,3,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,6,1,4,4]=>[1,2,4,3,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,6,4,1,4]=>[5,6,1,3,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,3,6,4,4,1]=>[1,2,4,6,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,1,3,4,6]=>[1,3,5,3,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,4,1,3,6,4]=>[6,1,3,1,2,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,1,4,3,6]=>[6,1,3,2,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,1,4,6,3]=>[6,1,3,2,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[2,4,1,6,3,4]=>[4,6,1,2,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,1,6,4,3]=>[4,6,1,2,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,3,1,4,6]=>[6,1,5,4,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,3,1,6,4]=>[3,5,2,1,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[2,4,3,4,1,6]=>[4,6,3,5,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,4,6,1]=>[2,4,1,3,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,4,3,6,1,4]=>[6,1,5,2,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,4,3,6,4,1]=>[6,1,5,2,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,4,1,3,6]=>[1,3,1,5,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,4,4,1,6,3]=>[4,6,4,1,2,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,4,3,1,6]=>[3,5,3,2,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,4,4,3,6,1]=>[2,4,2,1,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,4,6,1,3]=>[1,3,1,3,3,3]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[2,4,4,6,3,1]=>[1,3,1,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,4,6,1,3,4]=>[1,3,3,3,3,2]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[2,4,6,1,4,3]=>[6,1,1,1,2,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,4,6,3,1,4]=>[6,1,1,3,4,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,4,6,3,4,1]=>[1,3,3,5,2,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[2,4,6,4,1,3]=>[6,1,1,4,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,6,4,3,1]=>[3,5,5,1,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,6,1,3,4,4]=>[1,5,3,3,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,6,1,4,3,4]=>[2,6,4,5,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,1,4,4,3]=>[2,6,4,5,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,6,3,1,4,4]=>[5,2,2,3,1,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[2,6,3,4,1,4]=>[5,2,2,6,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,6,3,4,4,1]=>[4,1,1,5,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[2,6,4,1,3,4]=>[4,1,2,1,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,4,1,4,3]=>[5,2,3,2,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,6,4,3,1,4]=>[5,2,3,4,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,6,4,3,4,1]=>[4,1,2,3,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,4,4,1,3]=>[4,1,2,4,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,6,4,4,3,1]=>[4,1,2,4,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,1,2,4,4,6]=>[1,6,2,3,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,1,2,4,6,4]=>[3,1,4,5,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,1,2,6,4,4]=>[4,2,5,1,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,1,4,2,4,6]=>[6,4,2,4,1,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,4,2,6,4]=>[5,3,1,3,2,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,1,4,4,2,6]=>[5,3,1,5,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,1,4,4,6,2]=>[1,6,4,1,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,4,6,2,4]=>[6,4,2,1,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,1,4,6,4,2]=>[3,1,6,5,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,1,6,2,4,4]=>[3,1,1,6,5,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,6,4,2,4]=>[3,1,1,1,1,5]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[3,1,6,4,4,2]=>[3,1,1,1,3,1]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[3,2,1,4,4,6]=>[2,1,1,5,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,2,1,4,6,4]=>[3,2,2,6,5,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,2,1,6,4,4]=>[3,2,2,1,1,3]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,2,4,1,4,6]=>[6,5,1,3,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,2,4,1,6,4]=>[4,3,6,1,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,2,4,4,1,6]=>[4,3,6,4,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,2,4,4,6,1]=>[2,1,4,2,4,4]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[3,2,4,6,1,4]=>[6,5,1,1,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[3,2,4,6,4,1]=>[6,5,1,1,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,6,1,4,4]=>[2,1,6,4,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,2,6,4,1,4]=>[5,4,2,3,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,6,4,4,1]=>[4,3,1,2,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[3,4,1,2,4,6]=>[1,2,5,2,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[3,4,1,2,6,4]=>[4,5,1,5,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[3,4,1,4,2,6]=>[5,6,2,1,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,1,4,6,2]=>[1,2,5,4,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,1,6,2,4]=>[1,2,5,6,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,1,6,4,2]=>[4,5,1,2,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,4,2,1,4,6]=>[3,4,1,2,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,1,6,4]=>[3,4,1,2,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,4,2,4,1,6]=>[4,5,2,6,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,4,2,4,6,1]=>[1,2,6,3,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[3,4,2,6,1,4]=>[1,2,6,5,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,2,6,4,1]=>[4,5,2,1,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,4,1,2,6]=>[1,2,1,5,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[3,4,4,1,6,2]=>[1,2,1,5,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,4,2,1,6]=>[3,4,3,1,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,4,4,2,6,1]=>[1,2,1,6,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,4,6,1,2]=>[1,2,1,3,3,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[3,4,4,6,2,1]=>[2,3,2,4,5,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,4,6,1,2,4]=>[1,2,3,3,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,4,6,1,4,2]=>[1,2,3,3,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,4,6,2,1,4]=>[2,3,4,5,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,6,2,4,1]=>[1,2,3,4,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,6,4,1,2]=>[1,2,3,6,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,4,6,4,2,1]=>[3,4,5,1,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,6,1,2,4,4]=>[1,4,3,2,3,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,6,1,4,2,4]=>[6,2,1,2,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,6,1,4,4,2]=>[1,4,3,4,1,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,6,2,1,4,4]=>[5,1,1,4,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,6,2,4,1,4]=>[6,2,2,1,3,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,6,2,4,4,1]=>[1,4,4,3,1,5]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[3,6,4,1,2,4]=>[1,4,6,5,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,4,1,4,2]=>[5,1,3,2,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,6,4,2,1,4]=>[5,1,3,3,4,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,6,4,2,4,1]=>[6,2,4,4,1,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,6,4,4,1,2]=>[1,4,6,1,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,6,4,4,2,1]=>[3,6,1,3,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,2,3,4,6]=>[1,5,2,2,2,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,2,3,6,4]=>[1,5,2,2,4,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,2,4,3,6]=>[2,6,3,4,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,4,6,3]=>[1,5,2,3,3,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,1,2,6,3,4]=>[4,1,5,1,1,5]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[4,1,2,6,4,3]=>[4,1,5,1,2,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,3,2,4,6]=>[6,3,1,5,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[4,1,3,2,6,4]=>[4,1,6,3,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,3,4,2,6]=>[4,1,6,5,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,4,6,2]=>[1,5,3,2,3,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,3,6,2,4]=>[6,3,1,2,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,1,3,6,4,2]=>[6,3,1,2,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,1,4,2,3,6]=>[5,2,1,3,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,4,2,6,3]=>[5,2,1,3,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,4,3,2,6]=>[5,2,1,4,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,1,4,3,6,2]=>[5,2,1,4,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,1,4,6,2,3]=>[1,5,4,3,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,1,4,6,3,2]=>[6,3,2,1,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,6,2,3,4]=>[1,5,6,4,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,6,2,4,3]=>[6,3,4,2,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,3,2,4]=>[4,1,2,1,3,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,1,6,3,4,2]=>[4,1,2,1,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,1,6,4,2,3]=>[4,1,2,2,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[4,1,6,4,3,2]=>[4,1,2,2,3,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,1,3,4,6]=>[3,1,2,5,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,3,6,4]=>[3,1,2,5,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,2,1,4,3,6]=>[5,3,4,1,4,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,2,1,4,6,3]=>[6,4,5,2,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,1,6,3,4]=>[4,2,3,2,1,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,2,1,6,4,3]=>[3,1,2,1,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,2,3,1,4,6]=>[3,1,4,1,6,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,3,1,6,4]=>[3,1,4,1,1,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[4,2,3,4,1,6]=>[4,2,5,5,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,2,3,4,6,1]=>[1,6,2,2,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,2,3,6,1,4]=>[1,6,2,4,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,2,3,6,4,1]=>[5,3,6,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,4,1,3,6]=>[6,4,1,3,1,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,4,1,6,3]=>[4,2,6,1,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,4,3,1,6]=>[3,1,5,2,1,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[4,2,4,3,6,1]=>[6,4,1,5,2,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,2,4,6,1,3]=>[6,4,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[4,2,4,6,3,1]=>[6,4,1,1,3,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,6,1,3,4]=>[1,6,5,3,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,6,1,4,3]=>[6,4,3,1,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,6,3,1,4]=>[5,3,2,2,3,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,2,6,3,4,1]=>[4,2,1,1,5,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,2,6,4,1,3]=>[4,2,1,2,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,6,4,3,1]=>[4,2,1,2,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,1,2,4,6]=>[3,2,1,4,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,1,2,6,4]=>[4,3,2,5,1,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,1,4,2,6]=>[5,4,3,1,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,4,6,2]=>[6,5,4,2,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,1,6,2,4]=>[3,2,1,1,6,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,3,1,6,4,2]=>[3,2,1,1,1,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[4,3,2,1,4,6]=>[2,1,1,1,5,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,3,2,1,6,4]=>[3,2,2,2,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[4,3,2,4,1,6]=>[4,3,3,6,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,2,4,6,1]=>[2,1,1,4,4,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[4,3,2,6,1,4]=>[2,1,1,6,4,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,3,2,6,4,1]=>[4,3,3,1,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[4,3,4,1,2,6]=>[4,3,5,1,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[4,3,4,1,6,2]=>[5,4,6,2,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,4,2,1,6]=>[3,2,4,1,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,3,4,2,6,1]=>[4,3,5,2,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,4,6,1,2]=>[2,1,3,4,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,4,6,2,1]=>[2,1,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,6,1,2,4]=>[2,1,5,4,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,3,6,1,4,2]=>[6,5,2,1,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,6,2,1,4]=>[5,4,1,1,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,3,6,2,4,1]=>[6,5,2,2,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,6,4,1,2]=>[5,4,1,3,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,6,4,2,1]=>[3,2,6,1,1,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[4,4,1,2,3,6]=>[1,1,5,2,2,4]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,4,1,2,6,3]=>[4,4,1,5,1,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,4,1,3,2,6]=>[4,4,1,6,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,4,1,3,6,2]=>[1,1,5,3,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,4,1,6,2,3]=>[1,1,5,6,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,4,1,6,3,2]=>[4,4,1,2,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,4,2,1,3,6]=>[3,3,1,2,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,4,2,1,6,3]=>[4,4,2,3,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,4,2,3,1,6]=>[3,3,1,4,1,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[4,4,2,3,6,1]=>[1,1,6,2,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,4,2,6,1,3]=>[1,1,6,5,3,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,4,2,6,3,1]=>[4,4,2,1,1,2]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[4,4,3,1,2,6]=>[4,4,3,2,5,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,4,3,1,6,2]=>[3,3,2,1,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,4,3,2,1,6]=>[3,3,2,2,2,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[4,4,3,2,6,1]=>[2,2,1,1,6,4]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,4,3,6,1,2]=>[2,2,1,5,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,4,3,6,2,1]=>[2,2,1,5,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,4,6,1,2,3]=>[1,1,3,3,2,2]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[4,4,6,1,3,2]=>[2,2,4,4,4,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[4,4,6,2,1,3]=>[2,2,4,5,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,4,6,2,3,1]=>[1,1,3,4,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,4,6,3,1,2]=>[1,1,3,5,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,4,6,3,2,1]=>[2,2,4,6,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,6,1,2,3,4]=>[1,3,3,2,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[4,6,1,2,4,3]=>[2,4,4,3,4,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,6,1,3,2,4]=>[6,1,1,1,5,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[4,6,1,3,4,2]=>[1,3,3,3,2,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[4,6,1,4,2,3]=>[1,3,3,4,6,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,6,1,4,3,2]=>[2,4,4,5,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,6,2,1,3,4]=>[2,4,5,1,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,6,2,1,4,3]=>[2,4,5,1,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,6,2,3,1,4]=>[1,3,4,2,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,6,2,3,4,1]=>[1,3,4,2,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,6,2,4,1,3]=>[6,1,2,1,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,6,2,4,3,1]=>[6,1,2,1,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,6,3,1,2,4]=>[1,3,5,6,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,6,3,1,4,2]=>[6,1,3,4,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,6,3,2,1,4]=>[2,4,6,1,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,6,3,2,4,1]=>[6,1,3,5,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,6,3,4,1,2]=>[1,3,5,2,5,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[4,6,3,4,2,1]=>[4,6,1,5,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,4,1,2,3]=>[1,3,6,5,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,6,4,1,3,2]=>[6,1,4,3,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,6,4,2,1,3]=>[3,5,1,1,2,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,6,4,2,3,1]=>[3,5,1,1,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,6,4,3,1,2]=>[3,5,1,2,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,6,4,3,2,1]=>[3,5,1,2,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,1,2,3,4,4]=>[1,3,2,2,2,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[6,1,2,4,3,4]=>[2,4,3,4,1,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,2,4,4,3]=>[2,4,3,4,2,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[6,1,3,2,4,4]=>[2,4,4,1,4,2]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[6,1,3,4,2,4]=>[1,3,3,2,6,3]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[6,1,3,4,4,2]=>[1,3,3,2,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,1,4,2,3,4]=>[1,3,4,6,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,4,2,4,3]=>[6,1,2,4,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,1,4,3,2,4]=>[2,4,5,1,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[6,1,4,3,4,2]=>[3,5,6,2,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,4,4,2,3]=>[1,3,4,1,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,1,4,4,3,2]=>[2,4,5,2,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,1,3,4,4]=>[2,5,1,4,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,2,1,4,3,4]=>[2,5,1,5,1,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,2,1,4,4,3]=>[2,5,1,5,2,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,2,3,1,4,4]=>[1,4,2,6,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[6,2,3,4,1,4]=>[1,4,2,2,5,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,2,3,4,4,1]=>[1,4,2,2,1,5]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[6,2,4,1,3,4]=>[1,4,3,5,3,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,2,4,1,4,3]=>[6,2,1,3,2,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,2,4,3,1,4]=>[6,2,1,5,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,2,4,3,4,1]=>[2,5,4,1,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,4,4,1,3]=>[1,4,3,1,5,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[6,2,4,4,3,1]=>[3,6,5,3,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,1,2,4,4]=>[1,5,6,2,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,1,4,2,4]=>[6,3,4,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,3,1,4,4,2]=>[5,2,3,1,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[6,3,2,1,4,4]=>[2,6,1,1,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,3,2,4,1,4]=>[6,3,5,1,3,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,2,4,4,1]=>[4,1,3,6,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,3,4,1,2,4]=>[1,5,2,5,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,3,4,1,4,2]=>[5,2,6,2,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,4,2,1,4]=>[5,2,6,3,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,4,2,4,1]=>[4,1,5,2,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[6,3,4,4,1,2]=>[1,5,2,1,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[6,3,4,4,2,1]=>[4,1,5,4,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,1,2,3,4]=>[1,6,5,2,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[6,4,1,2,4,3]=>[4,2,1,5,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,1,3,2,4]=>[6,4,3,1,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,4,1,3,4,2]=>[4,2,1,6,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,4,1,4,2,3]=>[5,3,2,1,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,4,1,4,3,2]=>[5,3,2,1,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[6,4,2,1,3,4]=>[3,1,1,2,5,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,4,2,1,4,3]=>[3,1,1,2,6,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[6,4,2,3,1,4]=>[3,1,1,4,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[6,4,2,3,4,1]=>[4,2,2,5,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,4,2,4,1,3]=>[6,4,4,1,3,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[6,4,2,4,3,1]=>[3,1,1,5,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[6,4,3,1,2,4]=>[3,1,2,1,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,4,3,1,4,2]=>[3,1,2,1,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,4,3,2,1,4]=>[3,1,2,2,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[6,4,3,2,4,1]=>[4,2,3,3,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,4,3,4,1,2]=>[4,2,3,5,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,4,3,4,2,1]=>[3,1,2,4,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,4,1,2,3]=>[1,6,1,5,2,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,4,4,1,3,2]=>[4,2,4,1,6,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[6,4,4,2,1,3]=>[3,1,3,1,2,5]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,4,4,2,3,1]=>[3,1,3,1,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[6,4,4,3,1,2]=>[3,1,3,2,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[6,4,4,3,2,1]=>[3,1,3,2,2,2]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,2,3,4,5,5]=>[1,2,2,2,2,1]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,2,3,5,4,5]=>[2,3,3,4,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,3,5,5,4]=>[2,3,3,4,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,2,4,3,5,5]=>[2,3,4,1,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,2,4,5,3,5]=>[1,2,3,2,6,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,2,4,5,5,3]=>[1,2,3,2,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,2,5,3,4,5]=>[1,2,4,6,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,2,5,3,5,4]=>[3,4,6,1,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,4,3,5]=>[2,3,5,1,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,5,4,5,3]=>[3,4,6,2,4,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,5,5,3,4]=>[1,2,4,1,6,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,2,5,5,4,3]=>[2,3,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,2,4,5,5]=>[2,4,1,4,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,3,2,5,4,5]=>[2,4,1,5,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,3,2,5,5,4]=>[2,4,1,5,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,3,4,2,5,5]=>[1,3,2,6,4,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,3,4,5,2,5]=>[1,3,2,2,5,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,3,4,5,5,2]=>[1,3,2,2,1,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,3,5,2,4,5]=>[1,3,3,5,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,3,5,2,5,4]=>[6,1,1,3,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,5,4,2,5]=>[6,1,1,5,4,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,3,5,4,5,2]=>[2,4,4,1,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,5,5,2,4]=>[1,3,3,1,5,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,3,5,5,4,2]=>[3,5,5,3,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,4,2,3,5,5]=>[1,4,6,2,3,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,4,2,5,3,5]=>[6,2,4,2,4,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,4,2,5,5,3]=>[5,1,3,1,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,4,3,2,5,5]=>[2,5,1,1,5,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,4,3,5,2,5]=>[6,2,5,1,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,3,5,5,2]=>[2,5,1,4,2,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,4,5,2,3,5]=>[1,4,2,5,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,4,5,2,5,3]=>[5,1,6,2,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,5,3,2,5]=>[5,1,6,3,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,5,3,5,2]=>[1,4,2,6,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,5,2,3]=>[1,4,2,1,5,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,4,5,5,3,2]=>[3,6,4,3,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,5,2,3,4,5]=>[1,5,5,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,5,2,3,5,4]=>[4,1,1,5,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,2,4,3,5]=>[6,3,3,1,5,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,5,2,4,5,3]=>[4,1,1,6,5,2]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,5,2,5,3,4]=>[5,2,2,1,3,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,2,5,4,3]=>[5,2,2,1,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,3,2,4,5]=>[4,1,2,3,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,3,2,5,4]=>[5,2,3,4,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,3,4,2,5]=>[5,2,3,6,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,3,4,5,2]=>[4,1,2,5,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,3,5,2,4]=>[6,3,4,1,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,3,5,4,2]=>[4,1,2,6,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,4,2,3,5]=>[4,1,3,2,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,4,2,5,3]=>[5,2,4,3,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,4,3,2,5]=>[2,6,1,1,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,5,4,3,5,2]=>[4,1,3,3,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,4,5,2,3]=>[4,1,3,5,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,5,4,5,3,2]=>[4,1,3,5,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,5,5,2,3,4]=>[1,5,1,5,2,2]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,5,5,2,4,3]=>[4,1,4,1,6,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,5,5,3,2,4]=>[4,1,4,2,3,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,5,5,3,4,2]=>[4,1,4,2,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,5,5,4,2,3]=>[4,1,4,3,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,5,5,4,3,2]=>[2,6,2,1,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,1,3,4,5,5]=>[2,1,4,3,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,1,3,5,4,5]=>[2,1,4,4,1,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,3,5,5,4]=>[2,1,4,4,2,1]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[2,1,4,3,5,5]=>[2,1,5,1,4,2]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[2,1,4,5,3,5]=>[3,2,6,4,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,4,5,5,3]=>[3,2,6,4,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,5,3,4,5]=>[4,3,1,2,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,5,3,5,4]=>[4,3,1,2,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,5,4,3,5]=>[2,1,6,1,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[2,1,5,4,5,3]=>[4,3,1,3,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,5,5,3,4]=>[4,3,1,4,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,1,5,5,4,3]=>[2,1,6,2,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[2,3,1,4,5,5]=>[1,2,6,4,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[2,3,1,5,4,5]=>[4,5,2,1,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,1,5,5,4]=>[4,5,2,1,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,3,4,1,5,5]=>[1,2,2,5,5,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[2,3,4,5,1,5]=>[1,2,2,2,4,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,3,4,5,5,1]=>[1,2,2,2,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[2,3,5,1,4,5]=>[1,2,3,4,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,5,1,5,4]=>[2,3,4,5,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,4,1,5]=>[4,5,6,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,5,4,5,1]=>[2,3,4,1,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,5,5,1,4]=>[1,2,3,1,4,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,3,5,5,4,1]=>[2,3,4,2,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,1,3,5,5]=>[1,3,5,3,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[2,4,1,5,3,5]=>[6,1,3,3,4,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,1,5,5,3]=>[4,6,1,1,4,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[2,4,3,1,5,5]=>[4,6,3,2,1,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[2,4,3,5,1,5]=>[6,1,5,1,2,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,3,5,5,1]=>[2,4,1,4,2,5]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[2,4,5,1,3,5]=>[1,3,2,4,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,4,5,1,5,3]=>[1,3,2,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,5,3,1,5]=>[4,6,5,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,4,5,3,5,1]=>[1,3,2,6,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,5,5,1,3]=>[1,3,2,1,4,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[2,4,5,5,3,1]=>[3,5,4,3,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,1,3,4,5]=>[1,4,4,3,2,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,5,1,3,5,4]=>[6,2,2,1,1,5]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[2,5,1,4,3,5]=>[6,2,2,2,5,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[2,5,1,4,5,3]=>[5,1,1,1,6,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,5,1,5,3,4]=>[5,1,1,2,3,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,1,5,4,3]=>[5,1,1,2,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,5,3,1,4,5]=>[5,1,3,3,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[2,5,3,1,5,4]=>[5,1,3,3,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,5,3,4,1,5]=>[5,1,3,6,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,3,4,5,1]=>[1,4,6,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,5,3,5,1,4]=>[6,2,4,1,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,3,5,4,1]=>[6,2,4,1,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,4,1,3,5]=>[6,2,5,3,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,4,1,5,3]=>[5,1,4,2,2,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,4,3,1,5]=>[5,1,4,4,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[2,5,4,3,5,1]=>[2,5,1,1,4,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,4,5,1,3]=>[2,5,1,3,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,4,5,3,1]=>[3,6,2,4,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,5,5,1,3,4]=>[1,4,1,4,3,2]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,5,5,1,4,3]=>[5,1,5,1,1,4]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[2,5,5,3,1,4]=>[5,1,5,3,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[2,5,5,3,4,1]=>[1,4,1,6,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,5,5,4,1,3]=>[2,5,2,1,6,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[2,5,5,4,3,1]=>[3,6,3,2,2,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,1,2,4,5,5]=>[1,6,2,3,2,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[3,1,2,5,4,5]=>[3,1,4,6,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[3,1,2,5,5,4]=>[3,1,4,6,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,1,4,2,5,5]=>[5,3,1,3,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,1,4,5,2,5]=>[5,3,1,6,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,1,4,5,5,2]=>[1,6,4,2,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,4,5]=>[4,2,1,1,6,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,1,5,2,5,4]=>[5,3,2,2,1,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,1,5,4,2,5]=>[5,3,2,4,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,5,4,5,2]=>[4,2,1,3,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,1,5,5,2,4]=>[4,2,1,4,1,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,1,5,5,4,2]=>[4,2,1,4,3,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[3,2,1,4,5,5]=>[2,1,1,5,3,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,2,1,5,4,5]=>[2,1,1,6,1,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[3,2,1,5,5,4]=>[2,1,1,6,2,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[3,2,4,1,5,5]=>[4,3,6,1,1,4]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,2,4,5,1,5]=>[2,1,4,3,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,4,5,5,1]=>[2,1,4,3,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[3,2,5,1,4,5]=>[5,4,1,1,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,2,5,1,5,4]=>[5,4,1,1,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,5,4,1,5]=>[5,4,1,4,2,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,2,5,4,5,1]=>[2,1,5,1,3,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[3,2,5,5,1,4]=>[5,4,1,5,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[3,2,5,5,4,1]=>[2,1,5,2,1,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[3,4,1,2,5,5]=>[1,2,5,2,4,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[3,4,1,5,2,5]=>[5,6,2,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,4,1,5,5,2]=>[4,5,1,1,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[3,4,2,1,5,5]=>[4,5,2,3,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,4,2,5,1,5]=>[5,6,3,1,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,2,5,5,1]=>[1,2,6,4,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[3,4,5,1,2,5]=>[1,2,2,4,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[3,4,5,1,5,2]=>[1,2,2,4,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,5,2,1,5]=>[4,5,5,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,4,5,2,5,1]=>[1,2,2,5,4,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[3,4,5,5,1,2]=>[1,2,2,1,4,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[3,4,5,5,2,1]=>[2,3,3,2,6,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,5,1,2,4,5]=>[1,3,4,2,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,5,1,2,5,4]=>[2,4,5,3,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,5,1,4,2,5]=>[6,1,2,2,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,5,1,4,5,2]=>[1,3,4,4,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,5,1,5,2,4]=>[6,1,2,3,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,5,1,5,4,2]=>[6,1,2,3,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,1,4,5]=>[2,4,6,1,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,2,1,5,4]=>[4,6,1,3,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,2,4,1,5]=>[6,1,3,1,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[3,5,2,4,5,1]=>[1,3,5,3,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,2,5,1,4]=>[6,1,3,2,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,5,2,5,4,1]=>[6,1,3,2,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,5,4,1,2,5]=>[2,4,1,6,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,4,1,5,2]=>[4,6,3,1,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[3,5,4,2,1,5]=>[4,6,3,2,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,4,2,5,1]=>[6,1,5,4,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,4,5,1,2]=>[2,4,1,3,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,4,5,2,1]=>[2,4,1,3,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,5,1,2,4]=>[1,3,1,4,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[3,5,5,1,4,2]=>[1,3,1,4,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,5,5,2,1,4]=>[2,4,2,6,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[3,5,5,2,4,1]=>[1,3,1,5,3,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[3,5,5,4,1,2]=>[2,4,2,1,6,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,5,4,2,1]=>[3,5,3,2,1,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[4,1,2,3,5,5]=>[1,5,2,2,3,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,2,5,3,5]=>[1,5,2,4,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,2,5,5,3]=>[1,5,2,4,1,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[4,1,3,2,5,5]=>[2,6,4,1,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,1,3,5,2,5]=>[6,3,1,1,3,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,1,3,5,5,2]=>[1,5,3,3,1,5]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[4,1,5,2,3,5]=>[4,1,1,1,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,5,2,5,3]=>[5,2,2,2,1,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,5,3,2,5]=>[5,2,2,3,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,5,3,5,2]=>[4,1,1,2,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,1,5,5,2,3]=>[4,1,1,4,1,5]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[4,1,5,5,3,2]=>[4,1,1,4,2,3]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,2,1,3,5,5]=>[3,1,2,5,5,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,2,1,5,3,5]=>[4,2,3,1,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,1,5,5,3]=>[4,2,3,1,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[4,2,3,1,5,5]=>[4,2,5,2,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[4,2,3,5,1,5]=>[1,6,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,3,5,5,1]=>[1,6,2,3,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[4,2,5,1,3,5]=>[6,4,2,2,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,5,1,5,3]=>[5,3,1,1,2,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,5,3,1,5]=>[5,3,1,3,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[4,2,5,3,5,1]=>[6,4,2,4,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,5,5,1,3]=>[1,6,4,1,4,3]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,2,5,5,3,1]=>[3,1,6,3,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[4,3,1,2,5,5]=>[3,2,1,4,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,1,5,2,5]=>[5,4,3,2,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,1,5,5,2]=>[4,3,2,1,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[4,3,2,1,5,5]=>[2,1,1,1,6,2]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[4,3,2,5,1,5]=>[5,4,4,1,1,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,3,2,5,5,1]=>[2,1,1,5,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[4,3,5,1,2,5]=>[2,1,4,5,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,5,1,5,2]=>[6,5,1,2,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,3,5,2,1,5]=>[4,3,6,1,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,3,5,2,5,1]=>[6,5,1,3,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,3,5,5,1,2]=>[2,1,4,2,5,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,3,5,5,2,1]=>[2,1,4,2,6,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,5,1,2,3,5]=>[1,2,4,2,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,5,1,2,5,3]=>[1,2,4,2,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,5,1,3,2,5]=>[2,3,5,4,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,5,1,3,5,2]=>[1,2,4,3,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,5,1,5,2,3]=>[1,2,4,5,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,5,1,5,3,2]=>[5,6,1,2,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,1,3,5]=>[2,3,6,1,4,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,5,2,1,5,3]=>[4,5,1,3,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,5,2,3,1,5]=>[4,5,1,5,2,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[4,5,2,3,5,1]=>[1,2,5,2,3,4]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,2,5,1,3]=>[1,2,5,4,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[4,5,2,5,3,1]=>[5,6,2,1,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,5,3,1,2,5]=>[3,4,1,1,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[4,5,3,1,5,2]=>[4,5,2,2,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[4,5,3,2,1,5]=>[4,5,2,3,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,5,3,2,5,1]=>[5,6,3,4,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,5,3,5,1,2]=>[1,2,6,3,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,3,5,2,1]=>[4,5,2,6,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,5,1,2,3]=>[1,2,1,4,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[4,5,5,1,3,2]=>[2,3,2,5,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,5,2,1,3]=>[2,3,2,6,1,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,5,2,3,1]=>[1,2,1,5,2,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[4,5,5,3,1,2]=>[3,4,3,1,1,4]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[4,5,5,3,2,1]=>[3,4,3,1,2,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,1,2,3,4,5]=>[1,4,2,2,2,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[5,1,2,3,5,4]=>[2,5,3,3,4,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,4,3,5]=>[2,5,3,4,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,2,4,5,3]=>[1,4,2,3,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,1,2,5,3,4]=>[1,4,2,4,6,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,2,5,4,3]=>[2,5,3,5,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,1,3,2,4,5]=>[2,5,4,1,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,1,3,2,5,4]=>[2,5,4,1,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,1,3,4,2,5]=>[1,4,3,2,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,3,4,5,2]=>[1,4,3,2,2,5]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,1,3,5,2,4]=>[6,2,1,1,3,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,1,3,5,4,2]=>[6,2,1,1,5,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,1,4,2,3,5]=>[1,4,4,6,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,1,4,2,5,3]=>[5,1,1,3,1,3]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[5,1,4,3,2,5]=>[5,1,1,4,4,1]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[5,1,4,3,5,2]=>[6,2,2,5,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,4,5,2,3]=>[1,4,4,2,5,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,1,4,5,3,2]=>[5,1,1,6,3,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,1,5,2,3,4]=>[1,4,5,5,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,5,2,4,3]=>[6,2,3,3,1,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,5,3,2,4]=>[6,2,3,4,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,5,3,4,2]=>[5,1,2,3,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,5,4,2,3]=>[5,1,2,4,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,5,4,3,2]=>[2,5,6,1,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,2,1,3,4,5]=>[2,6,1,4,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,2,1,3,5,4]=>[2,6,1,4,4,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,2,1,4,3,5]=>[2,6,1,5,1,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,2,1,4,5,3]=>[5,2,4,1,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,5,3,4]=>[4,1,3,1,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,1,5,4,3]=>[4,1,3,1,3,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[5,2,3,1,4,5]=>[1,5,2,6,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,3,1,5,4]=>[4,1,5,2,1,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,3,4,1,5]=>[4,1,5,5,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[5,2,3,4,5,1]=>[1,5,2,2,2,4]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,2,3,5,1,4]=>[1,5,2,3,4,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,3,5,4,1]=>[4,1,5,6,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,2,4,1,3,5]=>[6,3,1,3,1,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,2,4,1,5,3]=>[4,1,6,1,1,2]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,2,4,3,1,5]=>[4,1,6,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,2,4,3,5,1]=>[6,3,1,5,1,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,4,5,1,3]=>[1,5,3,2,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,2,4,5,3,1]=>[4,1,6,5,2,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,2,5,1,3,4]=>[1,5,4,4,3,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,5,1,4,3]=>[5,2,1,1,1,4]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,2,5,3,1,4]=>[5,2,1,3,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[5,2,5,3,4,1]=>[5,2,1,3,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,5,4,1,3]=>[6,3,2,5,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,5,4,3,1]=>[5,2,1,4,4,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,1,2,4,5]=>[3,1,1,4,5,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[5,3,1,2,5,4]=>[3,1,1,4,6,2]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,1,4,2,5]=>[5,3,3,1,3,1]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[5,3,1,4,5,2]=>[5,3,3,1,6,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,1,5,2,4]=>[4,2,2,1,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,3,1,5,4,2]=>[4,2,2,1,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,3,2,1,4,5]=>[3,1,2,2,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,2,1,5,4]=>[4,2,3,3,1,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[5,3,2,4,1,5]=>[4,2,3,6,1,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,3,2,4,5,1]=>[3,1,2,5,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,2,5,1,4]=>[5,3,4,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,3,2,5,4,1]=>[5,3,4,1,4,2]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,3,4,1,2,5]=>[1,6,2,5,2,4]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,4,1,5,2]=>[4,2,5,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[5,3,4,2,1,5]=>[4,2,5,2,3,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,3,4,2,5,1]=>[5,3,6,3,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,3,4,5,1,2]=>[1,6,2,2,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[5,3,4,5,2,1]=>[4,2,5,5,1,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,3,5,1,2,4]=>[1,6,3,4,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,3,5,1,4,2]=>[6,4,1,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,3,5,2,1,4]=>[6,4,1,3,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,5,2,4,1]=>[6,4,1,3,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,3,5,4,1,2]=>[4,2,6,3,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,5,4,2,1]=>[3,1,5,2,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,4,1,2,3,5]=>[2,1,6,3,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,4,1,2,5,3]=>[5,4,2,6,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,3,2,5]=>[2,1,6,4,1,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,4,1,3,5,2]=>[6,5,3,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[5,4,1,5,2,3]=>[4,3,1,1,1,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,4,1,5,3,2]=>[4,3,1,1,2,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,2,1,3,5]=>[3,2,1,2,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[5,4,2,1,5,3]=>[4,3,2,3,1,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,2,3,1,5]=>[4,3,2,5,2,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,4,2,3,5,1]=>[3,2,1,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,2,5,1,3]=>[6,5,4,2,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,4,2,5,3,1]=>[3,2,1,6,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,4,3,1,2,5]=>[3,2,2,1,4,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,4,3,1,5,2]=>[4,3,3,2,1,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,3,2,1,5]=>[2,1,1,1,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[5,4,3,2,5,1]=>[2,1,1,1,5,5]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,4,3,5,1,2]=>[2,1,1,4,5,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,4,3,5,2,1]=>[2,1,1,4,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,4,5,1,2,3]=>[2,1,3,5,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,4,5,1,3,2]=>[2,1,3,5,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,4,5,2,1,3]=>[2,1,3,6,1,4]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,4,5,2,3,1]=>[4,3,5,1,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,4,5,3,1,2]=>[3,2,4,1,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,4,5,3,2,1]=>[3,2,4,1,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,5,1,2,3,4]=>[1,1,4,2,2,2]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[5,5,1,2,4,3]=>[2,2,5,3,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[5,5,1,3,2,4]=>[2,2,5,4,1,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[5,5,1,3,4,2]=>[1,1,4,3,2,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[5,5,1,4,2,3]=>[1,1,4,4,6,2]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[5,5,1,4,3,2]=>[2,2,5,5,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,5,2,1,3,4]=>[2,2,6,1,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,5,2,1,4,3]=>[2,2,6,1,5,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,5,2,3,1,4]=>[1,1,5,2,6,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[5,5,2,3,4,1]=>[1,1,5,2,2,5]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[5,5,2,4,1,3]=>[1,1,5,3,5,3]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[5,5,2,4,3,1]=>[4,4,1,6,3,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,5,3,1,2,4]=>[3,3,1,1,4,5]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[5,5,3,1,4,2]=>[3,3,1,1,6,1]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[5,5,3,2,1,4]=>[3,3,1,2,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,5,3,2,4,1]=>[4,4,2,3,6,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,5,3,4,1,2]=>[1,1,6,2,5,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[5,5,3,4,2,1]=>[3,3,1,4,1,2]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,5,4,1,2,3]=>[2,2,1,6,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,5,4,1,3,2]=>[2,2,1,6,4,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[5,5,4,2,1,3]=>[3,3,2,1,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,5,4,2,3,1]=>[3,3,2,1,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,5,4,3,1,2]=>[3,3,2,2,1,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,5,4,3,2,1]=>[2,2,1,1,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,2,3,4,5,6]=>[1,2,2,2,2,2]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,2,3,4,6,5]=>[2,3,3,3,4,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,2,3,5,4,6]=>[2,3,3,4,1,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,3,5,6,4]=>[1,2,2,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,2,3,6,4,5]=>[1,2,2,4,6,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,2,3,6,5,4]=>[2,3,3,5,1,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,2,4,3,5,6]=>[2,3,4,1,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,2,4,3,6,5]=>[2,3,4,1,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,2,4,5,3,6]=>[1,2,3,2,6,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,4,5,6,3]=>[1,2,3,2,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,2,4,6,3,5]=>[1,2,3,3,5,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,2,4,6,5,3]=>[3,4,5,5,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,5,3,4,6]=>[1,2,4,6,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,2,5,3,6,4]=>[5,6,1,3,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,2,5,4,3,6]=>[2,3,5,1,1,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,2,5,4,6,3]=>[2,3,5,1,4,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,5,6,3,4]=>[1,2,4,2,5,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,2,5,6,4,3]=>[3,4,6,4,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,2,6,3,4,5]=>[1,2,5,5,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,2,6,3,5,4]=>[4,5,1,1,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,2,6,4,3,5]=>[4,5,1,2,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,2,6,4,5,3]=>[4,5,1,2,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,2,6,5,3,4]=>[4,5,1,3,2,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,2,6,5,4,3]=>[2,3,6,1,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,3,2,4,5,6]=>[2,4,1,4,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,2,4,6,5]=>[2,4,1,4,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,3,2,5,4,6]=>[2,4,1,5,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,3,2,5,6,4]=>[3,5,2,6,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,6,4,5]=>[4,6,3,1,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,2,6,5,4]=>[2,4,1,6,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,3,4,2,5,6]=>[1,3,2,6,4,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,3,4,2,6,5]=>[4,6,5,2,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,4,5,2,6]=>[1,3,2,2,5,5]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,3,4,5,6,2]=>[1,3,2,2,2,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,3,4,6,2,5]=>[1,3,2,3,4,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,4,6,5,2]=>[2,4,3,4,1,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,3,5,2,4,6]=>[6,1,1,3,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,3,5,2,6,4]=>[6,1,1,3,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,3,5,4,2,6]=>[6,1,1,5,4,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,3,5,4,6,2]=>[6,1,1,5,1,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,3,5,6,2,4]=>[1,3,3,2,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,3,5,6,4,2]=>[3,5,5,4,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,3,6,2,4,5]=>[1,3,4,4,3,2]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,3,6,2,5,4]=>[6,1,2,2,2,5]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,3,6,4,2,5]=>[6,1,2,4,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,3,6,4,5,2]=>[1,3,4,6,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,3,6,5,2,4]=>[6,1,2,5,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,3,6,5,4,2]=>[3,5,6,2,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,2,3,5,6]=>[1,4,6,2,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,4,2,3,6,5]=>[5,1,3,6,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,4,2,5,3,6]=>[5,1,3,1,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,4,2,5,6,3]=>[5,1,3,1,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,4,2,6,3,5]=>[6,2,4,3,3,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,4,2,6,5,3]=>[5,1,3,2,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,4,3,2,5,6]=>[2,5,1,1,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,4,3,2,6,5]=>[2,5,1,1,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,4,3,5,2,6]=>[6,2,5,1,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,3,5,6,2]=>[2,5,1,4,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,4,3,6,2,5]=>[5,1,4,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,4,3,6,5,2]=>[5,1,4,1,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,4,5,2,3,6]=>[1,4,2,5,2,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,4,5,2,6,3]=>[5,1,6,2,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,4,5,3,2,6]=>[5,1,6,3,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,5,3,6,2]=>[5,1,6,3,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,4,5,6,2,3]=>[1,4,2,2,4,2]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,4,5,6,3,2]=>[2,5,3,3,6,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,4,6,2,3,5]=>[1,4,3,4,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,4,6,2,5,3]=>[6,2,1,2,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,4,6,3,2,5]=>[6,2,1,3,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,4,6,3,5,2]=>[6,2,1,3,1,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,4,6,5,2,3]=>[2,5,4,1,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,4,6,5,3,2]=>[3,6,5,2,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,2,3,4,6]=>[1,5,5,2,2,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,5,2,3,6,4]=>[5,2,2,6,1,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,5,2,4,3,6]=>[6,3,3,1,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,5,2,4,6,3]=>[6,3,3,1,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,5,2,6,3,4]=>[4,1,1,1,1,5]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,5,2,6,4,3]=>[4,1,1,1,2,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,5,3,2,4,6]=>[6,3,4,5,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,3,2,6,4]=>[4,1,2,3,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,5,3,4,2,6]=>[4,1,2,5,2,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,5,3,4,6,2]=>[1,5,6,2,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,3,6,2,4]=>[6,3,4,2,2,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,5,3,6,4,2]=>[5,2,3,1,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,5,4,2,3,6]=>[5,2,4,3,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,4,2,6,3]=>[4,1,3,2,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,5,4,3,2,6]=>[4,1,3,3,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,5,4,3,6,2]=>[5,2,4,4,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,5,4,6,2,3]=>[2,6,1,4,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,4,6,3,2]=>[4,1,3,6,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,5,6,2,3,4]=>[1,5,2,4,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,5,6,2,4,3]=>[2,6,3,5,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,5,6,3,2,4]=>[4,1,5,1,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,5,6,3,4,2]=>[4,1,5,1,5,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,5,6,4,2,3]=>[4,1,5,2,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,5,6,4,3,2]=>[4,1,5,2,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,6,2,3,4,5]=>[1,6,4,2,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,6,2,3,5,4]=>[3,1,6,4,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,2,4,3,5]=>[6,4,2,1,5,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,6,2,4,5,3]=>[3,1,6,5,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,6,2,5,3,4]=>[5,3,1,1,3,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,6,2,5,4,3]=>[5,3,1,1,4,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,6,3,2,4,5]=>[4,2,1,3,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,6,3,2,5,4]=>[5,3,2,4,1,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,6,3,4,2,5]=>[5,3,2,6,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,6,3,4,5,2]=>[4,2,1,5,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,6,3,5,2,4]=>[6,4,3,1,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,6,3,5,4,2]=>[4,2,1,6,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,4,2,3,5]=>[3,1,1,1,4,5]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,6,4,2,5,3]=>[3,1,1,1,6,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,6,4,3,2,5]=>[3,1,1,2,2,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,6,4,3,5,2]=>[4,2,2,3,6,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,6,4,5,2,3]=>[4,2,2,5,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,6,4,5,3,2]=>[3,1,1,4,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,6,5,2,3,4]=>[4,2,3,1,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,6,5,2,4,3]=>[4,2,3,1,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,6,5,3,2,4]=>[3,1,2,1,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,6,5,3,4,2]=>[3,1,2,1,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,6,5,4,2,3]=>[3,1,2,2,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,6,5,4,3,2]=>[3,1,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,1,3,4,5,6]=>[2,1,4,3,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[2,1,3,4,6,5]=>[2,1,4,3,4,1]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[2,1,3,5,4,6]=>[2,1,4,4,1,4]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[2,1,3,5,6,4]=>[3,2,5,5,4,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,3,6,4,5]=>[3,2,5,6,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,3,6,5,4]=>[2,1,4,5,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[2,1,4,3,5,6]=>[2,1,5,1,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,1,4,3,6,5]=>[2,1,5,1,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[2,1,4,5,3,6]=>[5,4,1,6,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,1,4,5,6,3]=>[2,1,5,3,3,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,1,4,6,3,5]=>[6,5,2,1,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,1,4,6,5,3]=>[3,2,6,5,2,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,1,5,3,4,6]=>[4,3,1,2,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,1,5,3,6,4]=>[5,4,2,3,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,5,4,3,6]=>[2,1,6,1,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,1,5,4,6,3]=>[4,3,1,3,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,1,5,6,3,4]=>[4,3,1,5,1,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[2,1,5,6,4,3]=>[4,3,1,5,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,1,6,3,4,5]=>[4,3,2,1,5,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,1,6,3,5,4]=>[4,3,2,1,6,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,1,6,4,3,5]=>[3,2,1,1,2,5]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,1,6,4,5,3]=>[3,2,1,1,4,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,1,6,5,3,4]=>[3,2,1,2,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,1,6,5,4,3]=>[3,2,1,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,3,1,4,5,6]=>[1,2,6,4,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,3,1,4,6,5]=>[3,4,1,6,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,5,4,6]=>[4,5,2,1,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,1,5,6,4]=>[4,5,2,1,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,3,1,6,4,5]=>[3,4,1,1,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[2,3,1,6,5,4]=>[3,4,1,1,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,3,4,1,5,6]=>[1,2,2,5,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[2,3,4,1,6,5]=>[4,5,5,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,3,4,5,1,6]=>[1,2,2,2,4,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,3,4,5,6,1]=>[1,2,2,2,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[2,3,4,6,1,5]=>[1,2,2,3,3,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,3,4,6,5,1]=>[2,3,3,4,1,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,3,5,1,4,6]=>[1,2,3,4,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,3,5,1,6,4]=>[3,4,5,6,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[2,3,5,4,1,6]=>[4,5,6,3,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,5,4,6,1]=>[2,3,4,1,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,3,5,6,1,4]=>[1,2,3,2,3,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,3,5,6,4,1]=>[1,2,3,2,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,6,1,4,5]=>[1,2,4,3,4,2]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[2,3,6,1,5,4]=>[2,3,5,4,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,3,6,4,1,5]=>[5,6,1,3,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,3,6,4,5,1]=>[1,2,4,6,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,3,6,5,1,4]=>[5,6,1,4,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,3,6,5,4,1]=>[2,3,5,1,1,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,1,3,5,6]=>[1,3,5,3,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[2,4,1,3,6,5]=>[6,1,3,1,2,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,1,5,3,6]=>[6,1,3,3,4,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,1,5,6,3]=>[4,6,1,1,5,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[2,4,1,6,3,5]=>[6,1,3,4,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,1,6,5,3]=>[4,6,1,2,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[2,4,3,1,5,6]=>[4,6,3,2,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,3,1,6,5]=>[3,5,2,1,1,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[2,4,3,5,1,6]=>[6,1,5,1,2,4]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,4,3,5,6,1]=>[2,4,1,4,3,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[2,4,3,6,1,5]=>[6,1,5,2,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,4,3,6,5,1]=>[2,4,1,5,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,4,5,1,3,6]=>[1,3,2,4,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,4,5,1,6,3]=>[1,3,2,4,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,4,5,3,1,6]=>[3,5,4,1,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[2,4,5,3,6,1]=>[1,3,2,6,4,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,4,5,6,1,3]=>[1,3,2,2,3,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[2,4,5,6,3,1]=>[1,3,2,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,4,6,1,3,5]=>[6,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[2,4,6,1,5,3]=>[6,1,1,1,3,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,4,6,3,1,5]=>[6,1,1,3,4,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,4,6,3,5,1]=>[6,1,1,3,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[2,4,6,5,1,3]=>[6,1,1,5,2,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,4,6,5,3,1]=>[3,5,5,2,1,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[2,5,1,3,4,6]=>[1,4,4,3,2,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[2,5,1,3,6,4]=>[6,2,2,1,2,4]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,1,4,3,6]=>[5,1,1,1,4,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[2,5,1,4,6,3]=>[6,2,2,2,1,3]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[2,5,1,6,3,4]=>[5,1,1,3,2,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,1,6,4,3]=>[5,1,1,3,3,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[2,5,3,1,4,6]=>[6,2,4,4,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[2,5,3,1,6,4]=>[3,6,1,1,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[2,5,3,4,1,6]=>[5,1,3,6,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[2,5,3,4,6,1]=>[1,4,6,2,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[2,5,3,6,1,4]=>[6,2,4,2,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[2,5,3,6,4,1]=>[5,1,3,1,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[2,5,4,1,3,6]=>[6,2,5,3,1,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,5,4,1,6,3]=>[5,1,4,2,3,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[2,5,4,3,1,6]=>[3,6,2,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[2,5,4,3,6,1]=>[2,5,1,1,5,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[2,5,4,6,1,3]=>[6,2,5,1,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[2,5,4,6,3,1]=>[6,2,5,1,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,6,1,3,4]=>[1,4,2,3,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[2,5,6,1,4,3]=>[2,5,3,4,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[2,5,6,3,1,4]=>[5,1,6,2,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,5,6,3,4,1]=>[1,4,2,5,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,5,6,4,1,3]=>[1,4,2,6,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,5,6,4,3,1]=>[3,6,4,1,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[2,6,1,3,4,5]=>[1,5,3,3,2,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[2,6,1,3,5,4]=>[6,3,1,1,1,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[2,6,1,4,3,5]=>[6,3,1,2,5,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[2,6,1,4,5,3]=>[1,5,3,4,2,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,1,5,3,4]=>[4,1,6,1,2,5]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[2,6,1,5,4,3]=>[4,1,6,1,3,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,6,3,1,4,5]=>[5,2,2,3,1,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[2,6,3,1,5,4]=>[4,1,1,2,1,3]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[2,6,3,4,1,5]=>[4,1,1,5,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[2,6,3,4,5,1]=>[1,5,5,2,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[2,6,3,5,1,4]=>[6,3,3,1,2,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[2,6,3,5,4,1]=>[4,1,1,6,3,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[2,6,4,1,3,5]=>[6,3,4,3,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,6,4,1,5,3]=>[4,1,2,1,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[2,6,4,3,1,5]=>[4,1,2,3,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[2,6,4,3,5,1]=>[6,3,4,5,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,4,5,1,3]=>[1,5,6,2,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,4,5,3,1]=>[4,1,2,5,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[2,6,5,1,3,4]=>[2,6,1,5,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[2,6,5,1,4,3]=>[5,2,4,1,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[2,6,5,3,1,4]=>[5,2,4,3,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[2,6,5,3,4,1]=>[4,1,3,2,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[2,6,5,4,1,3]=>[4,1,3,3,1,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[2,6,5,4,3,1]=>[4,1,3,3,3,2]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,1,2,4,5,6]=>[1,6,2,3,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[3,1,2,4,6,5]=>[3,1,4,5,5,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,1,2,5,4,6]=>[3,1,4,6,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,2,5,6,4]=>[3,1,4,6,4,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[3,1,2,6,4,5]=>[4,2,5,1,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,1,2,6,5,4]=>[4,2,5,1,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,4,2,5,6]=>[5,3,1,3,1,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,1,4,2,6,5]=>[5,3,1,3,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,1,4,5,2,6]=>[5,3,1,6,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,1,4,5,6,2]=>[1,6,4,2,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,1,4,6,2,5]=>[6,4,2,1,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,1,4,6,5,2]=>[6,4,2,1,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,2,4,6]=>[6,4,3,3,1,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,1,5,2,6,4]=>[4,2,1,1,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[3,1,5,4,2,6]=>[4,2,1,3,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,1,5,4,6,2]=>[6,4,3,5,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,6,2,4]=>[1,6,5,2,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,1,5,6,4,2]=>[4,2,1,5,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,6,2,4,5]=>[3,1,1,6,5,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,1,6,2,5,4]=>[5,3,3,1,1,4]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,1,6,4,2,5]=>[3,1,1,1,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,1,6,4,5,2]=>[4,2,2,2,5,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,1,6,5,2,4]=>[4,2,2,3,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,1,6,5,4,2]=>[3,1,1,2,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[3,2,1,4,5,6]=>[2,1,1,5,3,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[3,2,1,4,6,5]=>[2,1,1,5,4,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,2,1,5,4,6]=>[2,1,1,6,1,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,2,1,5,6,4]=>[4,3,3,1,5,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,2,1,6,4,5]=>[3,2,2,1,1,4]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,2,1,6,5,4]=>[3,2,2,1,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[3,2,4,1,5,6]=>[4,3,6,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,2,4,1,6,5]=>[4,3,6,1,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,2,4,5,1,6]=>[3,2,5,4,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,4,5,6,1]=>[2,1,4,3,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[3,2,4,6,1,5]=>[6,5,1,1,1,3]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,2,4,6,5,1]=>[2,1,4,4,1,5]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,5,1,4,6]=>[6,5,2,2,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[3,2,5,1,6,4]=>[5,4,1,1,3,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[3,2,5,4,1,6]=>[5,4,1,4,2,3]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,2,5,4,6,1]=>[2,1,5,1,4,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,5,6,1,4]=>[2,1,5,3,4,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,2,5,6,4,1]=>[5,4,1,6,3,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,1,4,5]=>[2,1,6,4,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,1,5,4]=>[4,3,1,6,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,2,6,4,1,5]=>[4,3,1,2,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[3,2,6,4,5,1]=>[5,4,2,3,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,2,6,5,1,4]=>[5,4,2,4,1,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,2,6,5,4,1]=>[4,3,1,3,3,1]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[3,4,1,2,5,6]=>[1,2,5,2,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,4,1,2,6,5]=>[4,5,1,5,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[3,4,1,5,2,6]=>[4,5,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[3,4,1,5,6,2]=>[1,2,5,5,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[3,4,1,6,2,5]=>[5,6,2,3,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,4,1,6,5,2]=>[4,5,1,2,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,4,2,1,5,6]=>[4,5,2,3,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,2,1,6,5]=>[3,4,1,2,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[3,4,2,5,1,6]=>[5,6,3,1,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[3,4,2,5,6,1]=>[1,2,6,4,2,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,4,2,6,1,5]=>[4,5,2,1,6,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[3,4,2,6,5,1]=>[5,6,3,2,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,5,1,2,6]=>[1,2,2,4,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[3,4,5,1,6,2]=>[1,2,2,4,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,4,5,2,1,6]=>[4,5,5,1,3,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,4,5,2,6,1]=>[1,2,2,5,5,3]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[3,4,5,6,1,2]=>[1,2,2,2,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[3,4,5,6,2,1]=>[2,3,3,3,5,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[3,4,6,1,2,5]=>[1,2,3,3,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,4,6,1,5,2]=>[1,2,3,3,5,5]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[3,4,6,2,1,5]=>[2,3,4,5,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,4,6,2,5,1]=>[1,2,3,4,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,4,6,5,1,2]=>[2,3,4,1,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,4,6,5,2,1]=>[2,3,4,1,6,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[3,5,1,2,4,6]=>[1,3,4,2,3,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[3,5,1,2,6,4]=>[1,3,4,2,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,1,4,2,6]=>[6,1,2,2,4,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,1,4,6,2]=>[6,1,2,2,1,2]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[3,5,1,6,2,4]=>[6,1,2,4,2,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[3,5,1,6,4,2]=>[3,5,6,1,1,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[3,5,2,1,4,6]=>[6,1,3,5,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,5,2,1,6,4]=>[4,6,1,3,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[3,5,2,4,1,6]=>[6,1,3,1,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[3,5,2,4,6,1]=>[6,1,3,1,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[3,5,2,6,1,4]=>[6,1,3,3,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,5,2,6,4,1]=>[4,6,1,1,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[3,5,4,1,2,6]=>[4,6,3,1,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,4,1,6,2]=>[6,1,5,3,4,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,5,4,2,1,6]=>[3,5,2,1,2,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[3,5,4,2,6,1]=>[6,1,5,4,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[3,5,4,6,1,2]=>[2,4,1,4,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,5,4,6,2,1]=>[2,4,1,4,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,5,6,1,2,4]=>[1,3,2,3,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[3,5,6,1,4,2]=>[1,3,2,3,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[3,5,6,2,1,4]=>[2,4,3,5,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,5,6,2,4,1]=>[1,3,2,4,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,5,6,4,1,2]=>[1,3,2,6,5,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[3,5,6,4,2,1]=>[3,5,4,1,1,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[3,6,1,2,4,5]=>[1,4,3,2,3,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[3,6,1,2,5,4]=>[2,5,4,3,5,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,6,1,4,2,5]=>[6,2,1,2,4,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[3,6,1,4,5,2]=>[1,4,3,4,2,5]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[3,6,1,5,2,4]=>[6,2,1,3,3,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[3,6,1,5,4,2]=>[6,2,1,3,5,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,2,1,4,5]=>[5,1,1,4,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[3,6,2,1,5,4]=>[5,1,1,4,2,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,6,2,4,1,5]=>[6,2,2,1,3,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[3,6,2,4,5,1]=>[1,4,4,3,2,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[3,6,2,5,1,4]=>[5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[3,6,2,5,4,1]=>[5,1,1,1,4,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[3,6,4,1,2,5]=>[5,1,3,2,6,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,4,1,5,2]=>[5,1,3,2,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[3,6,4,2,1,5]=>[5,1,3,3,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[3,6,4,2,5,1]=>[5,1,3,3,1,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[3,6,4,5,1,2]=>[1,4,6,2,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[3,6,4,5,2,1]=>[5,1,3,6,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[3,6,5,1,2,4]=>[2,5,1,5,3,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[3,6,5,1,4,2]=>[5,1,4,1,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[3,6,5,2,1,4]=>[5,1,4,2,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[3,6,5,2,4,1]=>[6,2,5,3,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[3,6,5,4,1,2]=>[2,5,1,1,6,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[3,6,5,4,2,1]=>[3,6,2,2,1,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,2,3,5,6]=>[1,5,2,2,3,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[4,1,2,3,6,5]=>[2,6,3,3,5,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,2,5,3,6]=>[5,2,6,1,3,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[4,1,2,5,6,3]=>[1,5,2,4,2,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,2,6,3,5]=>[4,1,5,1,1,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[4,1,2,6,5,3]=>[4,1,5,1,3,2]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,3,2,5,6]=>[2,6,4,1,5,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,3,2,6,5]=>[4,1,6,3,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,1,3,5,2,6]=>[6,3,1,1,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[4,1,3,5,6,2]=>[1,5,3,3,2,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,1,3,6,2,5]=>[6,3,1,2,2,2]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[4,1,3,6,5,2]=>[6,3,1,2,5,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,1,5,2,3,6]=>[5,2,2,2,6,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,1,5,2,6,3]=>[4,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[4,1,5,3,2,6]=>[4,1,1,2,3,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,1,5,3,6,2]=>[5,2,2,3,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[4,1,5,6,2,3]=>[1,5,5,2,4,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,1,5,6,3,2]=>[4,1,1,5,1,3]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[4,1,6,2,3,5]=>[1,5,6,4,2,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,1,6,2,5,3]=>[5,2,3,1,1,3]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,1,6,3,2,5]=>[5,2,3,2,4,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,1,6,3,5,2]=>[4,1,2,1,6,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,1,6,5,2,3]=>[4,1,2,3,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,1,6,5,3,2]=>[4,1,2,3,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,2,1,3,5,6]=>[3,1,2,5,5,4]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,2,1,3,6,5]=>[3,1,2,5,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,2,1,5,3,6]=>[5,3,4,2,3,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,2,1,5,6,3]=>[4,2,3,1,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,2,1,6,3,5]=>[4,2,3,2,1,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,2,1,6,5,3]=>[3,1,2,1,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[4,2,3,1,5,6]=>[4,2,5,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,2,3,1,6,5]=>[3,1,4,1,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,2,3,5,1,6]=>[3,1,4,5,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,3,5,6,1]=>[1,6,2,3,2,3]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[4,2,3,6,1,5]=>[1,6,2,4,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,3,6,5,1]=>[5,3,6,1,4,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,2,5,1,3,6]=>[6,4,2,2,1,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,2,5,1,6,3]=>[5,3,1,1,3,2]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[4,2,5,3,1,6]=>[3,1,6,1,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,2,5,3,6,1]=>[6,4,2,4,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,2,5,6,1,3]=>[1,6,4,2,3,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,5,6,3,1]=>[5,3,1,6,2,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,2,6,1,3,5]=>[6,4,3,1,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,2,6,1,5,3]=>[4,2,1,6,1,2]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[4,2,6,3,1,5]=>[4,2,1,1,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[4,2,6,3,5,1]=>[6,4,3,3,1,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,2,6,5,1,3]=>[6,4,3,5,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,2,6,5,3,1]=>[4,2,1,3,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[4,3,1,2,5,6]=>[3,2,1,4,6,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[4,3,1,2,6,5]=>[4,3,2,5,1,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,3,1,5,2,6]=>[4,3,2,1,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[4,3,1,5,6,2]=>[5,4,3,2,6,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,1,6,2,5]=>[5,4,3,3,1,1]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[4,3,1,6,5,2]=>[4,3,2,2,3,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[4,3,2,1,5,6]=>[2,1,1,1,6,3]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[4,3,2,1,6,5]=>[3,2,2,2,1,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[4,3,2,5,1,6]=>[5,4,4,1,1,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[4,3,2,5,6,1]=>[2,1,1,5,3,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,2,6,1,5]=>[4,3,3,1,6,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,3,2,6,5,1]=>[2,1,1,6,1,5]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,3,5,1,2,6]=>[2,1,4,5,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,3,5,1,6,2]=>[6,5,1,2,4,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[4,3,5,2,1,6]=>[4,3,6,1,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,3,5,2,6,1]=>[6,5,1,3,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,3,5,6,1,2]=>[2,1,4,3,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,3,5,6,2,1]=>[2,1,4,3,5,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,3,6,1,2,5]=>[2,1,5,4,3,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[4,3,6,1,5,2]=>[6,5,2,1,3,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[4,3,6,2,1,5]=>[5,4,1,1,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,3,6,2,5,1]=>[5,4,1,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[4,3,6,5,1,2]=>[2,1,5,1,5,3]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[4,3,6,5,2,1]=>[2,1,5,1,6,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,5,1,2,3,6]=>[1,2,4,2,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[4,5,1,2,6,3]=>[1,2,4,2,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,5,1,3,2,6]=>[2,3,5,4,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,1,3,6,2]=>[1,2,4,3,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[4,5,1,6,2,3]=>[1,2,4,6,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,5,1,6,3,2]=>[5,6,1,3,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,1,3,6]=>[2,3,6,1,4,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,2,1,6,3]=>[4,5,1,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,5,2,3,1,6]=>[4,5,1,5,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,5,2,3,6,1]=>[1,2,5,2,4,3]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[4,5,2,6,1,3]=>[1,2,5,5,3,3]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,5,2,6,3,1]=>[4,5,1,1,1,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[4,5,3,1,2,6]=>[4,5,2,2,5,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[4,5,3,1,6,2]=>[3,4,1,1,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[4,5,3,2,1,6]=>[3,4,1,2,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[4,5,3,2,6,1]=>[4,5,2,3,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,5,3,6,1,2]=>[1,2,6,4,3,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[4,5,3,6,2,1]=>[5,6,3,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,5,6,1,2,3]=>[1,2,2,3,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[4,5,6,1,3,2]=>[2,3,3,4,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,5,6,2,1,3]=>[2,3,3,5,1,4]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,5,6,2,3,1]=>[1,2,2,4,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[4,5,6,3,1,2]=>[1,2,2,5,6,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[4,5,6,3,2,1]=>[2,3,3,6,1,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[4,6,1,2,3,5]=>[1,3,3,2,2,3]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[4,6,1,2,5,3]=>[1,3,3,2,4,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[4,6,1,3,2,5]=>[6,1,1,1,5,2]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,6,1,3,5,2]=>[6,1,1,1,1,3]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[4,6,1,5,2,3]=>[1,3,3,5,5,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[4,6,1,5,3,2]=>[6,1,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[4,6,2,1,3,5]=>[6,1,2,5,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[4,6,2,1,5,3]=>[6,1,2,5,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,2,3,1,5]=>[1,3,4,2,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,2,3,5,1]=>[1,3,4,2,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[4,6,2,5,1,3]=>[6,1,2,2,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[4,6,2,5,3,1]=>[6,1,2,2,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[4,6,3,1,2,5]=>[1,3,5,6,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,3,1,5,2]=>[4,6,1,2,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[4,6,3,2,1,5]=>[4,6,1,3,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[4,6,3,2,5,1]=>[6,1,3,5,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[4,6,3,5,1,2]=>[1,3,5,3,4,2]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,6,3,5,2,1]=>[6,1,3,1,3,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[4,6,5,1,2,3]=>[2,4,1,5,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[4,6,5,1,3,2]=>[2,4,1,5,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[4,6,5,2,1,3]=>[2,4,1,6,1,4]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[4,6,5,2,3,1]=>[4,6,3,1,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[4,6,5,3,1,2]=>[3,5,2,1,1,4]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[4,6,5,3,2,1]=>[3,5,2,1,2,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,1,2,3,4,6]=>[1,4,2,2,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[5,1,2,3,6,4]=>[1,4,2,2,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,2,4,3,6]=>[2,5,3,4,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,1,2,4,6,3]=>[1,4,2,3,3,5]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,1,2,6,3,4]=>[1,4,2,5,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[5,1,2,6,4,3]=>[5,1,6,2,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,2,4,6]=>[6,2,1,5,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[5,1,3,2,6,4]=>[6,2,1,5,3,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,4,2,6]=>[1,4,3,2,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,3,4,6,2]=>[1,4,3,2,3,4]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,1,3,6,2,4]=>[6,2,1,2,2,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[5,1,3,6,4,2]=>[6,2,1,2,4,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,4,2,3,6]=>[5,1,1,3,6,1]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[5,1,4,2,6,3]=>[5,1,1,3,2,2]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[5,1,4,3,2,6]=>[5,1,1,4,4,2]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,1,4,3,6,2]=>[5,1,1,4,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[5,1,4,6,2,3]=>[1,4,4,3,4,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,1,4,6,3,2]=>[6,2,2,1,3,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,1,6,2,3,4]=>[1,4,6,4,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,1,6,2,4,3]=>[6,2,4,2,1,5]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,1,6,3,2,4]=>[6,2,4,3,5,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,1,6,3,4,2]=>[5,1,3,2,6,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,1,6,4,2,3]=>[3,6,1,1,1,4]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[5,1,6,4,3,2]=>[3,6,1,1,2,2]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,2,1,3,4,6]=>[2,6,1,4,3,4]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[5,2,1,3,6,4]=>[6,3,5,1,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,1,4,3,6]=>[5,2,4,1,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,2,1,4,6,3]=>[6,3,5,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,1,6,3,4]=>[4,1,3,2,1,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,2,1,6,4,3]=>[4,1,3,2,2,3]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,2,3,1,4,6]=>[1,5,2,6,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,2,3,1,6,4]=>[4,1,5,2,2,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,2,3,4,1,6]=>[4,1,5,5,1,2]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,2,3,4,6,1]=>[1,5,2,2,3,3]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[5,2,3,6,1,4]=>[1,5,2,4,3,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[5,2,3,6,4,1]=>[5,2,6,1,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,2,4,1,3,6]=>[6,3,1,3,1,2]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[5,2,4,1,6,3]=>[4,1,6,1,2,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,2,4,3,1,6]=>[4,1,6,3,2,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,2,4,3,6,1]=>[6,3,1,5,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,2,4,6,1,3]=>[6,3,1,1,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[5,2,4,6,3,1]=>[6,3,1,1,3,4]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,2,6,1,3,4]=>[1,5,5,3,3,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[5,2,6,1,4,3]=>[6,3,3,1,2,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,2,6,3,1,4]=>[5,2,2,2,3,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[5,2,6,3,4,1]=>[4,1,1,1,5,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[5,2,6,4,1,3]=>[4,1,1,2,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,2,6,4,3,1]=>[4,1,1,2,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,3,1,2,4,6]=>[3,1,1,4,5,5]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[5,3,1,2,6,4]=>[4,2,2,5,1,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,3,1,4,2,6]=>[5,3,3,1,3,2]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[5,3,1,4,6,2]=>[6,4,4,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,3,1,6,2,4]=>[3,1,1,1,6,5]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[5,3,1,6,4,2]=>[3,1,1,1,1,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[5,3,2,1,4,6]=>[3,1,2,2,6,5]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,3,2,1,6,4]=>[3,1,2,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[5,3,2,4,1,6]=>[4,2,3,6,1,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,2,4,6,1]=>[6,4,5,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[5,3,2,6,1,4]=>[6,4,5,3,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,2,6,4,1]=>[4,2,3,1,2,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,3,4,1,2,6]=>[4,2,5,1,5,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[5,3,4,1,6,2]=>[5,3,6,2,3,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,4,2,1,6]=>[3,1,4,1,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,3,4,2,6,1]=>[4,2,5,2,1,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[5,3,4,6,1,2]=>[1,6,2,3,3,2]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,3,4,6,2,1]=>[3,1,4,5,6,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,3,6,1,2,4]=>[1,6,4,3,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[5,3,6,1,4,2]=>[6,4,2,1,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,3,6,2,1,4]=>[5,3,1,1,4,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,3,6,2,4,1]=>[6,4,2,2,1,3]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,3,6,4,1,2]=>[5,3,1,3,2,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,3,6,4,2,1]=>[3,1,6,1,1,2]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[5,4,1,2,3,6]=>[2,1,6,3,3,5]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,4,1,2,6,3]=>[4,3,1,5,1,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[5,4,1,3,2,6]=>[4,3,1,6,3,1]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[5,4,1,3,6,2]=>[6,5,3,1,2,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,4,1,6,2,3]=>[5,4,2,3,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,1,6,3,2]=>[4,3,1,2,1,3]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[5,4,2,1,3,6]=>[3,2,1,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,4,2,1,6,3]=>[4,3,2,3,2,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[5,4,2,3,1,6]=>[3,2,1,4,1,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[5,4,2,3,6,1]=>[3,2,1,4,6,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,2,6,1,3]=>[6,5,4,3,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,4,2,6,3,1]=>[4,3,2,1,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[5,4,3,1,2,6]=>[4,3,3,2,5,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,4,3,1,6,2]=>[3,2,2,1,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[5,4,3,2,1,6]=>[3,2,2,2,2,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[5,4,3,2,6,1]=>[2,1,1,1,6,4]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,4,3,6,1,2]=>[2,1,1,5,4,3]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,4,3,6,2,1]=>[2,1,1,5,5,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[5,4,6,1,2,3]=>[2,1,4,4,3,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,4,6,1,3,2]=>[2,1,4,4,4,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[5,4,6,2,1,3]=>[2,1,4,5,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[5,4,6,2,3,1]=>[3,2,5,6,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,6,3,1,2]=>[4,3,6,1,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,4,6,3,2,1]=>[2,1,4,6,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[5,6,1,2,3,4]=>[1,2,3,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[5,6,1,2,4,3]=>[2,3,4,3,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[5,6,1,3,2,4]=>[2,3,4,4,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[5,6,1,3,4,2]=>[1,2,3,3,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[5,6,1,4,2,3]=>[1,2,3,4,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[5,6,1,4,3,2]=>[2,3,4,5,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,6,2,1,3,4]=>[2,3,5,1,4,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,6,2,1,4,3]=>[2,3,5,1,5,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[5,6,2,3,1,4]=>[1,2,4,2,6,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[5,6,2,3,4,1]=>[1,2,4,2,2,5]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[5,6,2,4,1,3]=>[1,2,4,3,5,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[5,6,2,4,3,1]=>[3,4,6,5,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,3,1,2,4]=>[1,2,5,6,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[5,6,3,1,4,2]=>[5,6,2,3,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[5,6,3,2,1,4]=>[2,3,6,1,1,5]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[5,6,3,2,4,1]=>[4,5,1,3,6,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[5,6,3,4,1,2]=>[1,2,5,2,5,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[5,6,3,4,2,1]=>[4,5,1,5,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[5,6,4,1,2,3]=>[1,2,6,5,2,2]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[5,6,4,1,3,2]=>[4,5,2,1,6,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[5,6,4,2,1,3]=>[3,4,1,1,2,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[5,6,4,2,3,1]=>[3,4,1,1,4,1]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[5,6,4,3,1,2]=>[3,4,1,2,1,4]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[5,6,4,3,2,1]=>[3,4,1,2,2,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,1,2,3,4,5]=>[1,3,2,2,2,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[6,1,2,3,5,4]=>[2,4,3,3,4,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,1,2,4,3,5]=>[2,4,3,4,1,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,1,2,4,5,3]=>[1,3,2,3,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[6,1,2,5,3,4]=>[1,3,2,4,6,2]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,1,2,5,4,3]=>[2,4,3,5,1,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,1,3,2,4,5]=>[2,4,4,1,4,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,1,3,2,5,4]=>[2,4,4,1,5,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[6,1,3,4,2,5]=>[1,3,3,2,6,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,1,3,4,5,2]=>[1,3,3,2,2,5]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[6,1,3,5,2,4]=>[6,1,1,1,3,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[6,1,3,5,4,2]=>[6,1,1,1,5,4]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[6,1,4,2,3,5]=>[1,3,4,6,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,1,4,2,5,3]=>[6,1,2,4,2,4]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,1,4,3,2,5]=>[2,4,5,1,1,5]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,1,4,3,5,2]=>[6,1,2,5,1,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,1,4,5,2,3]=>[1,3,4,2,5,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[6,1,4,5,3,2]=>[3,5,6,4,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,5,2,3,4]=>[1,3,5,5,2,2]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[6,1,5,2,4,3]=>[6,1,3,3,1,5]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,1,5,3,2,4]=>[6,1,3,4,5,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,1,5,3,4,2]=>[4,6,1,2,5,2]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[6,1,5,4,2,3]=>[4,6,1,3,2,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,1,5,4,3,2]=>[2,4,6,1,1,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,2,1,3,4,5]=>[2,5,1,4,3,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,2,1,3,5,4]=>[2,5,1,4,4,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[6,2,1,4,3,5]=>[2,5,1,5,1,4]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[6,2,1,4,5,3]=>[5,1,4,1,6,3]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,1,5,3,4]=>[5,1,4,2,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,1,5,4,3]=>[2,5,1,6,1,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,2,3,1,4,5]=>[1,4,2,6,4,2]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,2,3,1,5,4]=>[5,1,6,3,2,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,3,4,1,5]=>[1,4,2,2,5,5]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,2,3,4,5,1]=>[1,4,2,2,2,4]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[6,2,3,5,1,4]=>[1,4,2,3,4,4]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,2,3,5,4,1]=>[2,5,3,4,1,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,4,1,3,5]=>[6,2,1,3,1,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,2,4,1,5,3]=>[6,2,1,3,3,4]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,2,4,3,1,5]=>[6,2,1,5,4,3]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,2,4,3,5,1]=>[6,2,1,5,1,2]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[6,2,4,5,1,3]=>[1,4,3,2,4,3]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[6,2,4,5,3,1]=>[3,6,5,4,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,2,5,1,3,4]=>[1,4,4,4,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[6,2,5,1,4,3]=>[5,1,1,1,1,4]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[6,2,5,3,1,4]=>[5,1,1,3,3,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[6,2,5,3,4,1]=>[5,1,1,3,6,2]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,2,5,4,1,3]=>[6,2,2,5,3,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,2,5,4,3,1]=>[5,1,1,4,4,3]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,3,1,2,4,5]=>[1,5,6,2,3,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,1,2,5,4]=>[5,2,3,6,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,1,4,2,5]=>[5,2,3,1,3,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[6,3,1,4,5,2]=>[5,2,3,1,6,2]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,3,1,5,2,4]=>[4,1,2,1,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,3,1,5,4,2]=>[4,1,2,1,3,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,3,2,1,4,5]=>[2,6,1,1,5,3]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,2,1,5,4]=>[4,1,3,3,1,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[6,3,2,4,1,5]=>[4,1,3,6,1,1]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[6,3,2,4,5,1]=>[2,6,1,4,3,5]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,3,2,5,1,4]=>[5,2,4,1,1,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,3,2,5,4,1]=>[5,2,4,1,4,2]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[6,3,4,1,2,5]=>[1,5,2,5,2,4]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,3,4,1,5,2]=>[4,1,5,1,1,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[6,3,4,2,1,5]=>[4,1,5,2,3,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,3,4,2,5,1]=>[5,2,6,3,1,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[6,3,4,5,1,2]=>[1,5,2,2,4,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,3,4,5,2,1]=>[4,1,5,5,1,3]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,3,5,1,2,4]=>[1,5,3,4,2,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[6,3,5,1,4,2]=>[6,3,1,2,2,4]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[6,3,5,2,1,4]=>[6,3,1,3,5,2]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,3,5,2,4,1]=>[6,3,1,3,1,3]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[6,3,5,4,1,2]=>[4,1,6,3,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,3,5,4,2,1]=>[4,1,6,3,2,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,4,1,2,3,5]=>[1,6,5,2,2,3]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[6,4,1,2,5,3]=>[5,3,2,6,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[6,4,1,3,2,5]=>[6,4,3,1,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,1,3,5,2]=>[6,4,3,1,1,3]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[6,4,1,5,2,3]=>[4,2,1,1,1,5]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[6,4,1,5,3,2]=>[4,2,1,1,2,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,2,1,3,5]=>[3,1,1,2,5,5]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[6,4,2,1,5,3]=>[4,2,2,3,1,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,4,2,3,1,5]=>[4,2,2,5,2,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[6,4,2,3,5,1]=>[3,1,1,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,4,2,5,1,3]=>[6,4,4,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[6,4,2,5,3,1]=>[3,1,1,6,1,1]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[6,4,3,1,2,5]=>[3,1,2,1,4,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,4,3,1,5,2]=>[4,2,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,4,3,2,1,5]=>[4,2,3,3,3,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[6,4,3,2,5,1]=>[5,3,4,4,1,1]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[6,4,3,5,1,2]=>[3,1,2,5,6,4]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,3,5,2,1]=>[4,2,3,6,1,3]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,4,5,1,2,3]=>[1,6,2,4,2,2]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[6,4,5,1,3,2]=>[3,1,4,6,5,2]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,5,2,1,3]=>[4,2,5,1,3,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,4,5,2,3,1]=>[4,2,5,1,5,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[6,4,5,3,1,2]=>[3,1,4,1,1,4]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[6,4,5,3,2,1]=>[3,1,4,1,2,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,5,1,2,3,4]=>[2,1,5,3,3,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[6,5,1,2,4,3]=>[2,1,5,3,4,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,5,1,3,2,4]=>[2,1,5,4,1,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[6,5,1,3,4,2]=>[3,2,6,5,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,1,4,2,3]=>[5,4,1,1,3,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[6,5,1,4,3,2]=>[2,1,5,5,1,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[6,5,2,1,3,4]=>[2,1,6,1,4,3]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[6,5,2,1,4,3]=>[2,1,6,1,5,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[6,5,2,3,1,4]=>[5,4,2,6,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[6,5,2,3,4,1]=>[4,3,1,5,5,1]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[6,5,2,4,1,3]=>[6,5,3,1,3,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[6,5,2,4,3,1]=>[4,3,1,6,3,2]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,3,1,2,4]=>[3,2,1,1,4,5]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[6,5,3,1,4,2]=>[3,2,1,1,6,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[6,5,3,2,1,4]=>[3,2,1,2,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[6,5,3,2,4,1]=>[4,3,2,3,6,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[6,5,3,4,1,2]=>[4,3,2,5,1,5]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[6,5,3,4,2,1]=>[3,2,1,4,1,2]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,5,4,1,2,3]=>[2,1,1,6,3,3]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[6,5,4,1,3,2]=>[2,1,1,6,4,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[6,5,4,2,1,3]=>[3,2,2,1,2,5]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[6,5,4,2,3,1]=>[3,2,2,1,4,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[6,5,4,3,1,2]=>[3,2,2,2,1,4]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[6,5,4,3,2,1]=>[2,1,1,1,1,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
Map
repeats to leading
Description
The unique parking function obtained by computing successive differences to obtain a Prüfer code, then prepending 0 and cyclically shifting.
Pollak's map [1] sends a parking function $(p_1,\dots,p_n)$ to the Prüfer code $(c_1,\dots,c_{n-1})$ with $c_i = p_{i+1} - p_i \pmod{n+1}$.
Let $c_0 = 0$. This map returns the unique parking function $(q_1,\dots,q_n)$ such that $q_i - c_{i-1}$ is constant modulo $n+1$, see [2, sec 4].
This map sends the number of repeated elements to the number of occurrences of the first element.
Pollak's map [1] sends a parking function $(p_1,\dots,p_n)$ to the Prüfer code $(c_1,\dots,c_{n-1})$ with $c_i = p_{i+1} - p_i \pmod{n+1}$.
Let $c_0 = 0$. This map returns the unique parking function $(q_1,\dots,q_n)$ such that $q_i - c_{i-1}$ is constant modulo $n+1$, see [2, sec 4].
This map sends the number of repeated elements to the number of occurrences of the first element.
Map
to Dyck path
Description
Sends a parking function to its support Dyck word.
Map
Cori-Le Borgne involution
Description
The Cori-Le Borgne involution on Dyck paths.
Append an additional down step to the Dyck path and consider its (literal) reversal. The image of the involution is then the unique rotation of this word which is a Dyck word followed by an additional down step. Alternatively, it is the composite $\zeta\circ\mathrm{rev}\circ\zeta^{(-1)}$, where $\zeta$ is Mp00030zeta map.
Append an additional down step to the Dyck path and consider its (literal) reversal. The image of the involution is then the unique rotation of this word which is a Dyck word followed by an additional down step. Alternatively, it is the composite $\zeta\circ\mathrm{rev}\circ\zeta^{(-1)}$, where $\zeta$ is Mp00030zeta map.
searching the database
Sorry, this map was not found in the database.