Identifier
Mp00124:
Dyck paths
—Adin-Bagno-Roichman transformation⟶
Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2
[1,0]=>[1,0]=>[1,0]=>[1]
[1,0,1,0]=>[1,0,1,0]=>[1,0,1,0]=>[1,1]
[1,1,0,0]=>[1,1,0,0]=>[1,1,0,0]=>[2]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[1,1,1]
[1,0,1,1,0,0]=>[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[2,1]
[1,1,0,0,1,0]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,2]
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,1]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[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]=>[1,1,1,1]
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[2,1,1]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[1,2,1]
[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[2,1,1]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[3,1]
[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[1,1,2]
[1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[2,2]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,2,1]
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[2,1,1]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[3,1]
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[1,3]
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,2]
[1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[3,1]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,1,2]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,2,2]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[2,1,2]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[3,2]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,4]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,3]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[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]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[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]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,1,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[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]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[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]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,3]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,2]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[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]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,2]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,2]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,2]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,2,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,3,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,2,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,4,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,2,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,1,1,1,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,1,1,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,1,1,1,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,1,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,2,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,4,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,1,1,1,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,1,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,5,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,4,1,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,3,1,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,1,1,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,2,2,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,2,1,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,2,1,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,1,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,2,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,2,2,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,1,2,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,3,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,3,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,4,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,4,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,3,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[4,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,4,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,1,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,5,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,4,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,3,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,1,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,1,3,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,1,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,2,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,3,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,3,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,4,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,4,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,4,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,3,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,2,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,4,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,2,3,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,2,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,2,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,3,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,4,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,3,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,4,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,3,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,4,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,4,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,3,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,2,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,6,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,2,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,2,1,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,1,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,4,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,1,1,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,2,1,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,2,2,1,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,3,1,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,4,1,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,1,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,3,1,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,1,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,1,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,3,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,4,1,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,1,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,4,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,1,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,2,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,4,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,3,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,3,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,4,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,3,2,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,3,1,1]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,2,1,1]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,1,1,1]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,1,3,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,3,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,2,3,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,3,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,3,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,3,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,3,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,3,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,3,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,3,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,3,1,1]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,2,1,1]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,1,1]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,4,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,4,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,3,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,2,2,1]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,3,1,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,2,1,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,1,2,1]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,4,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,4,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,3,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,3,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,4,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,1,1,1]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,3,1,1]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,2,1,1]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,1,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,5,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,3,3,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,2,3,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,3,1]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,3,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,4,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,2,1]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,1]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,2,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,5,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,3,1,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,2,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,1,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,4,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,2,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,4,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,3]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,3,1,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,2,1,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,2,1,2]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,3,1,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,2,1,1,2]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,1,1,2]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,4,1,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,3,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,2]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,4,1,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,1,2]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,1,2]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,1,2]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,3,2]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,2,2]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,1,2]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,2,3,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,2,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,3,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,2,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,2,1]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,1]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,3,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,4,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,2,1,1]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,1,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,4,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,4,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,4,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,3,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,3,1]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,3,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,3,1]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,2,2,1]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,1,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,2,1,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,1,1,2,1]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,4,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,4,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,1,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,1,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,1,1,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,5,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,5,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,1]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,2,3,1]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,3,1]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,2,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,2,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,3,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,2,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,1,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,6,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,5,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,2,1]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,3,1,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,2,1,3]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,1,3]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,3]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,3]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,3,2]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,3,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,3,1,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,2,1,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,2,1,2]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,2,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,1,1,2]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,1,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,1,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,4,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,3,2]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,2,2]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,1,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,1,2]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,1,2]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,1,1,2]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,1,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,2]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,3,2]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,2,2]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,2]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,4,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,4,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,3,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,3,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,3,1]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,3,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,3,1]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,3,2,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,2,2,1]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,1,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,2,1,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,4,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,4,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,2,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,2,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,1,2,1,1]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,5,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,5,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,5,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,1]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,3,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,2,3,1]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,3,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,4,2,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,2,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,2,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,2,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,2,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,5,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,3,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,1,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,6,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,5,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,1]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,3,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,2,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,2,3]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,1,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,1,3]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,1,1,3]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,3]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,3]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,3]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,4,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,3,2]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,2,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,2]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,2,2]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,2,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,4,1,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,1,2]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,1,2]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,1,2]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,5,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,2]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,2,2]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,5,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,5,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,1]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,3,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,2,3,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,1,3,1]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,1,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,5,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,3,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,2,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,1,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,6,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,5,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,4]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,4]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,4]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,4,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,3]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,3]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,1,3]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,5,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,2]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,2,2]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,6,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,5,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,2,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,5]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,3]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,7,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,10]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,8,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,6,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,7,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,1,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,1]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,7]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,2]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,7,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,8]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,8]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,8,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[6,2,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,3,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,1]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,6,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,2,1,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,1,1,2,1]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,2,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,3,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,2,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,6,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,1,1,1,1,1,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,3]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,2]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,1,1,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,1,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,1,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,3,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,3,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,3,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,3,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,2,2]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,1]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,1]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,1,1,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,3]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,4]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,9,1]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,4]
Map
Adin-Bagno-Roichman transformation
Description
The Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.
This is a bijection preserving the number of up steps before each peak and sending the number of returns to the number of up steps after the last double up step.
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
searching the database
Sorry, this map was not found in the database.