Identifier
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2
[1,0]=>[1,0]=>[1,1,0,0]=>[2,1]
[1,0,1,0]=>[1,0,1,0]=>[1,1,0,1,0,0]=>[2,3,1]
[1,1,0,0]=>[1,1,0,0]=>[1,1,1,0,0,0]=>[3,2,1]
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[2,3,4,1]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[3,2,4,1]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0]=>[2,4,3,1]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[3,4,2,1]
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]
[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]
[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]
[1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]
[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]
[1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]
[1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]
[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]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]
[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]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,2,4,6,5,7,8,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]
[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]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]
[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]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,4,6,2,7,8,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,3,6,2,7,8,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]
[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]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]
[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]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,2,6,5,4,7,8,1]
[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]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,5,3,7,8,1]
[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]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,1]
[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]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,3,6,5,2,7,8,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,4,3,7,8,1]
[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]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,1]
[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]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,6,5,3,2,7,8,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,6,4,3,2,7,8,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,7,6,8,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,2,5,7,6,8,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,3,2,5,7,6,8,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,3,7,6,8,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]
[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]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,4,2,7,6,8,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,5,3,2,7,6,8,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]
[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]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,2,4,6,7,5,8,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]
[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]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[4,3,2,6,7,5,8,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,2,8,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]
[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]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]
[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]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,6,5,7,4,8,1]
[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]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]
[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]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]
[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]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]
[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]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,5,6,4,7,3,8,1]
[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]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,6,5,4,7,3,8,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]
[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]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,4,3,7,2,8,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]
[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]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,5,7,6,4,8,1]
[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]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,5,7,6,4,8,1]
[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]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,6,3,8,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,6,2,8,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,3,5,7,6,2,8,1]
[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]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]
[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]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,3,7,6,2,8,1]
[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]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,4,3,7,6,2,8,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,5,4,8,1]
[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]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]
[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]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]
[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]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,4,6,7,3,2,8,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,5,7,4,3,8,1]
[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]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,6,5,7,4,2,8,1]
[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]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,6,4,7,3,2,8,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]
[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]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]
[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]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,2,7,6,5,4,8,1]
[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]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,4,7,6,5,3,8,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]
[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]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[4,3,7,6,5,2,8,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,5,7,6,4,3,8,1]
[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]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,5,7,6,3,2,8,1]
[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]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,4,7,6,3,2,8,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,6,7,5,4,3,8,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,6,7,5,4,2,8,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,4,3,2,8,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,6,5,4,2,8,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]
[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]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,5,4,6,8,7,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,5,4,6,8,7,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,8,7,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,2,6,8,7,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,3,5,2,6,8,7,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]
[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]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,5,4,2,6,8,7,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,8,7,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,5,8,7,1]
[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]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,2,4,6,5,8,7,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]
[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]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,6,4,8,7,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,2,5,6,4,8,7,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[4,3,5,6,2,8,7,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,5,4,6,3,8,7,1]
[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]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,4,6,2,8,7,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]
[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]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,5,4,8,7,1]
[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]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]
[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]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]
[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]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,4,6,5,2,8,7,1]
[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]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,5,6,4,3,8,7,1]
[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]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,5,4,3,8,7,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,6,5,4,2,8,7,1]
[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]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,4,3,2,8,7,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,7,8,6,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,2,5,7,8,6,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,7,8,6,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,2,7,8,6,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,2,7,8,6,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]
[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]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,4,2,7,8,6,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,3,2,7,8,6,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,4,6,7,8,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,6,7,8,5,1]
[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]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,2,6,7,8,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,6,7,8,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]
[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]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,3,6,7,8,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,4,1]
[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]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,2,6,5,7,8,4,1]
[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]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]
[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]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]
[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]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,6,3,7,8,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,2,1]
[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]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[4,6,5,3,7,8,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,4,3,7,8,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,2,4,7,6,8,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,3,7,6,8,5,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,4,2,7,6,8,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,3,2,7,6,8,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,7,6,8,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]
[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]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]
[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]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,4,3,7,6,8,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,5,8,4,1]
[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]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,6,7,5,8,4,1]
[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]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,5,8,3,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,5,8,2,1]
[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]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,3,6,7,5,8,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,5,7,4,8,3,1]
[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]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,5,7,4,8,2,1]
[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]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,5,7,3,8,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,4,7,3,8,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,7,6,5,8,4,1]
[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]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,2,7,6,5,8,4,1]
[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]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]
[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]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]
[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]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,5,7,6,4,8,3,1]
[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]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,6,4,8,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,6,3,8,2,1]
[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]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,5,4,8,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,5,4,8,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,5,3,8,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,5,8,7,6,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,3,5,8,7,6,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,2,5,8,7,6,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,8,7,6,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,5,4,8,7,6,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,2,8,7,6,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]
[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]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,5,4,2,8,7,6,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,8,7,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,2,4,6,8,7,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]
[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]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,6,8,7,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,5,6,8,7,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,7,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,5,4,6,8,7,3,1]
[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]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,5,4,6,8,7,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]
[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]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,2,6,5,8,7,4,1]
[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]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]
[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]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,4,6,5,8,7,2,1]
[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]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,4,8,7,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,4,6,3,8,7,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,5,4,8,7,3,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]
[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]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,5,3,8,7,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,7,8,6,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,4,3,7,8,6,5,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]
[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]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]
[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]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,6,7,8,5,4,1]
[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]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,4,3,1]
[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]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,5,7,8,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,7,6,8,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,2,7,6,8,5,4,1]
[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]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,4,7,6,8,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,6,8,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,7,6,8,5,2,1]
[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]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,5,7,6,8,4,3,1]
[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]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,6,5,8,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,5,8,7,6,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,8,7,6,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,3,5,8,7,6,2,1]
[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]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]
[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]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,5,4,8,7,6,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,3,8,7,6,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,7,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]
[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]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,6,8,7,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,3,6,8,7,5,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,5,6,8,7,4,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,8,7,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,6,5,8,7,4,3,1]
[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]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,5,8,7,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,6,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]
[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]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,4,7,8,6,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]
[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]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,5,7,8,6,4,3,1]
[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]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]
[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]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]
[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]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,5,8,7,6,4,3,1]
[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]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,4,8,7,6,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,9,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,5,4,6,7,8,9,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,9,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,9,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,9,1]
[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]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,9,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,9,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,9,1]
[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]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,9,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,9,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,9,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,9,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,9,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,9,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,9,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,9,1]
[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]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,9,1]
[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]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,2,6,5,4,7,8,9,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,9,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,6,4,3,7,8,9,1]
[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]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,6,4,2,7,8,9,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,9,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,9,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,9,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,9,1]
[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]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[4,6,5,3,2,7,8,9,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,6,4,3,2,7,8,9,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,7,6,8,9,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,7,6,8,9,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,7,6,8,9,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,7,6,8,9,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,5,3,7,6,8,9,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,4,6,7,5,8,9,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,7,4,8,9,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,7,2,8,9,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,7,2,8,9,1]
[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]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,6,5,7,4,8,9,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,6,3,7,2,8,9,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,6,3,7,2,8,9,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,4,3,7,2,8,9,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,4,7,6,5,8,9,1]
[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]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,3,5,7,6,4,8,9,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,5,7,6,2,8,9,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,6,7,5,4,8,9,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,4,6,7,5,2,8,9,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,7,4,3,8,9,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,7,4,2,8,9,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,7,3,2,8,9,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,4,7,3,2,8,9,1]
[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]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,2,7,6,5,4,8,9,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,4,7,6,5,2,8,9,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,5,7,6,3,2,8,9,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,7,6,5,4,3,8,9,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[4,7,6,5,3,2,8,9,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[5,7,6,4,3,2,8,9,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[6,7,5,4,3,2,8,9,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,7,9,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,6,8,7,9,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,8,7,9,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,8,7,9,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,5,3,6,2,8,7,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,5,7,8,6,9,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,5,7,8,6,9,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,4,7,8,6,9,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,4,7,8,6,9,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,7,8,6,9,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,8,3,9,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,2,9,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,8,2,9,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,8,2,9,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,8,2,9,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,6,4,7,8,3,9,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,6,3,7,8,2,9,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[6,5,4,3,7,8,2,9,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,3,7,6,8,5,9,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,2,7,6,8,5,9,1]
[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]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,7,6,8,2,9,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,6,5,7,4,8,3,9,1]
[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]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,6,5,7,3,8,2,9,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,4,7,3,8,2,9,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,6,5,4,3,8,2,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,5,8,7,6,9,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,5,8,7,6,9,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,6,8,7,2,9,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,4,7,8,6,5,9,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,5,7,8,6,2,9,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,8,4,3,9,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,8,4,2,9,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,8,3,2,9,1]
[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]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[3,5,7,6,8,4,2,9,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[4,7,6,5,8,3,2,9,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[7,6,5,4,8,3,2,9,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,4,8,7,6,5,9,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[4,3,2,8,7,6,5,9,1]
[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]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,4,5,8,7,6,3,9,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,5,8,7,6,2,9,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[4,5,6,8,7,3,2,9,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,5,7,8,6,3,2,9,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,6,5,8,4,3,2,9,1]
[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]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,8,7,6,5,4,9,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,2,8,7,6,5,4,9,1]
[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]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,4,8,7,6,5,2,9,1]
[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]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[3,5,8,7,6,4,2,9,1]
[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]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,5,8,7,6,3,2,9,1]
[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]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[3,6,8,7,5,4,2,9,1]
[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]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[6,5,8,7,4,3,2,9,1]
[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]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,7,8,6,5,4,3,9,1]
[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]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[4,7,8,6,5,3,2,9,1]
[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]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,8,5,4,3,2,9,1]
[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]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,6,8,5,4,3,2,9,1]
[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]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,8,7,6,5,4,3,9,1]
[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]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,8,7,6,5,4,2,9,1]
[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]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[4,8,7,6,5,3,2,9,1]
[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]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[5,8,7,6,4,3,2,9,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,8,7,5,4,3,2,9,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,6,5,4,3,2,9,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,7,9,8,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,7,9,8,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,7,9,8,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,7,9,8,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,6,7,9,8,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,3,6,7,9,8,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,2,6,7,9,8,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,7,9,8,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,6,5,7,9,8,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,6,2,7,9,8,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,6,3,2,7,9,8,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[3,6,5,4,2,7,9,8,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,9,8,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[6,5,4,3,2,7,9,8,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,5,7,6,9,8,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,9,8,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,9,8,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,7,2,9,8,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,3,5,6,7,2,9,8,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,6,3,7,2,9,8,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,7,6,5,9,8,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,7,3,2,9,8,1]
[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]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[3,6,5,7,4,2,9,8,1]
[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]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,7,6,5,4,9,8,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,5,7,6,3,2,9,8,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[2,6,7,5,4,3,9,8,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[6,5,7,4,3,2,9,8,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,7,6,5,4,3,9,8,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[3,7,6,5,4,2,9,8,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[4,7,6,5,3,2,9,8,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,5,4,3,2,9,8,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,6,5,4,3,2,9,8,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,7,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,6,8,9,7,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,6,8,9,7,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,6,8,9,7,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,2,5,6,8,9,7,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,4,6,8,9,7,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,6,8,9,7,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,2,6,8,9,7,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[2,5,4,3,6,8,9,7,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,3,2,6,8,9,7,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,5,8,9,7,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,8,9,7,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,5,4,6,3,8,9,7,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,6,3,2,8,9,7,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,4,3,2,8,9,7,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,6,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,4,5,7,8,9,6,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,3,5,7,8,9,6,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,2,5,7,8,9,6,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,7,8,9,6,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,4,7,8,9,6,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,7,8,9,6,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[2,5,4,3,7,8,9,6,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,4,6,7,8,9,5,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,9,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,9,2,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,9,3,1]
[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]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,9,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,3,6,7,8,9,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,9,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,9,4,1]
[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]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,2,6,5,7,8,9,4,1]
[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]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,9,2,1]
[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]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,9,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,9,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,9,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,9,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,6,3,7,8,9,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,9,3,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,9,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,6,4,3,7,8,9,2,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,7,6,8,9,5,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,7,6,8,9,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,6,7,5,8,9,4,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,7,4,8,9,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,7,4,8,9,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,7,3,8,9,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[2,6,5,7,4,8,9,3,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,6,4,7,3,8,9,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,7,6,5,8,9,4,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,4,7,6,5,8,9,2,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[3,6,7,5,4,8,9,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,7,4,3,8,9,2,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[3,7,6,5,4,8,9,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[4,7,6,5,3,8,9,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,7,6,4,3,8,9,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[6,7,5,4,3,8,9,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[7,6,5,4,3,8,9,2,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,8,7,9,6,1]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,3,2,5,8,7,9,6,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,3,6,8,7,9,5,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,6,8,7,9,2,1]
[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]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,8,7,9,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,4,3,6,8,7,9,2,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,7,8,6,9,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,3,7,8,6,9,5,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,3,5,7,8,6,9,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,8,5,9,4,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,8,5,9,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,8,4,9,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,8,4,9,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,8,3,9,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,8,3,9,2,1]
[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]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,4,7,6,8,5,9,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[3,6,7,5,8,4,9,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,5,7,4,8,3,9,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[2,7,6,5,8,4,9,3,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,8,7,6,9,5,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,5,8,7,6,9,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,4,6,8,7,3,9,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,6,4,8,7,3,9,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,5,4,8,7,3,9,2,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,4,7,8,6,5,9,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,8,5,4,9,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,8,5,4,9,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,8,5,3,9,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,8,4,3,9,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[4,7,6,8,5,3,9,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[6,7,5,8,4,3,9,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[7,6,5,8,4,3,9,2,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,2,8,7,6,5,9,4,1]
[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]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,4,8,7,6,5,9,2,1]
[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]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,3,8,7,6,5,9,2,1]
[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]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[3,7,8,6,5,4,9,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,8,5,4,3,9,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[7,6,8,5,4,3,9,2,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,8,7,6,5,4,9,3,1]
[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]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,8,7,6,5,4,9,2,1]
[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]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[4,8,7,6,5,3,9,2,1]
[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]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,8,7,6,4,3,9,2,1]
[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]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,8,7,5,4,3,9,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,8,6,5,4,3,9,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,9,8,7,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,5,6,9,8,7,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,3,2,5,6,9,8,7,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,9,8,7,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,4,3,2,6,9,8,7,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,4,6,5,9,8,7,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,6,5,9,8,7,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,3,2,6,5,9,8,7,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,6,4,9,8,7,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,6,2,9,8,7,1]
[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]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,6,4,3,9,8,7,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,9,8,7,1]
[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]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,4,6,3,2,9,8,7,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[2,6,5,4,3,9,8,7,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,4,3,2,9,8,7,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,5,4,3,2,9,8,7,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,5,7,9,8,6,1]
[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]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,4,7,9,8,6,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,7,9,8,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,7,9,8,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,2,5,6,7,9,8,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,7,9,8,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,7,9,8,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,7,9,8,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,7,9,8,2,1]
[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]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,4,6,5,7,9,8,3,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,5,7,6,9,8,2,1]
[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]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,9,8,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,9,8,2,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,7,4,9,8,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,7,3,9,8,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,7,6,5,9,8,4,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,7,6,5,4,9,8,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[3,7,6,5,4,9,8,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[7,6,5,4,3,9,8,2,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,7,6,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,5,8,9,7,6,1]
[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]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[2,5,4,3,8,9,7,6,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,8,9,7,6,1]
[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]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,3,2,8,9,7,6,1]
[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]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,3,6,8,9,7,5,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,8,9,7,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,6,8,9,7,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,6,8,9,7,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,3,6,8,9,7,2,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[3,6,5,4,8,9,7,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[6,5,4,3,8,9,7,2,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,6,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,4,7,8,9,6,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,7,8,9,6,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,3,5,7,8,9,6,4,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,7,8,9,6,2,1]
[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]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,6,7,8,9,5,4,1]
[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]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,9,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,9,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,9,5,2,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,4,3,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,9,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,9,4,3,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,9,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,9,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,7,6,8,9,5,4,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,5,7,6,8,9,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[2,6,7,5,8,9,4,3,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,6,7,5,8,9,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,7,4,8,9,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[6,5,7,4,8,9,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[2,7,6,5,8,9,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[3,7,6,5,8,9,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,7,6,5,8,9,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[6,7,5,4,8,9,3,2,1]
[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]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,4,6,8,7,9,5,3,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,6,8,7,9,3,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,5,7,8,6,9,3,2,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,8,5,9,4,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,8,4,9,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[6,5,7,8,4,9,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[6,7,5,8,4,9,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,8,7,6,9,5,4,1]
[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]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,4,8,7,6,9,3,2,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[3,6,8,7,5,9,4,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,7,8,6,5,9,4,3,1]
[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]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,7,8,6,5,9,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,8,5,4,9,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[7,6,8,5,4,9,3,2,1]
[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]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[3,8,7,6,5,9,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,8,7,6,5,9,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,8,7,6,4,9,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[7,8,6,5,4,9,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,9,8,7,6,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,5,9,8,7,6,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,5,9,8,7,6,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,4,9,8,7,6,1]
[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]=>[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,3,9,8,7,6,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,2,9,8,7,6,1]
[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]=>[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,5,2,9,8,7,6,1]
[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]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,3,2,9,8,7,6,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,9,8,7,6,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,9,8,7,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,3,2,6,9,8,7,5,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,2,5,6,9,8,7,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,6,9,8,7,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,9,8,7,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,3,5,6,9,8,7,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[5,4,3,6,9,8,7,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,9,8,7,2,1]
[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]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[2,6,5,4,9,8,7,3,1]
[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]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,9,8,7,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[6,5,4,3,9,8,7,2,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,4,7,9,8,6,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,3,7,9,8,6,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,3,2,7,9,8,6,5,1]
[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]=>[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,2,5,7,9,8,6,4,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,7,9,8,6,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,3,5,7,9,8,6,2,1]
[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]=>[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,4,7,9,8,6,2,1]
[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]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,7,9,8,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,9,8,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,7,9,8,3,2,1]
[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]=>[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[4,6,5,7,9,8,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[6,5,4,7,9,8,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,9,8,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,7,4,9,8,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[6,5,7,4,9,8,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,7,6,5,9,8,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,7,6,5,9,8,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,7,6,5,9,8,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[6,7,5,4,9,8,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[7,6,5,4,9,8,3,2,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,8,9,7,6,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,8,9,7,6,5,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,2,8,9,7,6,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,2,8,9,7,6,5,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,8,9,7,6,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[5,4,3,8,9,7,6,2,1]
[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]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,4,6,8,9,7,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,4,6,8,9,7,5,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,6,8,9,7,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,6,4,8,9,7,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[6,5,4,8,9,7,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,7,8,9,6,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,7,8,9,6,5,4,1]
[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]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,7,8,9,6,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,7,8,9,6,5,2,1]
[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]=>[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,5,7,8,9,6,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,5,7,8,9,6,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,4,7,8,9,6,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,9,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,9,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,9,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,7,6,8,9,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,7,6,8,9,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,7,6,8,9,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[5,7,6,8,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[6,7,5,8,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[7,6,5,8,9,4,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,8,7,9,6,5,4,1]
[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]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,3,8,7,9,6,5,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,6,8,7,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[6,5,8,7,9,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[2,7,8,6,9,5,4,3,1]
[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]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[5,7,8,6,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,8,5,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,6,8,5,9,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,8,7,6,9,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,8,7,6,9,5,4,2,1]
[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]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,8,7,6,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[6,8,7,5,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[7,8,6,5,9,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,9,8,7,6,5,1]
[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]=>[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,4,9,8,7,6,5,1]
[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]=>[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,3,9,8,7,6,5,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,2,9,8,7,6,5,1]
[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]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,9,8,7,6,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,9,8,7,6,4,1]
[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]=>[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,2,5,9,8,7,6,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,5,9,8,7,6,3,1]
[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]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,9,8,7,6,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,3,9,8,7,6,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,9,8,7,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,6,4,9,8,7,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[6,5,4,9,8,7,3,2,1]
[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]=>[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,2,7,9,8,6,5,4,1]
[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]=>[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,4,7,9,8,6,3,2,1]
[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]=>[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,6,7,9,8,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,6,7,9,8,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,9,8,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[6,5,7,9,8,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,7,6,9,8,5,4,3,1]
[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]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,7,6,9,8,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[5,7,6,9,8,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[6,7,5,9,8,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[7,6,5,9,8,4,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,8,9,7,6,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,8,9,7,6,5,4,1]
[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]=>[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,8,9,7,6,5,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,5,8,9,7,6,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,4,8,9,7,6,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,6,8,9,7,5,4,3,1]
[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]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,6,8,9,7,5,3,2,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,6,8,9,7,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[6,5,8,9,7,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,7,8,9,6,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,7,8,9,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,7,8,9,6,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[5,7,8,9,6,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,5,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,8,7,9,6,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,8,7,9,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,8,7,9,6,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[5,8,7,9,6,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,8,7,9,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[7,8,6,9,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]
[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]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,8,7,6,5,4,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,9,8,7,6,5,4,1]
[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]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,9,8,7,6,5,3,1]
[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]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,9,8,7,6,5,2,1]
[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]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,3,9,8,7,6,5,2,1]
[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]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,5,9,8,7,6,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,9,8,7,6,3,2,1]
[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]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,6,9,8,7,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,6,9,8,7,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[4,6,9,8,7,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,6,9,8,7,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[6,5,9,8,7,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,7,9,8,6,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,7,9,8,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[4,7,9,8,6,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[5,7,9,8,6,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,9,8,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8,9,7,6,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,8,9,7,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,8,9,7,6,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,8,9,7,6,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,8,9,7,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]
[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]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,8,7,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,9,8,7,6,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,8,7,6,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,10,9,8,7,6,5,4,3,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,9,10,8,7,6,5,4,3,1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,9,7,6,5,4,3,2,10,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,12,11,10,9,8,7,6,5,4,3,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,10,11,9,8,7,6,5,4,3,1]
[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]=>[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,8,10,9,7,6,5,4,3,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,9,8,10,7,6,5,4,3,1]
[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]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[7,9,8,6,5,4,3,2,10,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[8,7,9,6,5,4,3,2,10,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,10,8,7,6,5,4,3,2,11,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[11,10,9,8,7,6,5,4,3,2,12,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2,10,9,11,8,7,6,5,4,3,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,8,9,10,7,6,5,4,3,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[2,9,8,7,10,6,5,4,3,1]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[6,9,8,7,5,4,3,2,10,1]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,9,6,5,4,3,2,10,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,9,10,11,8,7,6,5,4,3,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[2,8,7,9,10,6,5,4,3,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,7,8,9,10,6,5,4,3,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,2,10,9,8,7,6,5,4,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[3,9,8,7,6,5,4,2,10,1]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,8,9,5,4,3,2,10,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,7,6,5,4,3,2,10,9,1]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[8,7,6,5,4,3,9,2,10,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,8,9,10,11,7,6,5,4,3,1]
[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]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,10,9,8,7,6,5,4,1]
[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]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,9,8,7,6,5,4,3,10,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,9,10,8,7,6,5,4,1]
[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]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,10,9,1]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,10,1]
[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]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,2,11,10,9,8,7,6,5,4,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[2,8,9,7,6,5,4,3,10,1]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,8,6,5,4,3,2,9,10,1]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[9,8,7,6,5,4,3,2,11,10,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[2,10,9,8,7,6,5,4,3,11,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[2,7,6,8,9,10,5,4,3,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,8,9,10,7,6,5,4,1]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[6,8,7,5,4,3,2,9,10,1]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,11,1]
[]=>[]=>[1,0]=>[1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,9,10,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,9,10,2,1]
[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]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,3,6,7,8,9,10,2,1]
[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]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,9,10,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,3,8,9,10,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,6,8,7,9,10,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,7,8,3,9,10,2,1]
[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[7,8,6,5,4,3,9,10,2,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,6,7,9,8,10,2,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,5,6,8,9,7,10,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,8,9,3,10,2,1]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,7,5,8,4,9,3,10,2,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,6,9,8,7,10,2,1]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,8,9,4,3,10,2,1]
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,8,9,6,5,4,3,10,2,1]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[8,7,9,6,5,4,3,10,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[3,9,8,7,6,5,4,10,2,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[5,9,8,7,6,4,3,10,2,1]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,9,8,6,5,4,3,10,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[8,9,7,6,5,4,3,10,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,7,8,10,9,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,7,8,10,9,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,10,9,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,10,9,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,4,6,3,8,7,10,9,2,1]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[8,7,6,5,4,3,10,9,2,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,6,7,9,10,8,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,8,9,10,7,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,9,10,4,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]
[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]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,10,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,9,10,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,9,10,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,9,10,3,2,1]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,4,8,9,10,3,2,1]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,7,8,4,9,10,3,2,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[4,8,7,6,5,9,10,3,2,1]
[1,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[7,8,6,5,4,9,10,3,2,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,8,9,5,10,3,2,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,8,9,4,10,3,2,1]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,5,7,8,9,4,10,3,2,1]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,8,9,5,4,10,3,2,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[4,9,8,7,6,5,10,3,2,1]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[8,9,7,6,5,4,10,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,10,9,8,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,8,10,9,7,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,8,10,9,3,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,7,8,10,9,3,2,1]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,7,8,4,10,9,3,2,1]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[8,7,6,5,4,10,9,3,2,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,9,10,8,7,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,6,7,9,10,8,3,2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,5,8,9,10,7,6,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,4,7,8,9,10,6,5,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,7,8,9,10,6,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,9,10,5,4,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,9,10,5,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,5,8,9,10,4,3,2,1]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[6,7,8,5,9,10,4,3,2,1]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[7,8,6,5,9,10,4,3,2,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,8,9,5,10,4,3,2,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[4,9,8,7,6,10,5,3,2,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,9,8,7,6,10,4,3,2,1]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[8,9,7,6,5,10,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,10,9,8,7,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,10,9,8,3,2,1]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[7,6,5,4,10,9,8,3,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,6,7,8,10,9,5,3,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,10,9,4,3,2,1]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[8,7,6,5,10,9,4,3,2,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,5,7,9,10,8,6,4,2,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,6,7,9,10,8,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,5,8,9,10,7,6,3,2,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[5,6,8,9,10,7,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,7,8,9,10,6,5,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,7,8,9,10,6,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,10,5,4,3,2,1]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,8,6,9,10,5,4,3,2,1]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[8,7,9,6,10,5,4,3,2,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,9,8,7,10,6,5,3,2,1]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[6,9,8,7,10,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[8,9,7,6,10,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,10,9,8,7,6,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,10,9,8,7,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,10,9,8,4,3,2,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,8,10,9,5,4,3,2,1]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,6,8,10,9,5,4,3,2,1]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,8,6,10,9,5,4,3,2,1]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[8,7,6,10,9,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[6,7,9,10,8,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,6,9,10,8,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,8,9,10,7,6,5,4,2,1]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[6,8,9,10,7,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[8,7,9,10,6,5,4,3,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,9,8,10,7,6,5,4,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[4,9,8,10,7,6,5,3,2,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[7,9,8,10,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[8,9,7,10,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,10,9,8,7,6,5,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,3,10,9,8,7,6,5,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,5,10,9,8,7,6,3,2,1]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,7,10,9,8,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,6,10,9,8,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[6,8,10,9,7,5,4,3,2,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,8,10,9,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[8,7,10,9,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,9,10,8,7,6,5,4,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[4,9,10,8,7,6,5,3,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[5,9,10,8,7,6,4,3,2,1]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[6,9,10,8,7,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[7,9,10,8,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]
[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]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,10,9,8,7,6,5,4,2,1]
[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]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,10,9,8,7,6,5,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,10,9,8,7,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,10,9,8,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,10,9,7,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,8,2,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,2,10,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,11,1]
[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]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,10,11,1]
[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]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,10,11,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,9,10,11,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,4,5,7,6,2,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,10,11,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,5,6,8,7,2,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,2,9,10,11,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,6,7,9,8,2,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,2,10,11,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,10,2,11,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,11,12,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,10,11,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,10,1]
[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]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,7,8,9,11,10,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,12,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,10,11,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,6,4,3,2,7,8,9,10,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,8,11,10,9,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,6,7,3,2,8,9,10,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,10,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[3,6,7,5,8,4,2,9,10,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,10,11,9,8,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,7,8,3,2,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,10,11,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,8,9,4,2,10,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,5,6,9,10,11,8,7,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,8,9,3,2,10,1]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,10,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[3,6,8,7,5,9,4,2,10,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,8,9,4,3,2,10,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,4,5,8,9,10,11,7,6,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,10,11,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,4,7,8,9,10,11,6,5,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,9,10,11,4,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,9,10,11,5,4,2,1]
[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]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,10,1]
[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]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,9,10,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,9,10,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,10,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,4,7,6,5,8,9,10,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,4,3,7,6,5,8,9,10,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[2,3,7,6,5,4,8,9,10,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,6,8,7,9,10,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,8,7,9,10,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[2,8,7,6,5,4,3,9,10,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,7,9,8,10,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,6,7,9,8,10,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,10,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,4,7,6,5,9,8,10,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,5,6,9,8,7,10,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,2,9,8,7,6,5,4,10,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,7,8,10,9,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,7,8,10,9,1]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[7,6,5,4,3,2,8,10,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,10,9,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,10,9,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[2,8,7,6,5,4,3,10,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,10,9,8,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,10,9,8,1]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[7,6,5,4,3,2,10,9,8,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,10,9,8,7,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,6,10,9,8,7,1]
[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]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,5,4,3,2,10,9,8,7,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,10,9,8,7,6,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,4,3,2,10,9,8,7,6,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,10,9,8,7,6,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,4,10,9,8,7,6,5,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,3,2,10,9,8,7,6,5,1]
[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]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,10,11,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,10,11,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,7,9,10,11,1]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,10,11,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,10,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,7,8,9,11,10,1]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[8,7,6,5,4,3,2,11,10,9,1]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[7,6,5,4,3,2,11,10,9,8,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,11,10,9,8,7,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,11,10,9,8,7,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[5,4,3,2,11,10,9,8,7,6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,3,2,11,10,9,8,7,6,5,1]
[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]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,8,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,10,7,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,10,6,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,5,1]
[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]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,10,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,3,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,8,10,11,9,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,5,6,9,8,10,7,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,11,8,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,5,8,7,9,10,6,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,10,11,7,1]
[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]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,7,6,8,9,10,5,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,10,11,6,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,6,5,7,8,9,10,4,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,11,5,1]
[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]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,9,10,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,10,11,4,1]
[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]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,11,3,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,10,11,5,4,3,2,1]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,8,9,11,10,5,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,10,11,12,5,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,11,4,3,2,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,11,10,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,10,12,11,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,7,8,10,9,1]
[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]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,9,10,11,2,1]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[9,11,10,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,10,12,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,11,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,9,11,10,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[10,12,11,9,8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,6,7,9,10,8,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,6,7,9,10,8,1]
[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]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,10,4,3,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,9,10,5,4,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,7,8,9,10,6,5,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,8,9,10,7,6,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,6,9,10,8,7,1]
[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]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[10,9,8,7,6,5,4,3,11,2,1]
[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]=>[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,11,10,9,8,7,6,5,4,2,1]
[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]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,4,5,6,8,10,9,7,1]
[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]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[10,9,8,11,7,6,5,4,3,2,1]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[10,9,8,7,11,6,5,4,3,2,1]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[10,9,8,7,6,11,5,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[10,9,8,7,6,5,11,4,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[10,9,8,7,6,5,4,11,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,6,7,8,9,10,5,4,1]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,7,8,3,2,10,9,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,8,9,4,10,3,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,8,9,10,3,11,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,12,10,9,8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[7,6,5,4,3,2,9,10,8,1]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[6,5,4,3,2,9,10,8,7,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,3,2,9,10,8,7,6,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,2,9,10,8,7,6,5,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,4,5,7,8,9,6,10,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,4,5,7,8,6,9,10,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,7,8,10,9,3,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,8,9,2,10,1]
[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]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,9,10,4,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,7,8,2,10,9,1]
[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]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,11,4,3,2,1]
[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]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,6,4,3,2,10,9,8,7,1]
[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]=>[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,2,10,9,8,7,6,5,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[4,11,10,9,8,7,6,5,3,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,3,2,10,9,8,7,6,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[5,11,10,9,8,7,6,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[6,11,10,9,8,7,5,4,3,2,1]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,7,5,4,3,2,10,9,8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[7,11,10,9,8,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[8,11,10,9,7,6,5,4,3,2,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,5,10,9,8,7,6,4,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[4,8,7,6,5,3,2,10,9,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,3,2,7,10,9,8,6,5,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,7,6,4,3,2,10,9,8,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,9,10,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,7,10,11,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,4,5,6,8,9,10,7,11,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,2,7,8,10,9,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,9,10,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,7,6,8,9,10,11,2,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,9,10,11,8,7,6,5,4,2,1]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[8,9,10,7,6,5,4,3,11,2,1]
[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]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,11,3,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,7,8,9,11,10,3,2,1]
[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]=>[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,11,10,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,9,10,11,4,3,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,9,10,5,4,3,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,7,8,9,10,11,6,5,4,3,1]
[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]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,9,10,4,3,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,9,10,11,5,4,3,1]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,10,8,11,7,6,5,4,3,2,1]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,10,8,7,6,5,4,3,11,2,1]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[11,10,9,8,7,6,5,4,3,12,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,12,10,1]
[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]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,6,7,8,10,11,9,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,3,5,6,7,9,10,8,1]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,9,10,1]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,8,9,10,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,9,10,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,9,10,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,6,7,2,10,9,8,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,10,9,8,7,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,2,9,10,8,7,6,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,4,2,8,9,10,7,6,5,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,7,8,9,10,6,5,4,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,6,7,8,5,9,10,4,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,4,6,8,9,10,7,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,11,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[8,10,11,9,7,6,5,4,3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,5,6,8,9,7,10,1]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,11,8,7,6,5,4,3,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,3,2,8,9,10,7,6,1]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,8,9,10,5,11,4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,7,8,9,10,11,6,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,5,8,9,10,11,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,7,8,9,10,11,6,5,3,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,8,7,9,6,10,1]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[9,8,7,11,10,6,5,4,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,6,7,5,4,8,9,10,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,9,10,11,3,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,6,7,8,10,11,9,3,2,1]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,10,8,7,11,6,5,4,3,2,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,9,8,2,10,1]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,10,1]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,2,5,9,10,8,7,6,1]
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[11,10,9,12,8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[2,4,7,6,5,3,9,10,8,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,7,8,9,11,10,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,4,8,9,10,11,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,10,9,8,7,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,9,8,10,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,8,7,9,2,10,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,3,8,9,10,11,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,8,7,3,9,2,10,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[4,7,6,8,5,3,9,2,10,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,9,8,10,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[2,4,7,9,8,6,10,5,3,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,4,6,8,10,9,7,5,3,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[5,7,6,4,8,3,9,2,10,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,4,2,8,7,6,9,5,10,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,6,7,4,3,8,9,10,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[2,4,6,9,8,10,7,5,3,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,6,4,7,3,8,2,9,10,1]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[2,7,6,8,5,9,4,10,3,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[2,4,8,7,9,6,10,5,3,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[2,4,8,7,6,5,10,9,3,1]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,4,7,3,8,2,10,9,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,8,7,9,6,10,1]
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
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 312-avoiding permutation
searching the database
Sorry, this map was not found in the database.