Identifier
Mp00099:
Dyck paths
—bounce path⟶
Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00028: Dyck paths —reverse⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0009;cc-rep-4
[1,0]=>[1,0]=>[1,0]=>[2,1]=>{{1,2}}
[1,0,1,0]=>[1,0,1,0]=>[1,0,1,0]=>[3,1,2]=>{{1,2,3}}
[1,1,0,0]=>[1,1,0,0]=>[1,1,0,0]=>[2,3,1]=>{{1,2,3}}
[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[1,0,1,0,1,0]=>[4,1,2,3]=>{{1,2,3,4}}
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,4,1,3]=>{{1,2,3,4}}
[1,1,0,0,1,0]=>[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[3,1,4,2]=>{{1,2,3,4}}
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2,4,1,3]=>{{1,2,3,4}}
[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[1,1,1,0,0,0]=>[2,3,4,1]=>{{1,2,3,4}}
[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0]=>[5,1,2,3,4]=>{{1,2,3,4,5}}
[1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>{{1,2,3,4,5}}
[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}}
[1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0]=>[2,5,1,3,4]=>{{1,2,3,4,5}}
[1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}}
[1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0]=>[4,1,2,5,3]=>{{1,2,3,4,5}}
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}}
[1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0]=>[3,1,5,2,4]=>{{1,2,3,4,5}}
[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}}
[1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}}
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0]=>[3,1,4,5,2]=>{{1,2,3,4,5}}
[1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,4,1,5,3]=>{{1,2,3,4,5}}
[1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0]=>[2,3,5,1,4]=>{{1,2,3,4,5}}
[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>{{1,2,3,4,5}}
[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}
[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[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]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[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]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,1,2,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,8,1,3,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,8,1,4,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,2,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,4,1,8,3,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,8,2,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,5,1,3,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,3,5,1,8,4,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,2,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,4,1,5,8,3,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,5,8,2,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,1,2,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,7,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,7,2,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,3,7,1,4,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[4,1,2,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,7,3,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,4,7,2,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,7,1,5,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,6,1,3,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,2,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,3,6,1,4,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,3,4,6,1,8,5,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,1,2,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,6,1,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,6,1,3,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[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]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,6,2,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,3,5,1,7,4,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,5,1,3,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,2,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,5,1,6,8,4,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,1,3,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,1,2,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,1,6,3,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[4,1,2,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,5,7,3,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1,5,6,8,3,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,5,2,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,4,6,2,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,4,5,7,2,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,2]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,1,5,6,7,8,3]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,6,1,7,8,5]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,7,8}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,9,1,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,9,1,3,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,9,1,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,9,2,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,9,1,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,9,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,9,1,4,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[5,1,2,3,9,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,9,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,9,2,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,9,1,5,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,1,2,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[5,1,2,3,9,4,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,5,9,3,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,9,1,6,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,1,2,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,6,1,3,4,9,5,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,2,3,4,7,9,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,5,6,9,2,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,9,1,7,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,1,2,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,8,1,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,8,2,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,8,1,3,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,8,1,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,8,3,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,8,2,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,8,1,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,8,1,4,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,1,2,3,8,4,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,8,3,5,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,1,2,3,8,4,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[2,3,4,5,8,1,6,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,7,1,3,4,5,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,2,3,4,7,9,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,7,4,9,6,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,7,1,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,7,1,3,4,5,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,1,2,3,4,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,1,2,3,4,7,9,5,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[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]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,5,1,6,7,9,4,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,9,3,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,8,2,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,9,2,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,2]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,3]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,4]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,6,1,7,8,9,5]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,7,1,8,9,6]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,2]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[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]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,10,2,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,10,1,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[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]=>[2,3,4,5,6,10,1,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[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]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,11,2,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[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]=>[2,3,4,5,6,10,1,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,11,1,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[]=>[]=>[]=>[1]=>{{1}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,3]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,1,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,10,1,3,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,10,1,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,11,1,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,10,1,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,10,1,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,11,1,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,11,1,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,10,1,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,10,1,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,11,1,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,10,1,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,11,1,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,11,1,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,10,1,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,10,1,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,11,1,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,11,1,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,10,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,10,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,8,1,3,4,5,6,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,1,2,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[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]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,9,2,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,1,2,3,4,5,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,1,2,3,4,5,6,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,8,1,9,10,7]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,1,2,3,4,5,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,6]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,1,2,3,4,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,5]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[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]=>[2,5,1,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[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]=>[2,3,5,1,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,11,6,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,11,1,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[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]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[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]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,1,2,3,4,5,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,8,1,3,4,5,6,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,8,1,3,4,5,6,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,8,1,3,4,5,6,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,1,2,3,4,5,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[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]=>[2,4,1,5,6,7,8,10,3,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,6,7,8,9,10,4]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,10,3,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,11,6,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[2,3,4,5,6,10,1,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,10,1,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,10,1,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,10,1,4,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,11,1,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,11,1,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,10,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,9,2,4,5,6,7,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,10,2,5,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,11,1,4,5,6,7,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,10,4,6,7,8,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[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]=>[3,1,4,5,6,7,9,2,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,5,6,7,8,9,10,11,3]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,11,1,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,7,4,9,6,10,8]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,8,1,9,10,11,7]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,1,6,7,8,9,10,11,4]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,9,10,11,6]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,1,7,8,9,10,11,5]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,10,11,8]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,11,1,8,9,10]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,3,4,5,6,7,8,9,10}}
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,11,12}}
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
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
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
searching the database
Sorry, this map was not found in the database.