Identifier
Mp00199: Dyck paths prime Dyck pathDyck paths
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00087: Permutations inverse first fundamental transformationPermutations
Mp00068: Permutations Simion-Schmidt mapPermutations
Images
[1,0] => [1,1,0,0] => [1,2] => [1,2] => [1,2]
[1,0,1,0] => [1,1,0,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2]
[1,1,0,0] => [1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,3,2]
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [1,3,2,4] => [1,3,2,4] => [1,4,3,2]
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,3,4,2] => [1,4,2,3] => [1,4,3,2]
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,3,2] => [1,4,3,2]
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [1,2,4,3] => [1,2,4,3] => [1,4,3,2]
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,4,3,2]
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,5,4,3,2]
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,5,4,2,3] => [1,5,4,3,2]
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,5,4,3,2]
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [1,4,2,3,5] => [1,5,4,3,2]
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => [1,5,4,3,2]
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [1,5,3,2,4] => [1,5,4,3,2]
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [1,4,2,5,3] => [1,5,4,3,2]
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [1,4,3,2,5] => [1,5,4,3,2]
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,5,4,3,2]
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => [1,5,4,3,2]
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2]
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [1,2,5,4,3] => [1,5,4,3,2]
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [1,5,4,3,2]
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,6,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [1,5,4,2,3,6] => [1,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,6,5,4,3,2]
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [1,6,4,2,3,5] => [1,6,5,4,3,2]
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [1,5,2,3,6,4] => [1,6,5,4,3,2]
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,6,5,4,3,2]
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [1,6,5,4,2,3] => [1,6,5,4,3,2]
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,6,5,4,3,2]
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [1,6,5,2,3,4] => [1,6,5,4,3,2]
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,6,5,4,3,2]
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,6,5,4,3,2]
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,6,5,4,3,2]
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [1,5,3,2,4,6] => [1,6,5,4,3,2]
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [1,4,2,5,3,6] => [1,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [1,6,3,2,4,5] => [1,6,5,4,3,2]
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [1,4,2,6,3,5] => [1,6,5,4,3,2]
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [1,6,3,5,2,4] => [1,6,5,4,3,2]
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [1,6,5,3,2,4] => [1,6,5,4,3,2]
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [1,4,2,6,5,3] => [1,6,5,4,3,2]
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,6,5,4,3,2]
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [1,2,6,5,3,4] => [1,6,5,4,3,2]
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,6,5,4,3,2]
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,6,5,4,3,2]
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [1,5,3,2,6,4] => [1,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [1,6,4,2,5,3] => [1,6,5,4,3,2]
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [1,6,4,3,2,5] => [1,6,5,4,3,2]
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [1,2,6,4,3,5] => [1,6,5,4,3,2]
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [1,2,5,3,6,4] => [1,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [1,5,4,3,2,6] => [1,6,5,4,3,2]
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,6,5,4,3,2]
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2]
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [1,2,6,5,4,3] => [1,6,5,4,3,2]
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,6,5,4,3,2]
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,7,6] => [1,5,4,2,3,7,6] => [1,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,7,4,6] => [1,3,2,7,6,4,5] => [1,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,7,4,6] => [1,7,6,4,2,3,5] => [1,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,7,2,4,6] => [1,5,2,3,7,6,4] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7] => [1,5,4,2,3,6,7] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,5,6,4,7] => [1,3,2,6,4,5,7] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7] => [1,6,4,2,3,5,7] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7] => [1,5,2,3,6,4,7] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,5,6,7,4] => [1,3,2,7,4,5,6] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4] => [1,7,4,2,3,5,6] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4] => [1,5,2,3,7,4,6] => [1,7,6,5,4,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,6,7,2,4] => [1,7,4,6,2,3,5] => [1,7,6,5,4,3,2]
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5] => [1,3,2,7,5,4,6] => [1,7,6,5,4,3,2]
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,6,2,4,7,5] => [1,7,5,4,2,3,6] => [1,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5] => [1,3,2,6,4,7,5] => [1,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,7,4,5] => [1,6,4,2,3,7,5] => [1,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,6,7,2,4,5] => [1,7,5,2,3,6,4] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5,7] => [1,3,2,6,5,4,7] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,7] => [1,6,5,4,2,3,7] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,7] => [1,4,2,3,6,5,7] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,7] => [1,6,5,2,3,4,7] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,4,6,7,5] => [1,3,2,4,7,5,6] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5] => [1,4,2,3,7,5,6] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5] => [1,7,5,2,3,4,6] => [1,7,6,5,4,3,2]
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,7,2,5] => [1,6,2,3,4,7,5] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,7,4,5,6] => [1,3,2,7,6,5,4] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6] => [1,7,6,5,4,2,3] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,7,5,6] => [1,3,2,4,7,6,5] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,4,2,7,5,6] => [1,4,2,3,7,6,5] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,4,7,2,5,6] => [1,7,6,5,2,3,4] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,5,7,6] => [1,4,2,3,5,7,6] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => [1,7,6,5,4,3,2]
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6] => [1,7,6,2,3,4,5] => [1,7,6,5,4,3,2]
>>> Load all 608 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7] => [1,4,2,3,5,6,7] => [1,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7] => [1,5,2,3,4,6,7] => [1,7,6,5,4,3,2]
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7] => [1,6,2,3,4,5,7] => [1,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => [1,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6] => [1,5,3,2,4,7,6] => [1,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6] => [1,4,2,5,3,7,6] => [1,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6] => [1,7,6,3,2,4,5] => [1,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6] => [1,4,2,7,6,3,5] => [1,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,5,7,2,3,6] => [1,7,6,3,5,2,4] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,6,7] => [1,5,3,2,4,6,7] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7] => [1,4,2,5,3,6,7] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7] => [1,6,3,2,4,5,7] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7] => [1,4,2,6,3,5,7] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,7] => [1,6,3,5,2,4,7] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,6,7,3] => [1,7,3,2,4,5,6] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3] => [1,4,2,7,3,5,6] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3] => [1,7,3,5,2,4,6] => [1,7,6,5,4,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3] => [1,6,2,4,7,3,5] => [1,7,6,5,4,3,2]
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5] => [1,7,5,3,2,4,6] => [1,7,6,5,4,3,2]
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,7,5] => [1,4,2,7,5,3,6] => [1,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,4,2,6,7,3,5] => [1,6,3,2,4,7,5] => [1,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5] => [1,4,2,6,3,7,5] => [1,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5] => [1,6,3,7,5,2,4] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7] => [1,6,5,3,2,4,7] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,7] => [1,4,2,6,5,3,7] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5,7] => [1,4,3,2,6,5,7] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7] => [1,2,6,5,3,4,7] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,6,7,5] => [1,4,3,2,7,5,6] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5] => [1,2,7,5,3,4,6] => [1,7,6,5,4,3,2]
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5] => [1,2,6,3,4,7,5] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6] => [1,7,6,5,3,2,4] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,7,2,3,5,6] => [1,4,2,7,6,5,3] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6] => [1,4,3,2,7,6,5] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,7,5,6] => [1,2,4,3,7,6,5] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,7,3,5,6] => [1,2,7,6,5,3,4] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,2,3,5,7,6] => [1,4,3,2,5,7,6] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => [1,7,6,5,4,3,2]
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6] => [1,2,7,6,3,4,5] => [1,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7] => [1,4,3,2,5,6,7] => [1,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => [1,7,6,5,4,3,2]
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => [1,7,6,5,4,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => [1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4] => [1,5,3,2,7,4,6] => [1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,7,4] => [1,7,4,2,5,3,6] => [1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,6,7,3,4] => [1,7,4,6,3,2,5] => [1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,5,6,2,7,3,4] => [1,6,3,7,4,2,5] => [1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4] => [1,5,2,6,3,7,4] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,6,3,4,7] => [1,5,3,2,6,4,7] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,5,6,2,3,4,7] => [1,6,4,2,5,3,7] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,2,3,6,4,7] => [1,6,4,3,2,5,7] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,6,4,7] => [1,2,6,4,3,5,7] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7] => [1,2,5,3,6,4,7] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,7,4] => [1,7,4,3,2,5,6] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4] => [1,2,7,4,3,5,6] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4] => [1,2,5,3,7,4,6] => [1,7,6,5,4,3,2]
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,6,7,3,4] => [1,2,7,4,6,3,5] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6] => [1,5,3,2,7,6,4] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6] => [1,7,6,4,2,5,3] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,2,3,7,4,6] => [1,7,6,4,3,2,5] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,2,5,3,7,4,6] => [1,2,7,6,4,3,5] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6] => [1,2,5,3,7,6,4] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,7,6] => [1,5,4,3,2,7,6] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,7,6] => [1,2,5,4,3,7,6] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,7,6,5,4,3,2]
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6] => [1,2,3,7,6,4,5] => [1,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,5,2,3,4,6,7] => [1,5,4,3,2,6,7] => [1,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [1,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,7,6,5,4,3,2]
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => [1,7,6,5,4,3,2]
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,6,2,7,3,4,5] => [1,7,5,3,2,6,4] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5] => [1,6,4,2,7,5,3] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,7,4,5] => [1,6,4,3,2,7,5] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,6,4,3,7,5] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5] => [1,2,7,5,3,6,4] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5] => [1,7,5,4,3,2,6] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,7,5] => [1,2,7,5,4,3,6] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5] => [1,2,3,7,5,4,6] => [1,7,6,5,4,3,2]
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5] => [1,2,3,6,4,7,5] => [1,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7] => [1,6,5,4,3,2,7] => [1,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7] => [1,2,6,5,4,3,7] => [1,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,7] => [1,2,3,6,5,4,7] => [1,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,7,6,5,4,3,2]
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => [1,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6] => [1,7,6,5,4,3,2] => [1,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6] => [1,2,7,6,5,4,3] => [1,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6] => [1,2,3,7,6,5,4] => [1,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,7,6,5] => [1,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,5,4,7,8,6] => [1,3,2,5,4,8,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,2,7,4,8,6] => [1,8,6,4,2,3,5,7] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,5,2,7,8,4,6] => [1,7,4,2,3,5,8,6] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,3,5,7,2,8,4,6] => [1,5,2,3,7,4,8,6] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,5,7,8,2,4,6] => [1,7,4,8,6,2,3,5] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,8,6,7] => [1,3,2,5,4,8,7,6] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,3,5,2,4,8,6,7] => [1,5,4,2,3,8,7,6] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,5,8,4,6,7] => [1,3,2,8,7,6,4,5] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,3,5,2,8,4,6,7] => [1,8,7,6,4,2,3,5] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,8,2,4,6,7] => [1,5,2,3,8,7,6,4] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,2,6,4,8,7] => [1,6,4,2,3,5,8,7] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,2,4,8,7] => [1,5,2,3,6,4,8,7] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,5,6,8,4,7] => [1,3,2,8,7,4,5,6] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,3,5,2,6,8,4,7] => [1,8,7,4,2,3,5,6] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,6,2,8,4,7] => [1,5,2,3,8,7,4,6] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,6,8,2,4,7] => [1,8,7,4,6,2,3,5] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,5,2,4,6,7,8] => [1,5,4,2,3,6,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,5,2,6,4,7,8] => [1,6,4,2,3,5,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,3,5,6,2,4,7,8] => [1,5,2,3,6,4,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,5,2,6,7,4,8] => [1,7,4,2,3,5,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,5,6,2,7,4,8] => [1,5,2,3,7,4,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,3,2,5,6,7,8,4] => [1,3,2,8,4,5,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,3,5,2,6,7,8,4] => [1,8,4,2,3,5,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,3,5,6,2,7,8,4] => [1,5,2,3,8,4,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,5,6,7,8,2,4] => [1,7,2,3,5,8,4,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,6,4,7,5,8] => [1,3,2,7,5,4,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,2,6,7,4,5,8] => [1,3,2,6,4,7,5,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,7,8,5] => [1,3,2,8,5,4,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,7,8,5] => [1,8,5,4,2,3,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,4,8,5] => [1,3,2,6,4,8,5,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,2,6,7,8,4,5] => [1,3,2,8,5,7,4,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,6,2,7,8,4,5] => [1,8,5,7,4,2,3,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,3,6,7,8,2,4,5] => [1,6,2,3,7,4,8,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,2,6,8,4,5,7] => [1,3,2,6,4,8,7,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,6,2,8,4,5,7] => [1,6,4,2,3,8,7,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5,8,7] => [1,6,5,4,2,3,8,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7] => [1,4,2,3,6,5,8,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5,8,7] => [1,6,5,2,3,4,8,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,4,2,6,8,5,7] => [1,4,2,3,8,7,5,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,4,6,2,8,5,7] => [1,8,7,5,2,3,4,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,3,4,6,8,2,5,7] => [1,6,2,3,4,8,7,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,4,6,5,7,8] => [1,3,2,4,6,5,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,4,2,6,7,5,8] => [1,4,2,3,7,5,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,4,6,2,7,5,8] => [1,7,5,2,3,4,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,2,4,6,7,8,5] => [1,3,2,4,8,5,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,4,2,6,7,8,5] => [1,4,2,3,8,5,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,3,4,6,7,8,2,5] => [1,8,5,7,2,3,4,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,3,2,7,4,8,5,6] => [1,3,2,7,5,4,8,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,3,7,2,8,4,5,6] => [1,8,6,4,2,3,7,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,3,7,8,2,4,5,6] => [1,7,5,2,3,8,6,4] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,3,2,7,4,5,8,6] => [1,3,2,8,6,5,4,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,3,7,2,4,5,8,6] => [1,8,6,5,4,2,3,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,3,2,4,7,5,8,6] => [1,3,2,4,8,6,5,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,3,4,2,7,5,8,6] => [1,4,2,3,8,6,5,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,3,4,7,2,8,5,6] => [1,7,5,2,3,4,8,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,3,7,2,4,5,6,8] => [1,7,6,5,4,2,3,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,3,4,5,2,7,6,8] => [1,5,2,3,4,7,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,3,4,5,7,2,6,8] => [1,7,6,2,3,4,5,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,3,2,4,5,7,8,6] => [1,3,2,4,5,8,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,3,4,2,5,7,8,6] => [1,4,2,3,5,8,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,3,4,5,2,7,8,6] => [1,5,2,3,4,8,6,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,4,5,7,2,8,6] => [1,8,6,2,3,4,5,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,3,4,5,7,8,2,6] => [1,7,2,3,4,5,8,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,3,2,8,4,5,6,7] => [1,3,2,8,7,6,5,4] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,3,8,2,4,5,6,7] => [1,8,7,6,5,4,2,3] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,3,2,4,8,5,6,7] => [1,3,2,4,8,7,6,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,3,4,2,8,5,6,7] => [1,4,2,3,8,7,6,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,3,4,8,2,5,6,7] => [1,8,7,6,5,2,3,4] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,3,2,4,5,8,6,7] => [1,3,2,4,5,8,7,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,3,4,5,2,8,6,7] => [1,5,2,3,4,8,7,6] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,3,4,5,8,2,6,7] => [1,8,7,6,2,3,4,5] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,3,2,4,5,6,8,7] => [1,3,2,4,5,6,8,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,3,4,5,6,2,8,7] => [1,6,2,3,4,5,8,7] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8] => [1,4,2,3,5,6,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,3,4,5,2,6,7,8] => [1,5,2,3,4,6,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,3,4,5,6,2,7,8] => [1,6,2,3,4,5,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8] => [1,7,2,3,4,5,6,8] => [1,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2] => [1,8,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,8] => [1,5,3,2,4,7,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,8] => [1,4,2,5,3,7,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [1,4,2,5,7,3,6,8] => [1,7,6,3,2,4,5,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [1,4,5,2,7,3,6,8] => [1,4,2,7,6,3,5,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3,7,8,6] => [1,5,3,2,4,8,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3,7,8,6] => [1,4,2,5,3,8,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [1,4,2,5,7,3,8,6] => [1,8,6,3,2,4,5,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [1,4,2,5,7,8,3,6] => [1,7,3,2,4,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [1,4,5,2,7,8,3,6] => [1,4,2,7,3,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [1,4,5,7,2,8,3,6] => [1,7,3,5,2,4,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [1,4,5,7,8,2,3,6] => [1,8,6,2,4,7,3,5] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,8,6,7] => [1,5,3,2,4,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,8,6,7] => [1,4,2,5,3,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,8,3,6,7] => [1,8,7,6,3,2,4,5] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,8,3,6,7] => [1,4,2,8,7,6,3,5] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,8,2,3,6,7] => [1,8,7,6,3,5,2,4] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,2,6,3,8,7] => [1,4,2,6,3,5,8,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,6,2,3,8,7] => [1,6,3,5,2,4,8,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,5,6,8,3,7] => [1,8,7,3,2,4,5,6] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [1,4,5,2,6,8,3,7] => [1,4,2,8,7,3,5,6] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [1,4,5,6,8,2,3,7] => [1,6,2,4,8,7,3,5] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [1,4,5,2,3,6,7,8] => [1,4,2,5,3,6,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [1,4,2,5,6,3,7,8] => [1,6,3,2,4,5,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [1,4,5,2,6,3,7,8] => [1,4,2,6,3,5,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [1,4,5,2,6,7,3,8] => [1,4,2,7,3,5,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [1,4,5,6,2,7,3,8] => [1,7,3,5,2,4,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [1,4,5,6,7,2,3,8] => [1,6,2,4,7,3,5,8] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,3] => [1,8,3,2,4,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [1,4,5,2,6,7,8,3] => [1,4,2,8,3,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [1,4,5,6,7,2,8,3] => [1,6,2,4,8,3,5,7] => [1,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [1,4,5,6,7,8,2,3] => [1,8,3,5,7,2,4,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,2,6,3,7,5,8] => [1,7,5,3,2,4,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,6,2,7,3,5,8] => [1,4,2,6,3,7,5,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,6,7,2,3,5,8] => [1,6,3,7,5,2,4,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,2,6,3,7,8,5] => [1,8,5,3,2,4,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,6,2,3,7,8,5] => [1,4,2,8,5,3,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,6,2,7,3,8,5] => [1,4,2,6,3,8,5,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,6,7,2,3,8,5] => [1,6,3,8,5,2,4,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [1,4,2,6,7,8,3,5] => [1,8,5,7,3,2,4,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,2,6,3,8,5,7] => [1,8,7,5,3,2,4,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,6,2,3,8,5,7] => [1,4,2,8,7,5,3,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,6,8,2,3,5,7] => [1,6,3,8,7,5,2,4] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5,8,7] => [1,6,5,3,2,4,8,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5,8,7] => [1,4,2,6,5,3,8,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7] => [1,2,4,3,6,5,8,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,6,8,5,7] => [1,2,4,3,8,7,5,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [1,2,4,6,8,3,5,7] => [1,2,6,3,4,8,7,5] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [1,4,2,6,3,5,7,8] => [1,6,5,3,2,4,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [1,2,4,6,3,5,7,8] => [1,2,6,5,3,4,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [1,2,4,3,6,7,5,8] => [1,2,4,3,7,5,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [1,2,4,6,3,7,5,8] => [1,2,7,5,3,4,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [1,2,4,6,7,3,5,8] => [1,2,6,3,4,7,5,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [1,4,2,3,6,7,8,5] => [1,4,3,2,8,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [1,2,4,3,6,7,8,5] => [1,2,4,3,8,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [1,2,4,6,3,7,8,5] => [1,2,8,5,3,4,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [1,2,4,6,7,3,8,5] => [1,2,6,3,4,8,5,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [1,2,4,6,7,8,3,5] => [1,2,8,5,7,3,4,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,2,7,3,8,5,6] => [1,7,5,3,2,4,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,7,2,3,8,5,6] => [1,4,2,7,5,3,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,7,8,3,5,6] => [1,8,6,3,2,4,7,5] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,7,8,2,3,5,6] => [1,8,6,3,7,5,2,4] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,2,7,3,5,8,6] => [1,8,6,5,3,2,4,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,7,2,3,5,8,6] => [1,4,2,8,6,5,3,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,2,3,7,5,8,6] => [1,4,3,2,8,6,5,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [1,2,4,3,7,5,8,6] => [1,2,4,3,8,6,5,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,3,7,8,5,6] => [1,4,3,2,7,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [1,2,4,3,7,8,5,6] => [1,2,4,3,7,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [1,2,4,7,3,8,5,6] => [1,2,7,5,3,4,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [1,2,4,7,8,3,5,6] => [1,2,8,6,3,4,7,5] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,2,7,3,5,6,8] => [1,7,6,5,3,2,4,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,2,3,7,5,6,8] => [1,4,3,2,7,6,5,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [1,2,4,3,5,7,6,8] => [1,2,4,3,5,7,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [1,2,4,5,7,3,6,8] => [1,2,7,6,3,4,5,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,3,5,7,8,6] => [1,4,3,2,5,8,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,2,4,3,5,7,8,6] => [1,2,4,3,5,8,6,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,2,4,5,7,3,8,6] => [1,2,8,6,3,4,5,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [1,2,4,5,7,8,3,6] => [1,2,7,3,4,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [1,4,2,8,3,5,6,7] => [1,8,7,6,5,3,2,4] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [1,4,8,2,3,5,6,7] => [1,4,2,8,7,6,5,3] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [1,4,2,3,8,5,6,7] => [1,4,3,2,8,7,6,5] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [1,2,4,3,8,5,6,7] => [1,2,4,3,8,7,6,5] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [1,2,4,8,3,5,6,7] => [1,2,8,7,6,5,3,4] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,4,2,3,5,8,6,7] => [1,4,3,2,5,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [1,2,4,3,5,8,6,7] => [1,2,4,3,5,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [1,2,4,5,3,8,6,7] => [1,2,5,3,4,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [1,2,4,5,8,3,6,7] => [1,2,8,7,6,3,4,5] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [1,2,4,3,5,6,8,7] => [1,2,4,3,5,6,8,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [1,2,4,5,3,6,8,7] => [1,2,5,3,4,6,8,7] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [1,2,4,5,6,8,3,7] => [1,2,8,7,3,4,5,6] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8] => [1,4,3,2,5,6,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8] => [1,2,4,3,5,6,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [1,2,4,5,3,6,7,8] => [1,2,5,3,4,6,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [1,2,4,5,6,3,7,8] => [1,2,6,3,4,5,7,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [1,2,4,5,6,7,3,8] => [1,2,7,3,4,5,6,8] => [1,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,3] => [1,2,8,3,4,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [1,5,2,6,3,7,4,8] => [1,5,3,2,7,4,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,5,6,7,2,3,4,8] => [1,5,2,6,3,7,4,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [1,5,2,6,3,7,8,4] => [1,5,3,2,8,4,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [1,5,6,2,3,7,8,4] => [1,8,4,2,5,3,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [1,5,6,2,7,3,8,4] => [1,6,3,8,4,2,5,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [1,5,6,7,2,3,8,4] => [1,5,2,6,3,8,4,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [1,5,6,2,7,8,3,4] => [1,8,4,2,5,7,3,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [1,5,6,7,2,8,3,4] => [1,5,2,8,4,7,3,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [1,5,6,7,8,2,3,4] => [1,8,4,7,3,6,2,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [1,5,2,6,3,8,4,7] => [1,5,3,2,8,7,4,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [1,5,6,2,3,8,4,7] => [1,8,7,4,2,5,3,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [1,5,2,6,8,3,4,7] => [1,8,7,4,6,3,2,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [1,5,6,8,2,3,4,7] => [1,5,2,6,3,8,7,4] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,3,4,8,7] => [1,2,5,3,6,4,8,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [1,5,2,3,6,8,4,7] => [1,8,7,4,3,2,5,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [1,2,5,6,3,8,4,7] => [1,2,5,3,8,7,4,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [1,2,5,6,8,3,4,7] => [1,2,8,7,4,6,3,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4,7,8] => [1,2,5,3,6,4,7,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,6,7,4,8] => [1,2,7,4,3,5,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [1,2,5,6,3,7,4,8] => [1,2,5,3,7,4,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [1,5,2,3,6,7,8,4] => [1,8,4,3,2,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [1,2,5,3,6,7,8,4] => [1,2,8,4,3,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [1,2,5,6,3,7,8,4] => [1,2,5,3,8,4,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [1,2,5,6,7,3,8,4] => [1,2,8,4,6,3,5,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,5,6,7,8,3,4] => [1,2,7,3,5,8,4,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [1,5,2,7,3,8,4,6] => [1,5,3,2,7,4,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [1,5,7,2,3,8,4,6] => [1,7,4,2,5,3,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [1,5,2,7,8,3,4,6] => [1,7,4,8,6,3,2,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [1,5,7,2,8,3,4,6] => [1,8,6,3,7,4,2,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [1,5,7,8,2,3,4,6] => [1,5,2,8,6,3,7,4] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [1,5,2,7,3,4,8,6] => [1,5,3,2,8,6,4,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [1,5,7,2,3,4,8,6] => [1,8,6,4,2,5,3,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [1,2,5,3,7,4,8,6] => [1,2,8,6,4,3,5,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [1,2,5,7,3,4,8,6] => [1,2,5,3,8,6,4,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [1,5,2,3,7,8,4,6] => [1,7,4,3,2,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [1,2,5,7,3,8,4,6] => [1,2,5,3,7,4,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [1,2,5,7,8,3,4,6] => [1,2,7,4,8,6,3,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [1,5,2,7,3,4,6,8] => [1,5,3,2,7,6,4,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [1,5,7,2,3,4,6,8] => [1,7,6,4,2,5,3,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [1,2,5,7,3,4,6,8] => [1,2,5,3,7,6,4,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [1,2,3,5,7,4,6,8] => [1,2,3,7,6,4,5,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [1,2,5,3,4,7,8,6] => [1,2,5,4,3,8,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [1,2,3,5,4,7,8,6] => [1,2,3,5,4,8,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [1,2,3,5,7,4,8,6] => [1,2,3,8,6,4,5,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,2,3,5,7,8,4,6] => [1,2,3,7,4,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [1,5,2,8,3,4,6,7] => [1,5,3,2,8,7,6,4] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [1,5,8,2,3,4,6,7] => [1,8,7,6,4,2,5,3] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,5,2,3,8,4,6,7] => [1,8,7,6,4,3,2,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [1,2,5,3,8,4,6,7] => [1,2,8,7,6,4,3,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [1,2,5,8,3,4,6,7] => [1,2,5,3,8,7,6,4] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [1,5,2,3,4,8,6,7] => [1,5,4,3,2,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [1,2,5,3,4,8,6,7] => [1,2,5,4,3,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,8,6,7] => [1,2,3,5,4,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [1,2,3,5,8,4,6,7] => [1,2,3,8,7,6,4,5] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [1,2,3,5,4,6,8,7] => [1,2,3,5,4,6,8,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [1,2,3,5,6,4,8,7] => [1,2,3,6,4,5,8,7] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [1,2,3,5,6,8,4,7] => [1,2,3,8,7,4,5,6] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [1,2,5,3,4,6,7,8] => [1,2,5,4,3,6,7,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [1,2,3,5,6,4,7,8] => [1,2,3,6,4,5,7,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [1,2,3,5,6,7,4,8] => [1,2,3,7,4,5,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,4] => [1,2,3,8,4,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [1,6,7,2,3,8,4,5] => [1,8,5,3,7,4,2,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [1,6,2,7,8,3,4,5] => [1,6,3,2,7,4,8,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [1,6,7,2,8,3,4,5] => [1,7,4,2,6,3,8,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [1,6,7,8,2,3,4,5] => [1,8,5,2,6,3,7,4] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [1,6,2,7,3,4,8,5] => [1,8,5,3,2,6,4,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [1,6,7,2,3,4,8,5] => [1,6,4,2,8,5,3,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [1,2,6,3,7,4,8,5] => [1,2,6,4,3,8,5,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [1,2,6,7,3,4,8,5] => [1,2,8,5,3,6,4,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [1,6,2,3,7,8,4,5] => [1,8,5,7,4,3,2,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [1,2,6,3,7,8,4,5] => [1,2,8,5,7,4,3,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [1,2,6,7,3,8,4,5] => [1,2,7,4,8,5,3,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,2,6,7,8,3,4,5] => [1,2,6,3,7,4,8,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [1,6,7,2,3,4,5,8] => [1,6,4,2,7,5,3,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [1,2,6,7,3,4,5,8] => [1,2,7,5,3,6,4,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [1,6,2,3,4,7,5,8] => [1,7,5,4,3,2,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,2,3,6,4,7,5,8] => [1,2,3,7,5,4,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,2,3,6,7,4,5,8] => [1,2,3,6,4,7,5,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,7,8,5] => [1,8,5,4,3,2,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,7,8,5] => [1,2,8,5,4,3,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,7,8,5] => [1,2,3,8,5,4,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [1,2,3,6,7,4,8,5] => [1,2,3,6,4,8,5,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,6,7,8,4,5] => [1,2,3,8,5,7,4,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [1,6,8,2,3,4,5,7] => [1,6,4,2,8,7,5,3] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,6,2,3,8,4,5,7] => [1,6,4,3,2,8,7,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [1,2,6,8,3,4,5,7] => [1,2,8,7,5,3,6,4] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,6,2,3,4,8,5,7] => [1,8,7,5,4,3,2,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [1,2,6,3,4,8,5,7] => [1,2,8,7,5,4,3,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [1,2,3,6,4,8,5,7] => [1,2,3,8,7,5,4,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,2,3,6,8,4,5,7] => [1,2,3,6,4,8,7,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5,8,7] => [1,6,5,4,3,2,8,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5,8,7] => [1,2,3,6,5,4,8,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7] => [1,2,3,4,6,5,8,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,6,8,5,7] => [1,2,3,4,8,7,5,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [1,6,2,3,4,5,7,8] => [1,6,5,4,3,2,7,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [1,2,6,3,4,5,7,8] => [1,2,6,5,4,3,7,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8] => [1,2,3,4,6,5,7,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [1,2,3,4,6,7,5,8] => [1,2,3,4,7,5,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,5] => [1,2,3,4,8,5,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,7,2,8,3,4,5,6] => [1,7,5,3,2,8,6,4] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,8,2,3,4,5,6] => [1,8,6,4,2,7,5,3] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [1,7,2,3,8,4,5,6] => [1,8,6,4,3,2,7,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,2,7,3,8,4,5,6] => [1,2,8,6,4,3,7,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,2,7,8,3,4,5,6] => [1,2,7,5,3,8,6,4] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [1,2,7,3,4,8,5,6] => [1,2,7,5,4,3,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,2,3,7,4,8,5,6] => [1,2,3,7,5,4,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,2,3,7,8,4,5,6] => [1,2,3,8,6,4,7,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [1,7,2,3,4,5,8,6] => [1,8,6,5,4,3,2,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,2,7,3,4,5,8,6] => [1,2,8,6,5,4,3,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,2,3,7,4,5,8,6] => [1,2,3,8,6,5,4,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6] => [1,2,3,4,8,6,5,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6] => [1,2,3,4,7,5,8,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,8] => [1,7,6,5,4,3,2,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [1,2,7,3,4,5,6,8] => [1,2,7,6,5,4,3,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,2,3,7,4,5,6,8] => [1,2,3,7,6,5,4,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,6,8] => [1,2,3,4,7,6,5,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,6] => [1,2,3,4,5,8,6,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,8,3,4,5,6,7] => [1,2,8,7,6,5,4,3] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,8,4,5,6,7] => [1,2,3,8,7,6,5,4] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,8,5,6,7] => [1,2,3,4,8,7,6,5] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,7] => [1,2,3,4,5,8,7,6] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => [1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8] => [1,3,2,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7,9] => [1,4,2,3,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,3,4,5,6,8,9,2,7] => [1,8,2,3,4,5,6,9,7] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,3,2,9,4,5,6,7,8] => [1,3,2,9,8,7,6,5,4] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,3,9,2,4,5,6,7,8] => [1,9,8,7,6,5,4,2,3] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [1,3,4,9,2,5,6,7,8] => [1,9,8,7,6,5,2,3,4] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,9,8] => [1,3,2,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,9,8] => [1,7,2,3,4,5,6,9,8] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9] => [1,3,2,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,3,4,2,5,6,7,8,9] => [1,4,2,3,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,3,4,5,6,7,2,8,9] => [1,7,2,3,4,5,6,8,9] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,2,9] => [1,8,2,3,4,5,6,7,9] => [1,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2] => [1,9,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,2,5,3,7,6,9,8] => [1,5,3,2,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,4,5,2,3,7,6,9,8] => [1,4,2,5,3,7,6,9,8] => [1,9,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,4,2,5,6,7,8,9,3] => [1,9,3,2,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,4,5,6,7,8,9,2,3] => [1,8,2,4,6,9,3,5,7] => [1,9,8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,9] => [1,2,4,3,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,4,2,3,5,6,7,8,9] => [1,4,3,2,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9] => [1,2,4,3,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,3] => [1,2,9,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8] => [1,2,3,5,4,7,6,9,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9] => [1,2,3,5,4,6,7,8,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,4] => [1,2,3,9,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,6,7,8,9,2,3,4,5] => [1,6,2,7,3,8,4,9,5] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,9] => [1,2,3,4,6,5,8,7,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,6,8,9,5,7] => [1,2,3,4,8,5,6,9,7] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9] => [1,2,3,4,6,5,7,8,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,5] => [1,2,3,4,9,5,6,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,2,3,7,8,9,4,5,6] => [1,2,3,7,4,8,5,9,6] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,6,9] => [1,2,3,4,8,6,5,7,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,8,5,6,9] => [1,2,3,4,7,5,8,6,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [1,2,3,4,7,5,8,9,6] => [1,2,3,4,9,6,5,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [1,7,9,2,3,4,5,6,8] => [1,9,8,6,4,2,7,5,3] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [1,2,3,4,7,9,5,6,8] => [1,2,3,4,7,5,9,8,6] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [1,7,2,3,4,5,6,9,8] => [1,7,6,5,4,3,2,9,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,9,8] => [1,2,3,4,5,7,6,9,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9] => [1,2,3,4,5,7,6,8,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,6] => [1,2,3,4,5,9,6,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [1,8,2,9,3,4,5,6,7] => [1,9,7,5,3,2,8,6,4] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,8,9,2,3,4,5,6,7] => [1,8,6,4,2,9,7,5,3] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,9,7] => [1,9,7,6,5,4,3,2,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,2,3,4,5,8,6,9,7] => [1,2,3,4,5,9,7,6,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,8,6,9,7] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [1,8,2,3,4,5,6,7,9] => [1,8,7,6,5,4,3,2,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9] => [1,2,3,4,5,6,8,7,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,9,7,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8] => [1,9,8,7,6,5,4,3,2] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,9,3,4,5,6,7,8] => [1,2,9,8,7,6,5,4,3] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,9,4,5,6,7,8] => [1,2,3,9,8,7,6,5,4] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,9,5,6,7,8] => [1,2,3,4,9,8,7,6,5] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,9,6,7,8] => [1,2,3,4,5,9,8,7,6] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,7,8] => [1,2,3,4,5,6,9,8,7] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,9,8] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [1,10,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,2] => [1,10,2,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2] => [1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,8,10] => [1,9,8,7,6,5,4,3,2,10] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,2,10] => [1,9,2,3,4,5,6,7,8,10] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,3,4,5,6,7,8,9,10,11,2] => [1,11,2,3,4,5,6,7,8,9,10] => [1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => [1,12,2,3,4,5,6,7,8,9,10,11] => [1,12,11,10,9,8,7,6,5,4,3,2] => [1,12,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [1,9,2,3,4,5,6,7,10,8] => [1,10,8,7,6,5,4,3,2,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [1,9,10,2,3,4,5,6,7,8] => [1,10,8,6,4,2,9,7,5,3] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,3,2,4,5,6,7,8,9,10] => [1,3,2,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2]
[] => [1,0] => [1] => [1] => [1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5,8,7,10,9] => [1,2,4,3,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,2,4,3,5,6,7,8,9,10] => [1,2,4,3,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,4,5,6,7,8,9,10,3] => [1,2,10,3,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,7,6,9,8,10] => [1,2,3,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0] => [1,2,3,5,4,10,6,7,8,9] => [1,2,3,5,4,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,2,3,5,4,6,7,8,9,10] => [1,2,3,5,4,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,5,6,7,8,9,10,4] => [1,2,3,10,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5,8,7,10,9] => [1,2,3,4,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,6,5,7,8,9,10] => [1,2,3,4,6,5,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,6,7,8,9,10,5] => [1,2,3,4,10,5,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [1,2,7,8,9,10,3,4,5,6] => [1,2,7,3,8,4,9,5,10,6] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,7,6,8,9,10] => [1,2,3,4,5,7,6,8,9,10] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,7,8,9,10,6] => [1,2,3,4,5,10,6,7,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,8,9,10,5,6,7] => [1,2,3,4,8,5,9,6,10,7] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,10,9] => [1,2,3,4,5,6,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,7,9,10] => [1,2,3,4,5,6,8,7,9,10] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,8,9,10,7] => [1,2,3,4,5,6,10,7,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,9,10,7,8] => [1,2,3,4,5,6,9,7,10,8] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,8,10] => [1,2,3,4,5,6,7,9,8,10] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,9,10,8] => [1,2,3,4,5,6,7,10,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [1,2,10,3,4,5,6,7,8,9] => [1,2,10,9,8,7,6,5,4,3] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [1,2,3,10,4,5,6,7,8,9] => [1,2,3,10,9,8,7,6,5,4] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [1,2,3,4,10,5,6,7,8,9] => [1,2,3,4,10,9,8,7,6,5] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [1,2,3,4,5,10,6,7,8,9] => [1,2,3,4,5,10,9,8,7,6] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,10,7,8,9] => [1,2,3,4,5,6,10,9,8,7] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,10,8,9] => [1,2,3,4,5,6,7,10,9,8] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,10,9] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,10] => [1,3,2,5,4,7,6,9,8,10] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5,8,7,10,9] => [1,4,2,3,6,5,8,7,10,9] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,10] => [1,3,2,5,4,7,6,9,8,11,10] => [1,11,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [1,3,2,5,4,7,6,10,8,9] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,7,6,10,8,9] => [1,3,2,5,4,7,6,10,9,8] => [1,10,9,8,7,6,5,4,3,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [1,3,10,2,4,5,6,7,8,9] => [1,10,9,8,7,6,5,4,2,3] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [1,8,9,10,2,3,4,5,6,7] => [1,8,5,2,9,6,3,10,7,4] => [1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10,11] => [1,2,3,4,5,6,7,8,9,10,11] => [1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,11,9] => [1,2,3,4,5,6,7,8,11,9,10] => [1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,11,9,10] => [1,2,3,4,5,6,7,8,11,10,9] => [1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,12,10] => [1,2,3,4,5,6,7,8,9,12,10,11] => [1,12,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [1,2,3,4,5,6,7,8,9,11,10] => [1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,10,9,11] => [1,2,3,4,5,6,7,8,10,9,11] => [1,11,10,9,8,7,6,5,4,3,2]
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].