Identifier
Identifier
Mp00087: Permutations inverse first fundamental transformationPermutations
Images
[1] => [1]
[1,2] => [1,2]
[2,1] => [2,1]
[1,2,3] => [1,2,3]
[1,3,2] => [1,3,2]
[2,1,3] => [2,1,3]
[2,3,1] => [3,1,2]
[3,1,2] => [3,2,1]
[3,2,1] => [2,3,1]
[1,2,3,4] => [1,2,3,4]
[1,2,4,3] => [1,2,4,3]
[1,3,2,4] => [1,3,2,4]
[1,3,4,2] => [1,4,2,3]
[1,4,2,3] => [1,4,3,2]
[1,4,3,2] => [1,3,4,2]
[2,1,3,4] => [2,1,3,4]
[2,1,4,3] => [2,1,4,3]
[2,3,1,4] => [3,1,2,4]
[2,3,4,1] => [4,1,2,3]
[2,4,1,3] => [4,3,1,2]
[2,4,3,1] => [3,4,1,2]
[3,1,2,4] => [3,2,1,4]
[3,1,4,2] => [4,2,1,3]
[3,2,1,4] => [2,3,1,4]
[3,2,4,1] => [2,4,1,3]
[3,4,1,2] => [3,1,4,2]
[3,4,2,1] => [4,1,3,2]
[4,1,2,3] => [4,3,2,1]
[4,1,3,2] => [3,4,2,1]
[4,2,1,3] => [2,4,3,1]
[4,2,3,1] => [2,3,4,1]
[4,3,1,2] => [4,2,3,1]
[4,3,2,1] => [3,2,4,1]
[1,2,3,4,5] => [1,2,3,4,5]
[1,2,3,5,4] => [1,2,3,5,4]
[1,2,4,3,5] => [1,2,4,3,5]
[1,2,4,5,3] => [1,2,5,3,4]
[1,2,5,3,4] => [1,2,5,4,3]
[1,2,5,4,3] => [1,2,4,5,3]
[1,3,2,4,5] => [1,3,2,4,5]
[1,3,2,5,4] => [1,3,2,5,4]
[1,3,4,2,5] => [1,4,2,3,5]
[1,3,4,5,2] => [1,5,2,3,4]
[1,3,5,2,4] => [1,5,4,2,3]
[1,3,5,4,2] => [1,4,5,2,3]
[1,4,2,3,5] => [1,4,3,2,5]
[1,4,2,5,3] => [1,5,3,2,4]
[1,4,3,2,5] => [1,3,4,2,5]
[1,4,3,5,2] => [1,3,5,2,4]
[1,4,5,2,3] => [1,4,2,5,3]
[1,4,5,3,2] => [1,5,2,4,3]
[1,5,2,3,4] => [1,5,4,3,2]
[1,5,2,4,3] => [1,4,5,3,2]
[1,5,3,2,4] => [1,3,5,4,2]
[1,5,3,4,2] => [1,3,4,5,2]
[1,5,4,2,3] => [1,5,3,4,2]
[1,5,4,3,2] => [1,4,3,5,2]
[2,1,3,4,5] => [2,1,3,4,5]
[2,1,3,5,4] => [2,1,3,5,4]
[2,1,4,3,5] => [2,1,4,3,5]
[2,1,4,5,3] => [2,1,5,3,4]
[2,1,5,3,4] => [2,1,5,4,3]
[2,1,5,4,3] => [2,1,4,5,3]
[2,3,1,4,5] => [3,1,2,4,5]
[2,3,1,5,4] => [3,1,2,5,4]
[2,3,4,1,5] => [4,1,2,3,5]
[2,3,4,5,1] => [5,1,2,3,4]
[2,3,5,1,4] => [5,4,1,2,3]
[2,3,5,4,1] => [4,5,1,2,3]
[2,4,1,3,5] => [4,3,1,2,5]
[2,4,1,5,3] => [5,3,1,2,4]
[2,4,3,1,5] => [3,4,1,2,5]
[2,4,3,5,1] => [3,5,1,2,4]
[2,4,5,1,3] => [4,1,2,5,3]
[2,4,5,3,1] => [5,1,2,4,3]
[2,5,1,3,4] => [5,4,3,1,2]
[2,5,1,4,3] => [4,5,3,1,2]
[2,5,3,1,4] => [3,5,4,1,2]
[2,5,3,4,1] => [3,4,5,1,2]
[2,5,4,1,3] => [5,3,4,1,2]
[2,5,4,3,1] => [4,3,5,1,2]
[3,1,2,4,5] => [3,2,1,4,5]
[3,1,2,5,4] => [3,2,1,5,4]
[3,1,4,2,5] => [4,2,1,3,5]
[3,1,4,5,2] => [5,2,1,3,4]
[3,1,5,2,4] => [5,4,2,1,3]
[3,1,5,4,2] => [4,5,2,1,3]
[3,2,1,4,5] => [2,3,1,4,5]
[3,2,1,5,4] => [2,3,1,5,4]
[3,2,4,1,5] => [2,4,1,3,5]
[3,2,4,5,1] => [2,5,1,3,4]
[3,2,5,1,4] => [2,5,4,1,3]
[3,2,5,4,1] => [2,4,5,1,3]
[3,4,1,2,5] => [3,1,4,2,5]
[3,4,1,5,2] => [3,1,5,2,4]
[3,4,2,1,5] => [4,1,3,2,5]
[3,4,2,5,1] => [5,1,3,2,4]
[3,4,5,1,2] => [5,2,4,1,3]
[3,4,5,2,1] => [4,2,5,1,3]
[3,5,1,2,4] => [3,1,5,4,2]
[3,5,1,4,2] => [3,1,4,5,2]
[3,5,2,1,4] => [5,4,1,3,2]
[3,5,2,4,1] => [4,5,1,3,2]
[3,5,4,1,2] => [4,1,3,5,2]
[3,5,4,2,1] => [5,1,3,4,2]
[4,1,2,3,5] => [4,3,2,1,5]
[4,1,2,5,3] => [5,3,2,1,4]
[4,1,3,2,5] => [3,4,2,1,5]
[4,1,3,5,2] => [3,5,2,1,4]
[4,1,5,2,3] => [4,2,1,5,3]
[4,1,5,3,2] => [5,2,1,4,3]
[4,2,1,3,5] => [2,4,3,1,5]
[4,2,1,5,3] => [2,5,3,1,4]
[4,2,3,1,5] => [2,3,4,1,5]
[4,2,3,5,1] => [2,3,5,1,4]
[4,2,5,1,3] => [2,4,1,5,3]
[4,2,5,3,1] => [2,5,1,4,3]
[4,3,1,2,5] => [4,2,3,1,5]
[4,3,1,5,2] => [5,2,3,1,4]
[4,3,2,1,5] => [3,2,4,1,5]
[4,3,2,5,1] => [3,2,5,1,4]
[4,3,5,1,2] => [4,1,5,2,3]
[4,3,5,2,1] => [5,1,4,2,3]
[4,5,1,2,3] => [5,3,1,4,2]
[4,5,1,3,2] => [4,3,1,5,2]
[4,5,2,1,3] => [4,1,5,3,2]
[4,5,2,3,1] => [5,1,4,3,2]
[4,5,3,1,2] => [3,4,1,5,2]
[4,5,3,2,1] => [3,5,1,4,2]
[5,1,2,3,4] => [5,4,3,2,1]
[5,1,2,4,3] => [4,5,3,2,1]
[5,1,3,2,4] => [3,5,4,2,1]
[5,1,3,4,2] => [3,4,5,2,1]
[5,1,4,2,3] => [5,3,4,2,1]
[5,1,4,3,2] => [4,3,5,2,1]
[5,2,1,3,4] => [2,5,4,3,1]
[5,2,1,4,3] => [2,4,5,3,1]
[5,2,3,1,4] => [2,3,5,4,1]
[5,2,3,4,1] => [2,3,4,5,1]
[5,2,4,1,3] => [2,5,3,4,1]
[5,2,4,3,1] => [2,4,3,5,1]
[5,3,1,2,4] => [5,4,2,3,1]
[5,3,1,4,2] => [4,5,2,3,1]
[5,3,2,1,4] => [3,2,5,4,1]
[5,3,2,4,1] => [3,2,4,5,1]
[5,3,4,1,2] => [5,2,3,4,1]
[5,3,4,2,1] => [4,2,3,5,1]
[5,4,1,2,3] => [4,2,5,3,1]
[5,4,1,3,2] => [5,2,4,3,1]
[5,4,2,1,3] => [5,3,2,4,1]
[5,4,2,3,1] => [4,3,2,5,1]
[5,4,3,1,2] => [3,5,2,4,1]
[5,4,3,2,1] => [3,4,2,5,1]
[1,2,3,4,5,6] => [1,2,3,4,5,6]
[1,2,3,4,6,5] => [1,2,3,4,6,5]
[1,2,3,5,4,6] => [1,2,3,5,4,6]
[1,2,3,5,6,4] => [1,2,3,6,4,5]
[1,2,3,6,4,5] => [1,2,3,6,5,4]
[1,2,3,6,5,4] => [1,2,3,5,6,4]
[1,2,4,3,5,6] => [1,2,4,3,5,6]
[1,2,4,3,6,5] => [1,2,4,3,6,5]
[1,2,4,5,3,6] => [1,2,5,3,4,6]
[1,2,4,5,6,3] => [1,2,6,3,4,5]
[1,2,4,6,3,5] => [1,2,6,5,3,4]
[1,2,4,6,5,3] => [1,2,5,6,3,4]
[1,2,5,3,4,6] => [1,2,5,4,3,6]
[1,2,5,3,6,4] => [1,2,6,4,3,5]
[1,2,5,4,3,6] => [1,2,4,5,3,6]
[1,2,5,4,6,3] => [1,2,4,6,3,5]
[1,2,5,6,3,4] => [1,2,5,3,6,4]
[1,2,5,6,4,3] => [1,2,6,3,5,4]
[1,2,6,3,4,5] => [1,2,6,5,4,3]
[1,2,6,3,5,4] => [1,2,5,6,4,3]
[1,2,6,4,3,5] => [1,2,4,6,5,3]
[1,2,6,4,5,3] => [1,2,4,5,6,3]
[1,2,6,5,3,4] => [1,2,6,4,5,3]
[1,2,6,5,4,3] => [1,2,5,4,6,3]
[1,3,2,4,5,6] => [1,3,2,4,5,6]
[1,3,2,4,6,5] => [1,3,2,4,6,5]
[1,3,2,5,4,6] => [1,3,2,5,4,6]
[1,3,2,5,6,4] => [1,3,2,6,4,5]
[1,3,2,6,4,5] => [1,3,2,6,5,4]
[1,3,2,6,5,4] => [1,3,2,5,6,4]
[1,3,4,2,5,6] => [1,4,2,3,5,6]
[1,3,4,2,6,5] => [1,4,2,3,6,5]
[1,3,4,5,2,6] => [1,5,2,3,4,6]
[1,3,4,5,6,2] => [1,6,2,3,4,5]
[1,3,4,6,2,5] => [1,6,5,2,3,4]
[1,3,4,6,5,2] => [1,5,6,2,3,4]
[1,3,5,2,4,6] => [1,5,4,2,3,6]
[1,3,5,2,6,4] => [1,6,4,2,3,5]
[1,3,5,4,2,6] => [1,4,5,2,3,6]
[1,3,5,4,6,2] => [1,4,6,2,3,5]
[1,3,5,6,2,4] => [1,5,2,3,6,4]
[1,3,5,6,4,2] => [1,6,2,3,5,4]
[1,3,6,2,4,5] => [1,6,5,4,2,3]
[1,3,6,2,5,4] => [1,5,6,4,2,3]
[1,3,6,4,2,5] => [1,4,6,5,2,3]
[1,3,6,4,5,2] => [1,4,5,6,2,3]
[1,3,6,5,2,4] => [1,6,4,5,2,3]
[1,3,6,5,4,2] => [1,5,4,6,2,3]
[1,4,2,3,5,6] => [1,4,3,2,5,6]
[1,4,2,3,6,5] => [1,4,3,2,6,5]
[1,4,2,5,3,6] => [1,5,3,2,4,6]
[1,4,2,5,6,3] => [1,6,3,2,4,5]
[1,4,2,6,3,5] => [1,6,5,3,2,4]
[1,4,2,6,5,3] => [1,5,6,3,2,4]
[1,4,3,2,5,6] => [1,3,4,2,5,6]
[1,4,3,2,6,5] => [1,3,4,2,6,5]
[1,4,3,5,2,6] => [1,3,5,2,4,6]
[1,4,3,5,6,2] => [1,3,6,2,4,5]
[1,4,3,6,2,5] => [1,3,6,5,2,4]
[1,4,3,6,5,2] => [1,3,5,6,2,4]
[1,4,5,2,3,6] => [1,4,2,5,3,6]
[1,4,5,2,6,3] => [1,4,2,6,3,5]
[1,4,5,3,2,6] => [1,5,2,4,3,6]
[1,4,5,3,6,2] => [1,6,2,4,3,5]
[1,4,5,6,2,3] => [1,6,3,5,2,4]
[1,4,5,6,3,2] => [1,5,3,6,2,4]
[1,4,6,2,3,5] => [1,4,2,6,5,3]
[1,4,6,2,5,3] => [1,4,2,5,6,3]
[1,4,6,3,2,5] => [1,6,5,2,4,3]
[1,4,6,3,5,2] => [1,5,6,2,4,3]
[1,4,6,5,2,3] => [1,5,2,4,6,3]
[1,4,6,5,3,2] => [1,6,2,4,5,3]
[1,5,2,3,4,6] => [1,5,4,3,2,6]
[1,5,2,3,6,4] => [1,6,4,3,2,5]
[1,5,2,4,3,6] => [1,4,5,3,2,6]
[1,5,2,4,6,3] => [1,4,6,3,2,5]
[1,5,2,6,3,4] => [1,5,3,2,6,4]
[1,5,2,6,4,3] => [1,6,3,2,5,4]
[1,5,3,2,4,6] => [1,3,5,4,2,6]
[1,5,3,2,6,4] => [1,3,6,4,2,5]
[1,5,3,4,2,6] => [1,3,4,5,2,6]
[1,5,3,4,6,2] => [1,3,4,6,2,5]
[1,5,3,6,2,4] => [1,3,5,2,6,4]
[1,5,3,6,4,2] => [1,3,6,2,5,4]
[1,5,4,2,3,6] => [1,5,3,4,2,6]
[1,5,4,2,6,3] => [1,6,3,4,2,5]
[1,5,4,3,2,6] => [1,4,3,5,2,6]
[1,5,4,3,6,2] => [1,4,3,6,2,5]
[1,5,4,6,2,3] => [1,5,2,6,3,4]
[1,5,4,6,3,2] => [1,6,2,5,3,4]
[1,5,6,2,3,4] => [1,6,4,2,5,3]
[1,5,6,2,4,3] => [1,5,4,2,6,3]
[1,5,6,3,2,4] => [1,5,2,6,4,3]
[1,5,6,3,4,2] => [1,6,2,5,4,3]
[1,5,6,4,2,3] => [1,4,5,2,6,3]
[1,5,6,4,3,2] => [1,4,6,2,5,3]
[1,6,2,3,4,5] => [1,6,5,4,3,2]
[1,6,2,3,5,4] => [1,5,6,4,3,2]
[1,6,2,4,3,5] => [1,4,6,5,3,2]
[1,6,2,4,5,3] => [1,4,5,6,3,2]
[1,6,2,5,3,4] => [1,6,4,5,3,2]
[1,6,2,5,4,3] => [1,5,4,6,3,2]
[1,6,3,2,4,5] => [1,3,6,5,4,2]
[1,6,3,2,5,4] => [1,3,5,6,4,2]
[1,6,3,4,2,5] => [1,3,4,6,5,2]
[1,6,3,4,5,2] => [1,3,4,5,6,2]
[1,6,3,5,2,4] => [1,3,6,4,5,2]
[1,6,3,5,4,2] => [1,3,5,4,6,2]
[1,6,4,2,3,5] => [1,6,5,3,4,2]
[1,6,4,2,5,3] => [1,5,6,3,4,2]
[1,6,4,3,2,5] => [1,4,3,6,5,2]
[1,6,4,3,5,2] => [1,4,3,5,6,2]
[1,6,4,5,2,3] => [1,6,3,4,5,2]
[1,6,4,5,3,2] => [1,5,3,4,6,2]
[1,6,5,2,3,4] => [1,5,3,6,4,2]
[1,6,5,2,4,3] => [1,6,3,5,4,2]
[1,6,5,3,2,4] => [1,6,4,3,5,2]
[1,6,5,3,4,2] => [1,5,4,3,6,2]
[1,6,5,4,2,3] => [1,4,6,3,5,2]
[1,6,5,4,3,2] => [1,4,5,3,6,2]
[2,1,3,4,5,6] => [2,1,3,4,5,6]
[2,1,3,4,6,5] => [2,1,3,4,6,5]
[2,1,3,5,4,6] => [2,1,3,5,4,6]
[2,1,3,5,6,4] => [2,1,3,6,4,5]
[2,1,3,6,4,5] => [2,1,3,6,5,4]
[2,1,3,6,5,4] => [2,1,3,5,6,4]
[2,1,4,3,5,6] => [2,1,4,3,5,6]
[2,1,4,3,6,5] => [2,1,4,3,6,5]
[2,1,4,5,3,6] => [2,1,5,3,4,6]
[2,1,4,5,6,3] => [2,1,6,3,4,5]
[2,1,4,6,3,5] => [2,1,6,5,3,4]
[2,1,4,6,5,3] => [2,1,5,6,3,4]
[2,1,5,3,4,6] => [2,1,5,4,3,6]
[2,1,5,3,6,4] => [2,1,6,4,3,5]
[2,1,5,4,3,6] => [2,1,4,5,3,6]
[2,1,5,4,6,3] => [2,1,4,6,3,5]
[2,1,5,6,3,4] => [2,1,5,3,6,4]
[2,1,5,6,4,3] => [2,1,6,3,5,4]
[2,1,6,3,4,5] => [2,1,6,5,4,3]
[2,1,6,3,5,4] => [2,1,5,6,4,3]
[2,1,6,4,3,5] => [2,1,4,6,5,3]
[2,1,6,4,5,3] => [2,1,4,5,6,3]
[2,1,6,5,3,4] => [2,1,6,4,5,3]
[2,1,6,5,4,3] => [2,1,5,4,6,3]
[2,3,1,4,5,6] => [3,1,2,4,5,6]
[2,3,1,4,6,5] => [3,1,2,4,6,5]
[2,3,1,5,4,6] => [3,1,2,5,4,6]
[2,3,1,5,6,4] => [3,1,2,6,4,5]
[2,3,1,6,4,5] => [3,1,2,6,5,4]
[2,3,1,6,5,4] => [3,1,2,5,6,4]
[2,3,4,1,5,6] => [4,1,2,3,5,6]
[2,3,4,1,6,5] => [4,1,2,3,6,5]
[2,3,4,5,1,6] => [5,1,2,3,4,6]
[2,3,4,5,6,1] => [6,1,2,3,4,5]
[2,3,4,6,1,5] => [6,5,1,2,3,4]
[2,3,4,6,5,1] => [5,6,1,2,3,4]
[2,3,5,1,4,6] => [5,4,1,2,3,6]
[2,3,5,1,6,4] => [6,4,1,2,3,5]
[2,3,5,4,1,6] => [4,5,1,2,3,6]
[2,3,5,4,6,1] => [4,6,1,2,3,5]
[2,3,5,6,1,4] => [5,1,2,3,6,4]
[2,3,5,6,4,1] => [6,1,2,3,5,4]
[2,3,6,1,4,5] => [6,5,4,1,2,3]
[2,3,6,1,5,4] => [5,6,4,1,2,3]
[2,3,6,4,1,5] => [4,6,5,1,2,3]
[2,3,6,4,5,1] => [4,5,6,1,2,3]
[2,3,6,5,1,4] => [6,4,5,1,2,3]
[2,3,6,5,4,1] => [5,4,6,1,2,3]
[2,4,1,3,5,6] => [4,3,1,2,5,6]
[2,4,1,3,6,5] => [4,3,1,2,6,5]
[2,4,1,5,3,6] => [5,3,1,2,4,6]
[2,4,1,5,6,3] => [6,3,1,2,4,5]
[2,4,1,6,3,5] => [6,5,3,1,2,4]
[2,4,1,6,5,3] => [5,6,3,1,2,4]
[2,4,3,1,5,6] => [3,4,1,2,5,6]
[2,4,3,1,6,5] => [3,4,1,2,6,5]
[2,4,3,5,1,6] => [3,5,1,2,4,6]
[2,4,3,5,6,1] => [3,6,1,2,4,5]
[2,4,3,6,1,5] => [3,6,5,1,2,4]
[2,4,3,6,5,1] => [3,5,6,1,2,4]
[2,4,5,1,3,6] => [4,1,2,5,3,6]
[2,4,5,1,6,3] => [4,1,2,6,3,5]
[2,4,5,3,1,6] => [5,1,2,4,3,6]
[2,4,5,3,6,1] => [6,1,2,4,3,5]
[2,4,5,6,1,3] => [6,3,5,1,2,4]
[2,4,5,6,3,1] => [5,3,6,1,2,4]
[2,4,6,1,3,5] => [4,1,2,6,5,3]
[2,4,6,1,5,3] => [4,1,2,5,6,3]
[2,4,6,3,1,5] => [6,5,1,2,4,3]
[2,4,6,3,5,1] => [5,6,1,2,4,3]
[2,4,6,5,1,3] => [5,1,2,4,6,3]
[2,4,6,5,3,1] => [6,1,2,4,5,3]
[2,5,1,3,4,6] => [5,4,3,1,2,6]
[2,5,1,3,6,4] => [6,4,3,1,2,5]
[2,5,1,4,3,6] => [4,5,3,1,2,6]
[2,5,1,4,6,3] => [4,6,3,1,2,5]
[2,5,1,6,3,4] => [5,3,1,2,6,4]
[2,5,1,6,4,3] => [6,3,1,2,5,4]
[2,5,3,1,4,6] => [3,5,4,1,2,6]
[2,5,3,1,6,4] => [3,6,4,1,2,5]
[2,5,3,4,1,6] => [3,4,5,1,2,6]
[2,5,3,4,6,1] => [3,4,6,1,2,5]
[2,5,3,6,1,4] => [3,5,1,2,6,4]
[2,5,3,6,4,1] => [3,6,1,2,5,4]
[2,5,4,1,3,6] => [5,3,4,1,2,6]
[2,5,4,1,6,3] => [6,3,4,1,2,5]
[2,5,4,3,1,6] => [4,3,5,1,2,6]
[2,5,4,3,6,1] => [4,3,6,1,2,5]
[2,5,4,6,1,3] => [5,1,2,6,3,4]
[2,5,4,6,3,1] => [6,1,2,5,3,4]
[2,5,6,1,3,4] => [6,4,1,2,5,3]
[2,5,6,1,4,3] => [5,4,1,2,6,3]
[2,5,6,3,1,4] => [5,1,2,6,4,3]
[2,5,6,3,4,1] => [6,1,2,5,4,3]
[2,5,6,4,1,3] => [4,5,1,2,6,3]
[2,5,6,4,3,1] => [4,6,1,2,5,3]
[2,6,1,3,4,5] => [6,5,4,3,1,2]
[2,6,1,3,5,4] => [5,6,4,3,1,2]
[2,6,1,4,3,5] => [4,6,5,3,1,2]
[2,6,1,4,5,3] => [4,5,6,3,1,2]
[2,6,1,5,3,4] => [6,4,5,3,1,2]
[2,6,1,5,4,3] => [5,4,6,3,1,2]
[2,6,3,1,4,5] => [3,6,5,4,1,2]
[2,6,3,1,5,4] => [3,5,6,4,1,2]
[2,6,3,4,1,5] => [3,4,6,5,1,2]
[2,6,3,4,5,1] => [3,4,5,6,1,2]
[2,6,3,5,1,4] => [3,6,4,5,1,2]
[2,6,3,5,4,1] => [3,5,4,6,1,2]
[2,6,4,1,3,5] => [6,5,3,4,1,2]
[2,6,4,1,5,3] => [5,6,3,4,1,2]
[2,6,4,3,1,5] => [4,3,6,5,1,2]
[2,6,4,3,5,1] => [4,3,5,6,1,2]
[2,6,4,5,1,3] => [6,3,4,5,1,2]
[2,6,4,5,3,1] => [5,3,4,6,1,2]
[2,6,5,1,3,4] => [5,3,6,4,1,2]
[2,6,5,1,4,3] => [6,3,5,4,1,2]
[2,6,5,3,1,4] => [6,4,3,5,1,2]
[2,6,5,3,4,1] => [5,4,3,6,1,2]
[2,6,5,4,1,3] => [4,6,3,5,1,2]
[2,6,5,4,3,1] => [4,5,3,6,1,2]
[3,1,2,4,5,6] => [3,2,1,4,5,6]
[3,1,2,4,6,5] => [3,2,1,4,6,5]
[3,1,2,5,4,6] => [3,2,1,5,4,6]
[3,1,2,5,6,4] => [3,2,1,6,4,5]
[3,1,2,6,4,5] => [3,2,1,6,5,4]
[3,1,2,6,5,4] => [3,2,1,5,6,4]
[3,1,4,2,5,6] => [4,2,1,3,5,6]
[3,1,4,2,6,5] => [4,2,1,3,6,5]
[3,1,4,5,2,6] => [5,2,1,3,4,6]
[3,1,4,5,6,2] => [6,2,1,3,4,5]
[3,1,4,6,2,5] => [6,5,2,1,3,4]
[3,1,4,6,5,2] => [5,6,2,1,3,4]
[3,1,5,2,4,6] => [5,4,2,1,3,6]
[3,1,5,2,6,4] => [6,4,2,1,3,5]
[3,1,5,4,2,6] => [4,5,2,1,3,6]
[3,1,5,4,6,2] => [4,6,2,1,3,5]
[3,1,5,6,2,4] => [5,2,1,3,6,4]
[3,1,5,6,4,2] => [6,2,1,3,5,4]
[3,1,6,2,4,5] => [6,5,4,2,1,3]
[3,1,6,2,5,4] => [5,6,4,2,1,3]
[3,1,6,4,2,5] => [4,6,5,2,1,3]
[3,1,6,4,5,2] => [4,5,6,2,1,3]
[3,1,6,5,2,4] => [6,4,5,2,1,3]
[3,1,6,5,4,2] => [5,4,6,2,1,3]
[3,2,1,4,5,6] => [2,3,1,4,5,6]
[3,2,1,4,6,5] => [2,3,1,4,6,5]
[3,2,1,5,4,6] => [2,3,1,5,4,6]
[3,2,1,5,6,4] => [2,3,1,6,4,5]
[3,2,1,6,4,5] => [2,3,1,6,5,4]
[3,2,1,6,5,4] => [2,3,1,5,6,4]
[3,2,4,1,5,6] => [2,4,1,3,5,6]
[3,2,4,1,6,5] => [2,4,1,3,6,5]
[3,2,4,5,1,6] => [2,5,1,3,4,6]
[3,2,4,5,6,1] => [2,6,1,3,4,5]
[3,2,4,6,1,5] => [2,6,5,1,3,4]
[3,2,4,6,5,1] => [2,5,6,1,3,4]
[3,2,5,1,4,6] => [2,5,4,1,3,6]
[3,2,5,1,6,4] => [2,6,4,1,3,5]
[3,2,5,4,1,6] => [2,4,5,1,3,6]
[3,2,5,4,6,1] => [2,4,6,1,3,5]
[3,2,5,6,1,4] => [2,5,1,3,6,4]
[3,2,5,6,4,1] => [2,6,1,3,5,4]
[3,2,6,1,4,5] => [2,6,5,4,1,3]
[3,2,6,1,5,4] => [2,5,6,4,1,3]
[3,2,6,4,1,5] => [2,4,6,5,1,3]
[3,2,6,4,5,1] => [2,4,5,6,1,3]
[3,2,6,5,1,4] => [2,6,4,5,1,3]
[3,2,6,5,4,1] => [2,5,4,6,1,3]
[3,4,1,2,5,6] => [3,1,4,2,5,6]
[3,4,1,2,6,5] => [3,1,4,2,6,5]
[3,4,1,5,2,6] => [3,1,5,2,4,6]
[3,4,1,5,6,2] => [3,1,6,2,4,5]
[3,4,1,6,2,5] => [3,1,6,5,2,4]
[3,4,1,6,5,2] => [3,1,5,6,2,4]
[3,4,2,1,5,6] => [4,1,3,2,5,6]
[3,4,2,1,6,5] => [4,1,3,2,6,5]
[3,4,2,5,1,6] => [5,1,3,2,4,6]
[3,4,2,5,6,1] => [6,1,3,2,4,5]
[3,4,2,6,1,5] => [6,5,1,3,2,4]
[3,4,2,6,5,1] => [5,6,1,3,2,4]
[3,4,5,1,2,6] => [5,2,4,1,3,6]
[3,4,5,1,6,2] => [6,2,4,1,3,5]
[3,4,5,2,1,6] => [4,2,5,1,3,6]
[3,4,5,2,6,1] => [4,2,6,1,3,5]
[3,4,5,6,1,2] => [5,1,3,6,2,4]
[3,4,5,6,2,1] => [6,1,3,5,2,4]
[3,4,6,1,2,5] => [6,5,2,4,1,3]
[3,4,6,1,5,2] => [5,6,2,4,1,3]
[3,4,6,2,1,5] => [4,2,6,5,1,3]
[3,4,6,2,5,1] => [4,2,5,6,1,3]
[3,4,6,5,1,2] => [6,2,4,5,1,3]
[3,4,6,5,2,1] => [5,2,4,6,1,3]
[3,5,1,2,4,6] => [3,1,5,4,2,6]
[3,5,1,2,6,4] => [3,1,6,4,2,5]
[3,5,1,4,2,6] => [3,1,4,5,2,6]
[3,5,1,4,6,2] => [3,1,4,6,2,5]
[3,5,1,6,2,4] => [3,1,5,2,6,4]
[3,5,1,6,4,2] => [3,1,6,2,5,4]
[3,5,2,1,4,6] => [5,4,1,3,2,6]
[3,5,2,1,6,4] => [6,4,1,3,2,5]
[3,5,2,4,1,6] => [4,5,1,3,2,6]
[3,5,2,4,6,1] => [4,6,1,3,2,5]
[3,5,2,6,1,4] => [5,1,3,2,6,4]
[3,5,2,6,4,1] => [6,1,3,2,5,4]
[3,5,4,1,2,6] => [4,1,3,5,2,6]
[3,5,4,1,6,2] => [4,1,3,6,2,5]
[3,5,4,2,1,6] => [5,1,3,4,2,6]
[3,5,4,2,6,1] => [6,1,3,4,2,5]
[3,5,4,6,1,2] => [6,2,5,1,3,4]
[3,5,4,6,2,1] => [5,2,6,1,3,4]
[3,5,6,1,2,4] => [5,2,6,4,1,3]
[3,5,6,1,4,2] => [6,2,5,4,1,3]
[3,5,6,2,1,4] => [6,4,2,5,1,3]
[3,5,6,2,4,1] => [5,4,2,6,1,3]
[3,5,6,4,1,2] => [4,6,2,5,1,3]
[3,5,6,4,2,1] => [4,5,2,6,1,3]
[3,6,1,2,4,5] => [3,1,6,5,4,2]
[3,6,1,2,5,4] => [3,1,5,6,4,2]
[3,6,1,4,2,5] => [3,1,4,6,5,2]
[3,6,1,4,5,2] => [3,1,4,5,6,2]
[3,6,1,5,2,4] => [3,1,6,4,5,2]
[3,6,1,5,4,2] => [3,1,5,4,6,2]
[3,6,2,1,4,5] => [6,5,4,1,3,2]
[3,6,2,1,5,4] => [5,6,4,1,3,2]
[3,6,2,4,1,5] => [4,6,5,1,3,2]
[3,6,2,4,5,1] => [4,5,6,1,3,2]
[3,6,2,5,1,4] => [6,4,5,1,3,2]
[3,6,2,5,4,1] => [5,4,6,1,3,2]
[3,6,4,1,2,5] => [4,1,3,6,5,2]
[3,6,4,1,5,2] => [4,1,3,5,6,2]
[3,6,4,2,1,5] => [6,5,1,3,4,2]
[3,6,4,2,5,1] => [5,6,1,3,4,2]
[3,6,4,5,1,2] => [5,1,3,4,6,2]
[3,6,4,5,2,1] => [6,1,3,4,5,2]
[3,6,5,1,2,4] => [6,4,1,3,5,2]
[3,6,5,1,4,2] => [5,4,1,3,6,2]
[3,6,5,2,1,4] => [5,1,3,6,4,2]
[3,6,5,2,4,1] => [6,1,3,5,4,2]
[3,6,5,4,1,2] => [4,5,1,3,6,2]
[3,6,5,4,2,1] => [4,6,1,3,5,2]
[4,1,2,3,5,6] => [4,3,2,1,5,6]
[4,1,2,3,6,5] => [4,3,2,1,6,5]
[4,1,2,5,3,6] => [5,3,2,1,4,6]
[4,1,2,5,6,3] => [6,3,2,1,4,5]
[4,1,2,6,3,5] => [6,5,3,2,1,4]
[4,1,2,6,5,3] => [5,6,3,2,1,4]
[4,1,3,2,5,6] => [3,4,2,1,5,6]
[4,1,3,2,6,5] => [3,4,2,1,6,5]
[4,1,3,5,2,6] => [3,5,2,1,4,6]
[4,1,3,5,6,2] => [3,6,2,1,4,5]
[4,1,3,6,2,5] => [3,6,5,2,1,4]
[4,1,3,6,5,2] => [3,5,6,2,1,4]
[4,1,5,2,3,6] => [4,2,1,5,3,6]
[4,1,5,2,6,3] => [4,2,1,6,3,5]
[4,1,5,3,2,6] => [5,2,1,4,3,6]
[4,1,5,3,6,2] => [6,2,1,4,3,5]
[4,1,5,6,2,3] => [6,3,5,2,1,4]
[4,1,5,6,3,2] => [5,3,6,2,1,4]
[4,1,6,2,3,5] => [4,2,1,6,5,3]
[4,1,6,2,5,3] => [4,2,1,5,6,3]
[4,1,6,3,2,5] => [6,5,2,1,4,3]
[4,1,6,3,5,2] => [5,6,2,1,4,3]
[4,1,6,5,2,3] => [5,2,1,4,6,3]
[4,1,6,5,3,2] => [6,2,1,4,5,3]
[4,2,1,3,5,6] => [2,4,3,1,5,6]
[4,2,1,3,6,5] => [2,4,3,1,6,5]
[4,2,1,5,3,6] => [2,5,3,1,4,6]
[4,2,1,5,6,3] => [2,6,3,1,4,5]
[4,2,1,6,3,5] => [2,6,5,3,1,4]
[4,2,1,6,5,3] => [2,5,6,3,1,4]
[4,2,3,1,5,6] => [2,3,4,1,5,6]
[4,2,3,1,6,5] => [2,3,4,1,6,5]
[4,2,3,5,1,6] => [2,3,5,1,4,6]
[4,2,3,5,6,1] => [2,3,6,1,4,5]
[4,2,3,6,1,5] => [2,3,6,5,1,4]
[4,2,3,6,5,1] => [2,3,5,6,1,4]
[4,2,5,1,3,6] => [2,4,1,5,3,6]
[4,2,5,1,6,3] => [2,4,1,6,3,5]
[4,2,5,3,1,6] => [2,5,1,4,3,6]
[4,2,5,3,6,1] => [2,6,1,4,3,5]
[4,2,5,6,1,3] => [2,6,3,5,1,4]
[4,2,5,6,3,1] => [2,5,3,6,1,4]
[4,2,6,1,3,5] => [2,4,1,6,5,3]
[4,2,6,1,5,3] => [2,4,1,5,6,3]
[4,2,6,3,1,5] => [2,6,5,1,4,3]
[4,2,6,3,5,1] => [2,5,6,1,4,3]
[4,2,6,5,1,3] => [2,5,1,4,6,3]
[4,2,6,5,3,1] => [2,6,1,4,5,3]
[4,3,1,2,5,6] => [4,2,3,1,5,6]
[4,3,1,2,6,5] => [4,2,3,1,6,5]
[4,3,1,5,2,6] => [5,2,3,1,4,6]
[4,3,1,5,6,2] => [6,2,3,1,4,5]
[4,3,1,6,2,5] => [6,5,2,3,1,4]
[4,3,1,6,5,2] => [5,6,2,3,1,4]
[4,3,2,1,5,6] => [3,2,4,1,5,6]
[4,3,2,1,6,5] => [3,2,4,1,6,5]
[4,3,2,5,1,6] => [3,2,5,1,4,6]
[4,3,2,5,6,1] => [3,2,6,1,4,5]
[4,3,2,6,1,5] => [3,2,6,5,1,4]
[4,3,2,6,5,1] => [3,2,5,6,1,4]
[4,3,5,1,2,6] => [4,1,5,2,3,6]
[4,3,5,1,6,2] => [4,1,6,2,3,5]
[4,3,5,2,1,6] => [5,1,4,2,3,6]
[4,3,5,2,6,1] => [6,1,4,2,3,5]
[4,3,5,6,1,2] => [6,2,3,5,1,4]
[4,3,5,6,2,1] => [5,2,3,6,1,4]
[4,3,6,1,2,5] => [4,1,6,5,2,3]
[4,3,6,1,5,2] => [4,1,5,6,2,3]
[4,3,6,2,1,5] => [6,5,1,4,2,3]
[4,3,6,2,5,1] => [5,6,1,4,2,3]
[4,3,6,5,1,2] => [5,1,4,6,2,3]
[4,3,6,5,2,1] => [6,1,4,5,2,3]
[4,5,1,2,3,6] => [5,3,1,4,2,6]
[4,5,1,2,6,3] => [6,3,1,4,2,5]
[4,5,1,3,2,6] => [4,3,1,5,2,6]
[4,5,1,3,6,2] => [4,3,1,6,2,5]
[4,5,1,6,2,3] => [5,2,6,3,1,4]
[4,5,1,6,3,2] => [6,2,5,3,1,4]
[4,5,2,1,3,6] => [4,1,5,3,2,6]
[4,5,2,1,6,3] => [4,1,6,3,2,5]
[4,5,2,3,1,6] => [5,1,4,3,2,6]
[4,5,2,3,6,1] => [6,1,4,3,2,5]
[4,5,2,6,1,3] => [6,3,2,5,1,4]
[4,5,2,6,3,1] => [5,3,2,6,1,4]
[4,5,3,1,2,6] => [3,4,1,5,2,6]
[4,5,3,1,6,2] => [3,4,1,6,2,5]
[4,5,3,2,1,6] => [3,5,1,4,2,6]
[4,5,3,2,6,1] => [3,6,1,4,2,5]
[4,5,3,6,1,2] => [3,6,2,5,1,4]
[4,5,3,6,2,1] => [3,5,2,6,1,4]
[4,5,6,1,2,3] => [4,1,5,2,6,3]
[4,5,6,1,3,2] => [4,1,6,2,5,3]
[4,5,6,2,1,3] => [5,1,4,2,6,3]
[4,5,6,2,3,1] => [6,1,4,2,5,3]
[4,5,6,3,1,2] => [6,2,5,1,4,3]
[4,5,6,3,2,1] => [5,2,6,1,4,3]
[4,6,1,2,3,5] => [6,5,3,1,4,2]
[4,6,1,2,5,3] => [5,6,3,1,4,2]
[4,6,1,3,2,5] => [4,3,1,6,5,2]
[4,6,1,3,5,2] => [4,3,1,5,6,2]
[4,6,1,5,2,3] => [6,3,1,4,5,2]
[4,6,1,5,3,2] => [5,3,1,4,6,2]
[4,6,2,1,3,5] => [4,1,6,5,3,2]
[4,6,2,1,5,3] => [4,1,5,6,3,2]
[4,6,2,3,1,5] => [6,5,1,4,3,2]
[4,6,2,3,5,1] => [5,6,1,4,3,2]
[4,6,2,5,1,3] => [5,1,4,6,3,2]
[4,6,2,5,3,1] => [6,1,4,5,3,2]
[4,6,3,1,2,5] => [3,4,1,6,5,2]
[4,6,3,1,5,2] => [3,4,1,5,6,2]
[4,6,3,2,1,5] => [3,6,5,1,4,2]
[4,6,3,2,5,1] => [3,5,6,1,4,2]
[4,6,3,5,1,2] => [3,5,1,4,6,2]
[4,6,3,5,2,1] => [3,6,1,4,5,2]
[4,6,5,1,2,3] => [4,1,6,3,5,2]
[4,6,5,1,3,2] => [4,1,5,3,6,2]
[4,6,5,2,1,3] => [6,3,5,1,4,2]
[4,6,5,2,3,1] => [5,3,6,1,4,2]
[4,6,5,3,1,2] => [5,1,4,3,6,2]
[4,6,5,3,2,1] => [6,1,4,3,5,2]
[5,1,2,3,4,6] => [5,4,3,2,1,6]
[5,1,2,3,6,4] => [6,4,3,2,1,5]
[5,1,2,4,3,6] => [4,5,3,2,1,6]
[5,1,2,4,6,3] => [4,6,3,2,1,5]
[5,1,2,6,3,4] => [5,3,2,1,6,4]
[5,1,2,6,4,3] => [6,3,2,1,5,4]
[5,1,3,2,4,6] => [3,5,4,2,1,6]
[5,1,3,2,6,4] => [3,6,4,2,1,5]
[5,1,3,4,2,6] => [3,4,5,2,1,6]
[5,1,3,4,6,2] => [3,4,6,2,1,5]
[5,1,3,6,2,4] => [3,5,2,1,6,4]
[5,1,3,6,4,2] => [3,6,2,1,5,4]
[5,1,4,2,3,6] => [5,3,4,2,1,6]
[5,1,4,2,6,3] => [6,3,4,2,1,5]
[5,1,4,3,2,6] => [4,3,5,2,1,6]
[5,1,4,3,6,2] => [4,3,6,2,1,5]
[5,1,4,6,2,3] => [5,2,1,6,3,4]
[5,1,4,6,3,2] => [6,2,1,5,3,4]
[5,1,6,2,3,4] => [6,4,2,1,5,3]
[5,1,6,2,4,3] => [5,4,2,1,6,3]
[5,1,6,3,2,4] => [5,2,1,6,4,3]
[5,1,6,3,4,2] => [6,2,1,5,4,3]
[5,1,6,4,2,3] => [4,5,2,1,6,3]
[5,1,6,4,3,2] => [4,6,2,1,5,3]
[5,2,1,3,4,6] => [2,5,4,3,1,6]
[5,2,1,3,6,4] => [2,6,4,3,1,5]
[5,2,1,4,3,6] => [2,4,5,3,1,6]
[5,2,1,4,6,3] => [2,4,6,3,1,5]
[5,2,1,6,3,4] => [2,5,3,1,6,4]
[5,2,1,6,4,3] => [2,6,3,1,5,4]
[5,2,3,1,4,6] => [2,3,5,4,1,6]
[5,2,3,1,6,4] => [2,3,6,4,1,5]
[5,2,3,4,1,6] => [2,3,4,5,1,6]
[5,2,3,4,6,1] => [2,3,4,6,1,5]
[5,2,3,6,1,4] => [2,3,5,1,6,4]
[5,2,3,6,4,1] => [2,3,6,1,5,4]
[5,2,4,1,3,6] => [2,5,3,4,1,6]
[5,2,4,1,6,3] => [2,6,3,4,1,5]
[5,2,4,3,1,6] => [2,4,3,5,1,6]
[5,2,4,3,6,1] => [2,4,3,6,1,5]
[5,2,4,6,1,3] => [2,5,1,6,3,4]
[5,2,4,6,3,1] => [2,6,1,5,3,4]
[5,2,6,1,3,4] => [2,6,4,1,5,3]
[5,2,6,1,4,3] => [2,5,4,1,6,3]
[5,2,6,3,1,4] => [2,5,1,6,4,3]
[5,2,6,3,4,1] => [2,6,1,5,4,3]
[5,2,6,4,1,3] => [2,4,5,1,6,3]
[5,2,6,4,3,1] => [2,4,6,1,5,3]
[5,3,1,2,4,6] => [5,4,2,3,1,6]
[5,3,1,2,6,4] => [6,4,2,3,1,5]
[5,3,1,4,2,6] => [4,5,2,3,1,6]
[5,3,1,4,6,2] => [4,6,2,3,1,5]
[5,3,1,6,2,4] => [5,2,3,1,6,4]
[5,3,1,6,4,2] => [6,2,3,1,5,4]
[5,3,2,1,4,6] => [3,2,5,4,1,6]
[5,3,2,1,6,4] => [3,2,6,4,1,5]
[5,3,2,4,1,6] => [3,2,4,5,1,6]
[5,3,2,4,6,1] => [3,2,4,6,1,5]
[5,3,2,6,1,4] => [3,2,5,1,6,4]
[5,3,2,6,4,1] => [3,2,6,1,5,4]
[5,3,4,1,2,6] => [5,2,3,4,1,6]
[5,3,4,1,6,2] => [6,2,3,4,1,5]
[5,3,4,2,1,6] => [4,2,3,5,1,6]
[5,3,4,2,6,1] => [4,2,3,6,1,5]
[5,3,4,6,1,2] => [5,1,6,2,3,4]
[5,3,4,6,2,1] => [6,1,5,2,3,4]
[5,3,6,1,2,4] => [6,4,1,5,2,3]
[5,3,6,1,4,2] => [5,4,1,6,2,3]
[5,3,6,2,1,4] => [5,1,6,4,2,3]
[5,3,6,2,4,1] => [6,1,5,4,2,3]
[5,3,6,4,1,2] => [4,5,1,6,2,3]
[5,3,6,4,2,1] => [4,6,1,5,2,3]
[5,4,1,2,3,6] => [4,2,5,3,1,6]
[5,4,1,2,6,3] => [4,2,6,3,1,5]
[5,4,1,3,2,6] => [5,2,4,3,1,6]
[5,4,1,3,6,2] => [6,2,4,3,1,5]
[5,4,1,6,2,3] => [6,3,1,5,2,4]
[5,4,1,6,3,2] => [5,3,1,6,2,4]
[5,4,2,1,3,6] => [5,3,2,4,1,6]
[5,4,2,1,6,3] => [6,3,2,4,1,5]
[5,4,2,3,1,6] => [4,3,2,5,1,6]
[5,4,2,3,6,1] => [4,3,2,6,1,5]
[5,4,2,6,1,3] => [5,1,6,3,2,4]
[5,4,2,6,3,1] => [6,1,5,3,2,4]
[5,4,3,1,2,6] => [3,5,2,4,1,6]
[5,4,3,1,6,2] => [3,6,2,4,1,5]
[5,4,3,2,1,6] => [3,4,2,5,1,6]
[5,4,3,2,6,1] => [3,4,2,6,1,5]
[5,4,3,6,1,2] => [3,5,1,6,2,4]
[5,4,3,6,2,1] => [3,6,1,5,2,4]
[5,4,6,1,2,3] => [5,2,4,1,6,3]
[5,4,6,1,3,2] => [6,2,4,1,5,3]
[5,4,6,2,1,3] => [4,2,5,1,6,3]
[5,4,6,2,3,1] => [4,2,6,1,5,3]
[5,4,6,3,1,2] => [5,1,6,2,4,3]
[5,4,6,3,2,1] => [6,1,5,2,4,3]
[5,6,1,2,3,4] => [5,3,1,6,4,2]
[5,6,1,2,4,3] => [6,3,1,5,4,2]
[5,6,1,3,2,4] => [6,4,3,1,5,2]
[5,6,1,3,4,2] => [5,4,3,1,6,2]
[5,6,1,4,2,3] => [4,6,3,1,5,2]
[5,6,1,4,3,2] => [4,5,3,1,6,2]
[5,6,2,1,3,4] => [6,4,1,5,3,2]
[5,6,2,1,4,3] => [5,4,1,6,3,2]
[5,6,2,3,1,4] => [5,1,6,4,3,2]
[5,6,2,3,4,1] => [6,1,5,4,3,2]
[5,6,2,4,1,3] => [4,5,1,6,3,2]
[5,6,2,4,3,1] => [4,6,1,5,3,2]
[5,6,3,1,2,4] => [3,6,4,1,5,2]
[5,6,3,1,4,2] => [3,5,4,1,6,2]
[5,6,3,2,1,4] => [3,5,1,6,4,2]
[5,6,3,2,4,1] => [3,6,1,5,4,2]
[5,6,3,4,1,2] => [3,4,5,1,6,2]
[5,6,3,4,2,1] => [3,4,6,1,5,2]
[5,6,4,1,2,3] => [6,3,4,1,5,2]
[5,6,4,1,3,2] => [5,3,4,1,6,2]
[5,6,4,2,1,3] => [5,1,6,3,4,2]
[5,6,4,2,3,1] => [6,1,5,3,4,2]
[5,6,4,3,1,2] => [4,3,5,1,6,2]
[5,6,4,3,2,1] => [4,3,6,1,5,2]
[6,1,2,3,4,5] => [6,5,4,3,2,1]
[6,1,2,3,5,4] => [5,6,4,3,2,1]
[6,1,2,4,3,5] => [4,6,5,3,2,1]
[6,1,2,4,5,3] => [4,5,6,3,2,1]
[6,1,2,5,3,4] => [6,4,5,3,2,1]
[6,1,2,5,4,3] => [5,4,6,3,2,1]
[6,1,3,2,4,5] => [3,6,5,4,2,1]
[6,1,3,2,5,4] => [3,5,6,4,2,1]
[6,1,3,4,2,5] => [3,4,6,5,2,1]
[6,1,3,4,5,2] => [3,4,5,6,2,1]
[6,1,3,5,2,4] => [3,6,4,5,2,1]
[6,1,3,5,4,2] => [3,5,4,6,2,1]
[6,1,4,2,3,5] => [6,5,3,4,2,1]
[6,1,4,2,5,3] => [5,6,3,4,2,1]
[6,1,4,3,2,5] => [4,3,6,5,2,1]
[6,1,4,3,5,2] => [4,3,5,6,2,1]
[6,1,4,5,2,3] => [6,3,4,5,2,1]
[6,1,4,5,3,2] => [5,3,4,6,2,1]
[6,1,5,2,3,4] => [5,3,6,4,2,1]
[6,1,5,2,4,3] => [6,3,5,4,2,1]
[6,1,5,3,2,4] => [6,4,3,5,2,1]
[6,1,5,3,4,2] => [5,4,3,6,2,1]
[6,1,5,4,2,3] => [4,6,3,5,2,1]
[6,1,5,4,3,2] => [4,5,3,6,2,1]
[6,2,1,3,4,5] => [2,6,5,4,3,1]
[6,2,1,3,5,4] => [2,5,6,4,3,1]
[6,2,1,4,3,5] => [2,4,6,5,3,1]
[6,2,1,4,5,3] => [2,4,5,6,3,1]
[6,2,1,5,3,4] => [2,6,4,5,3,1]
[6,2,1,5,4,3] => [2,5,4,6,3,1]
[6,2,3,1,4,5] => [2,3,6,5,4,1]
[6,2,3,1,5,4] => [2,3,5,6,4,1]
[6,2,3,4,1,5] => [2,3,4,6,5,1]
[6,2,3,4,5,1] => [2,3,4,5,6,1]
[6,2,3,5,1,4] => [2,3,6,4,5,1]
[6,2,3,5,4,1] => [2,3,5,4,6,1]
[6,2,4,1,3,5] => [2,6,5,3,4,1]
[6,2,4,1,5,3] => [2,5,6,3,4,1]
[6,2,4,3,1,5] => [2,4,3,6,5,1]
[6,2,4,3,5,1] => [2,4,3,5,6,1]
[6,2,4,5,1,3] => [2,6,3,4,5,1]
[6,2,4,5,3,1] => [2,5,3,4,6,1]
[6,2,5,1,3,4] => [2,5,3,6,4,1]
[6,2,5,1,4,3] => [2,6,3,5,4,1]
[6,2,5,3,1,4] => [2,6,4,3,5,1]
[6,2,5,3,4,1] => [2,5,4,3,6,1]
[6,2,5,4,1,3] => [2,4,6,3,5,1]
[6,2,5,4,3,1] => [2,4,5,3,6,1]
[6,3,1,2,4,5] => [6,5,4,2,3,1]
[6,3,1,2,5,4] => [5,6,4,2,3,1]
[6,3,1,4,2,5] => [4,6,5,2,3,1]
[6,3,1,4,5,2] => [4,5,6,2,3,1]
[6,3,1,5,2,4] => [6,4,5,2,3,1]
[6,3,1,5,4,2] => [5,4,6,2,3,1]
[6,3,2,1,4,5] => [3,2,6,5,4,1]
[6,3,2,1,5,4] => [3,2,5,6,4,1]
[6,3,2,4,1,5] => [3,2,4,6,5,1]
[6,3,2,4,5,1] => [3,2,4,5,6,1]
[6,3,2,5,1,4] => [3,2,6,4,5,1]
[6,3,2,5,4,1] => [3,2,5,4,6,1]
[6,3,4,1,2,5] => [6,5,2,3,4,1]
[6,3,4,1,5,2] => [5,6,2,3,4,1]
[6,3,4,2,1,5] => [4,2,3,6,5,1]
[6,3,4,2,5,1] => [4,2,3,5,6,1]
[6,3,4,5,1,2] => [6,2,3,4,5,1]
[6,3,4,5,2,1] => [5,2,3,4,6,1]
[6,3,5,1,2,4] => [5,2,3,6,4,1]
[6,3,5,1,4,2] => [6,2,3,5,4,1]
[6,3,5,2,1,4] => [6,4,2,3,5,1]
[6,3,5,2,4,1] => [5,4,2,3,6,1]
[6,3,5,4,1,2] => [4,6,2,3,5,1]
[6,3,5,4,2,1] => [4,5,2,3,6,1]
[6,4,1,2,3,5] => [4,2,6,5,3,1]
[6,4,1,2,5,3] => [4,2,5,6,3,1]
[6,4,1,3,2,5] => [6,5,2,4,3,1]
[6,4,1,3,5,2] => [5,6,2,4,3,1]
[6,4,1,5,2,3] => [5,2,4,6,3,1]
[6,4,1,5,3,2] => [6,2,4,5,3,1]
[6,4,2,1,3,5] => [6,5,3,2,4,1]
[6,4,2,1,5,3] => [5,6,3,2,4,1]
[6,4,2,3,1,5] => [4,3,2,6,5,1]
[6,4,2,3,5,1] => [4,3,2,5,6,1]
[6,4,2,5,1,3] => [6,3,2,4,5,1]
[6,4,2,5,3,1] => [5,3,2,4,6,1]
[6,4,3,1,2,5] => [3,6,5,2,4,1]
[6,4,3,1,5,2] => [3,5,6,2,4,1]
[6,4,3,2,1,5] => [3,4,2,6,5,1]
[6,4,3,2,5,1] => [3,4,2,5,6,1]
[6,4,3,5,1,2] => [3,6,2,4,5,1]
[6,4,3,5,2,1] => [3,5,2,4,6,1]
[6,4,5,1,2,3] => [6,3,5,2,4,1]
[6,4,5,1,3,2] => [5,3,6,2,4,1]
[6,4,5,2,1,3] => [4,2,6,3,5,1]
[6,4,5,2,3,1] => [4,2,5,3,6,1]
[6,4,5,3,1,2] => [6,2,4,3,5,1]
[6,4,5,3,2,1] => [5,2,4,3,6,1]
[6,5,1,2,3,4] => [6,4,2,5,3,1]
[6,5,1,2,4,3] => [5,4,2,6,3,1]
[6,5,1,3,2,4] => [5,2,6,4,3,1]
[6,5,1,3,4,2] => [6,2,5,4,3,1]
[6,5,1,4,2,3] => [4,5,2,6,3,1]
[6,5,1,4,3,2] => [4,6,2,5,3,1]
[6,5,2,1,3,4] => [5,3,2,6,4,1]
[6,5,2,1,4,3] => [6,3,2,5,4,1]
[6,5,2,3,1,4] => [6,4,3,2,5,1]
[6,5,2,3,4,1] => [5,4,3,2,6,1]
[6,5,2,4,1,3] => [4,6,3,2,5,1]
[6,5,2,4,3,1] => [4,5,3,2,6,1]
[6,5,3,1,2,4] => [3,5,2,6,4,1]
[6,5,3,1,4,2] => [3,6,2,5,4,1]
[6,5,3,2,1,4] => [3,6,4,2,5,1]
[6,5,3,2,4,1] => [3,5,4,2,6,1]
[6,5,3,4,1,2] => [3,4,6,2,5,1]
[6,5,3,4,2,1] => [3,4,5,2,6,1]
[6,5,4,1,2,3] => [5,2,6,3,4,1]
[6,5,4,1,3,2] => [6,2,5,3,4,1]
[6,5,4,2,1,3] => [6,3,4,2,5,1]
[6,5,4,2,3,1] => [5,3,4,2,6,1]
[6,5,4,3,1,2] => [4,3,6,2,5,1]
[6,5,4,3,2,1] => [4,3,5,2,6,1]
[1,2,3,4,5,6,7] => [1,2,3,4,5,6,7]
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6]
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7]
[1,2,3,4,6,7,5] => [1,2,3,4,7,5,6]
[1,2,3,4,7,5,6] => [1,2,3,4,7,6,5]
[1,2,3,4,7,6,5] => [1,2,3,4,6,7,5]
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7]
[1,2,3,5,4,7,6] => [1,2,3,5,4,7,6]
[1,2,3,5,6,4,7] => [1,2,3,6,4,5,7]
[1,2,3,5,6,7,4] => [1,2,3,7,4,5,6]
[1,2,3,5,7,4,6] => [1,2,3,7,6,4,5]
[1,2,3,5,7,6,4] => [1,2,3,6,7,4,5]
[1,2,3,6,4,5,7] => [1,2,3,6,5,4,7]
[1,2,3,6,4,7,5] => [1,2,3,7,5,4,6]
[1,2,3,6,5,4,7] => [1,2,3,5,6,4,7]
[1,2,3,6,5,7,4] => [1,2,3,5,7,4,6]
[1,2,3,6,7,4,5] => [1,2,3,6,4,7,5]
[1,2,3,6,7,5,4] => [1,2,3,7,4,6,5]
[1,2,3,7,4,5,6] => [1,2,3,7,6,5,4]
[1,2,3,7,4,6,5] => [1,2,3,6,7,5,4]
[1,2,3,7,5,4,6] => [1,2,3,5,7,6,4]
[1,2,3,7,5,6,4] => [1,2,3,5,6,7,4]
[1,2,3,7,6,4,5] => [1,2,3,7,5,6,4]
[1,2,3,7,6,5,4] => [1,2,3,6,5,7,4]
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7]
[1,2,4,3,5,7,6] => [1,2,4,3,5,7,6]
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7]
[1,2,4,3,6,7,5] => [1,2,4,3,7,5,6]
[1,2,4,3,7,5,6] => [1,2,4,3,7,6,5]
[1,2,4,3,7,6,5] => [1,2,4,3,6,7,5]
[1,2,4,5,3,6,7] => [1,2,5,3,4,6,7]
[1,2,4,5,3,7,6] => [1,2,5,3,4,7,6]
[1,2,4,5,6,3,7] => [1,2,6,3,4,5,7]
[1,2,4,5,6,7,3] => [1,2,7,3,4,5,6]
[1,2,4,5,7,3,6] => [1,2,7,6,3,4,5]
[1,2,4,5,7,6,3] => [1,2,6,7,3,4,5]
[1,2,4,6,3,5,7] => [1,2,6,5,3,4,7]
[1,2,4,6,3,7,5] => [1,2,7,5,3,4,6]
[1,2,4,6,5,3,7] => [1,2,5,6,3,4,7]
[1,2,4,6,5,7,3] => [1,2,5,7,3,4,6]
[1,2,4,6,7,3,5] => [1,2,6,3,4,7,5]
[1,2,4,6,7,5,3] => [1,2,7,3,4,6,5]
[1,2,4,7,3,5,6] => [1,2,7,6,5,3,4]
[1,2,4,7,3,6,5] => [1,2,6,7,5,3,4]
[1,2,4,7,5,3,6] => [1,2,5,7,6,3,4]
[1,2,4,7,5,6,3] => [1,2,5,6,7,3,4]
[1,2,4,7,6,3,5] => [1,2,7,5,6,3,4]
[1,2,4,7,6,5,3] => [1,2,6,5,7,3,4]
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7]
[1,2,5,3,4,7,6] => [1,2,5,4,3,7,6]
[1,2,5,3,6,4,7] => [1,2,6,4,3,5,7]
[1,2,5,3,6,7,4] => [1,2,7,4,3,5,6]
[1,2,5,3,7,4,6] => [1,2,7,6,4,3,5]
[1,2,5,3,7,6,4] => [1,2,6,7,4,3,5]
[1,2,5,4,3,6,7] => [1,2,4,5,3,6,7]
[1,2,5,4,3,7,6] => [1,2,4,5,3,7,6]
[1,2,5,4,6,3,7] => [1,2,4,6,3,5,7]
[1,2,5,4,6,7,3] => [1,2,4,7,3,5,6]
[1,2,5,4,7,3,6] => [1,2,4,7,6,3,5]
[1,2,5,4,7,6,3] => [1,2,4,6,7,3,5]
[1,2,5,6,3,4,7] => [1,2,5,3,6,4,7]
[1,2,5,6,3,7,4] => [1,2,5,3,7,4,6]
[1,2,5,6,4,3,7] => [1,2,6,3,5,4,7]
[1,2,5,6,4,7,3] => [1,2,7,3,5,4,6]
[1,2,5,6,7,3,4] => [1,2,7,4,6,3,5]
[1,2,5,6,7,4,3] => [1,2,6,4,7,3,5]
[1,2,5,7,3,4,6] => [1,2,5,3,7,6,4]
[1,2,5,7,3,6,4] => [1,2,5,3,6,7,4]
[1,2,5,7,4,3,6] => [1,2,7,6,3,5,4]
[1,2,5,7,4,6,3] => [1,2,6,7,3,5,4]
[1,2,5,7,6,3,4] => [1,2,6,3,5,7,4]
[1,2,5,7,6,4,3] => [1,2,7,3,5,6,4]
[1,2,6,3,4,5,7] => [1,2,6,5,4,3,7]
[1,2,6,3,4,7,5] => [1,2,7,5,4,3,6]
[1,2,6,3,5,4,7] => [1,2,5,6,4,3,7]
[1,2,6,3,5,7,4] => [1,2,5,7,4,3,6]
[1,2,6,3,7,4,5] => [1,2,6,4,3,7,5]
[1,2,6,3,7,5,4] => [1,2,7,4,3,6,5]
[1,2,6,4,3,5,7] => [1,2,4,6,5,3,7]
[1,2,6,4,3,7,5] => [1,2,4,7,5,3,6]
[1,2,6,4,5,3,7] => [1,2,4,5,6,3,7]
[1,2,6,4,5,7,3] => [1,2,4,5,7,3,6]
[1,2,6,4,7,3,5] => [1,2,4,6,3,7,5]
[1,2,6,4,7,5,3] => [1,2,4,7,3,6,5]
[1,2,6,5,3,4,7] => [1,2,6,4,5,3,7]
[1,2,6,5,3,7,4] => [1,2,7,4,5,3,6]
[1,2,6,5,4,3,7] => [1,2,5,4,6,3,7]
[1,2,6,5,4,7,3] => [1,2,5,4,7,3,6]
[1,2,6,5,7,3,4] => [1,2,6,3,7,4,5]
[1,2,6,5,7,4,3] => [1,2,7,3,6,4,5]
[1,2,6,7,3,4,5] => [1,2,7,5,3,6,4]
[1,2,6,7,3,5,4] => [1,2,6,5,3,7,4]
[1,2,6,7,4,3,5] => [1,2,6,3,7,5,4]
[1,2,6,7,4,5,3] => [1,2,7,3,6,5,4]
[1,2,6,7,5,3,4] => [1,2,5,6,3,7,4]
[1,2,6,7,5,4,3] => [1,2,5,7,3,6,4]
[1,2,7,3,4,5,6] => [1,2,7,6,5,4,3]
[1,2,7,3,4,6,5] => [1,2,6,7,5,4,3]
[1,2,7,3,5,4,6] => [1,2,5,7,6,4,3]
[1,2,7,3,5,6,4] => [1,2,5,6,7,4,3]
[1,2,7,3,6,4,5] => [1,2,7,5,6,4,3]
[1,2,7,3,6,5,4] => [1,2,6,5,7,4,3]
[1,2,7,4,3,5,6] => [1,2,4,7,6,5,3]
[1,2,7,4,3,6,5] => [1,2,4,6,7,5,3]
[1,2,7,4,5,3,6] => [1,2,4,5,7,6,3]
[1,2,7,4,5,6,3] => [1,2,4,5,6,7,3]
[1,2,7,4,6,3,5] => [1,2,4,7,5,6,3]
[1,2,7,4,6,5,3] => [1,2,4,6,5,7,3]
[1,2,7,5,3,4,6] => [1,2,7,6,4,5,3]
[1,2,7,5,3,6,4] => [1,2,6,7,4,5,3]
[1,2,7,5,4,3,6] => [1,2,5,4,7,6,3]
[1,2,7,5,4,6,3] => [1,2,5,4,6,7,3]
[1,2,7,5,6,3,4] => [1,2,7,4,5,6,3]
[1,2,7,5,6,4,3] => [1,2,6,4,5,7,3]
[1,2,7,6,3,4,5] => [1,2,6,4,7,5,3]
[1,2,7,6,3,5,4] => [1,2,7,4,6,5,3]
[1,2,7,6,4,3,5] => [1,2,7,5,4,6,3]
[1,2,7,6,4,5,3] => [1,2,6,5,4,7,3]
[1,2,7,6,5,3,4] => [1,2,5,7,4,6,3]
[1,2,7,6,5,4,3] => [1,2,5,6,4,7,3]
[1,3,2,4,5,6,7] => [1,3,2,4,5,6,7]
[1,3,2,4,5,7,6] => [1,3,2,4,5,7,6]
[1,3,2,4,6,5,7] => [1,3,2,4,6,5,7]
[1,3,2,4,6,7,5] => [1,3,2,4,7,5,6]
[1,3,2,4,7,5,6] => [1,3,2,4,7,6,5]
[1,3,2,4,7,6,5] => [1,3,2,4,6,7,5]
[1,3,2,5,4,6,7] => [1,3,2,5,4,6,7]
[1,3,2,5,4,7,6] => [1,3,2,5,4,7,6]
[1,3,2,5,6,4,7] => [1,3,2,6,4,5,7]
[1,3,2,5,6,7,4] => [1,3,2,7,4,5,6]
[1,3,2,5,7,4,6] => [1,3,2,7,6,4,5]
[1,3,2,5,7,6,4] => [1,3,2,6,7,4,5]
[1,3,2,6,4,5,7] => [1,3,2,6,5,4,7]
[1,3,2,6,4,7,5] => [1,3,2,7,5,4,6]
[1,3,2,6,5,4,7] => [1,3,2,5,6,4,7]
[1,3,2,6,5,7,4] => [1,3,2,5,7,4,6]
[1,3,2,6,7,4,5] => [1,3,2,6,4,7,5]
[1,3,2,6,7,5,4] => [1,3,2,7,4,6,5]
[1,3,2,7,4,5,6] => [1,3,2,7,6,5,4]
[1,3,2,7,4,6,5] => [1,3,2,6,7,5,4]
[1,3,2,7,5,4,6] => [1,3,2,5,7,6,4]
[1,3,2,7,5,6,4] => [1,3,2,5,6,7,4]
[1,3,2,7,6,4,5] => [1,3,2,7,5,6,4]
[1,3,2,7,6,5,4] => [1,3,2,6,5,7,4]
[1,3,4,2,5,6,7] => [1,4,2,3,5,6,7]
[1,3,4,2,5,7,6] => [1,4,2,3,5,7,6]
[1,3,4,2,6,5,7] => [1,4,2,3,6,5,7]
[1,3,4,2,6,7,5] => [1,4,2,3,7,5,6]
[1,3,4,2,7,5,6] => [1,4,2,3,7,6,5]
[1,3,4,2,7,6,5] => [1,4,2,3,6,7,5]
[1,3,4,5,2,6,7] => [1,5,2,3,4,6,7]
[1,3,4,5,2,7,6] => [1,5,2,3,4,7,6]
[1,3,4,5,6,2,7] => [1,6,2,3,4,5,7]
[1,3,4,5,6,7,2] => [1,7,2,3,4,5,6]
[1,3,4,5,7,2,6] => [1,7,6,2,3,4,5]
[1,3,4,5,7,6,2] => [1,6,7,2,3,4,5]
[1,3,4,6,2,5,7] => [1,6,5,2,3,4,7]
[1,3,4,6,2,7,5] => [1,7,5,2,3,4,6]
[1,3,4,6,5,2,7] => [1,5,6,2,3,4,7]
[1,3,4,6,5,7,2] => [1,5,7,2,3,4,6]
[1,3,4,6,7,2,5] => [1,6,2,3,4,7,5]
[1,3,4,6,7,5,2] => [1,7,2,3,4,6,5]
[1,3,4,7,2,5,6] => [1,7,6,5,2,3,4]
[1,3,4,7,2,6,5] => [1,6,7,5,2,3,4]
[1,3,4,7,5,2,6] => [1,5,7,6,2,3,4]
[1,3,4,7,5,6,2] => [1,5,6,7,2,3,4]
[1,3,4,7,6,2,5] => [1,7,5,6,2,3,4]
[1,3,4,7,6,5,2] => [1,6,5,7,2,3,4]
[1,3,5,2,4,6,7] => [1,5,4,2,3,6,7]
[1,3,5,2,4,7,6] => [1,5,4,2,3,7,6]
[1,3,5,2,6,4,7] => [1,6,4,2,3,5,7]
[1,3,5,2,6,7,4] => [1,7,4,2,3,5,6]
[1,3,5,2,7,4,6] => [1,7,6,4,2,3,5]
[1,3,5,2,7,6,4] => [1,6,7,4,2,3,5]
[1,3,5,4,2,6,7] => [1,4,5,2,3,6,7]
[1,3,5,4,2,7,6] => [1,4,5,2,3,7,6]
[1,3,5,4,6,2,7] => [1,4,6,2,3,5,7]
[1,3,5,4,6,7,2] => [1,4,7,2,3,5,6]
[1,3,5,4,7,2,6] => [1,4,7,6,2,3,5]
[1,3,5,4,7,6,2] => [1,4,6,7,2,3,5]
[1,3,5,6,2,4,7] => [1,5,2,3,6,4,7]
[1,3,5,6,2,7,4] => [1,5,2,3,7,4,6]
[1,3,5,6,4,2,7] => [1,6,2,3,5,4,7]
[1,3,5,6,4,7,2] => [1,7,2,3,5,4,6]
[1,3,5,6,7,2,4] => [1,7,4,6,2,3,5]
[1,3,5,6,7,4,2] => [1,6,4,7,2,3,5]
[1,3,5,7,2,4,6] => [1,5,2,3,7,6,4]
[1,3,5,7,2,6,4] => [1,5,2,3,6,7,4]
[1,3,5,7,4,2,6] => [1,7,6,2,3,5,4]
[1,3,5,7,4,6,2] => [1,6,7,2,3,5,4]
[1,3,5,7,6,2,4] => [1,6,2,3,5,7,4]
[1,3,5,7,6,4,2] => [1,7,2,3,5,6,4]
[1,3,6,2,4,5,7] => [1,6,5,4,2,3,7]
[1,3,6,2,4,7,5] => [1,7,5,4,2,3,6]
[1,3,6,2,5,4,7] => [1,5,6,4,2,3,7]
[1,3,6,2,5,7,4] => [1,5,7,4,2,3,6]
[1,3,6,2,7,4,5] => [1,6,4,2,3,7,5]
[1,3,6,2,7,5,4] => [1,7,4,2,3,6,5]
[1,3,6,4,2,5,7] => [1,4,6,5,2,3,7]
[1,3,6,4,2,7,5] => [1,4,7,5,2,3,6]
[1,3,6,4,5,2,7] => [1,4,5,6,2,3,7]
[1,3,6,4,5,7,2] => [1,4,5,7,2,3,6]
[1,3,6,4,7,2,5] => [1,4,6,2,3,7,5]
[1,3,6,4,7,5,2] => [1,4,7,2,3,6,5]
[1,3,6,5,2,4,7] => [1,6,4,5,2,3,7]
[1,3,6,5,2,7,4] => [1,7,4,5,2,3,6]
[1,3,6,5,4,2,7] => [1,5,4,6,2,3,7]
[1,3,6,5,4,7,2] => [1,5,4,7,2,3,6]
[1,3,6,5,7,2,4] => [1,6,2,3,7,4,5]
[1,3,6,5,7,4,2] => [1,7,2,3,6,4,5]
[1,3,6,7,2,4,5] => [1,7,5,2,3,6,4]
[1,3,6,7,2,5,4] => [1,6,5,2,3,7,4]
[1,3,6,7,4,2,5] => [1,6,2,3,7,5,4]
[1,3,6,7,4,5,2] => [1,7,2,3,6,5,4]
[1,3,6,7,5,2,4] => [1,5,6,2,3,7,4]
[1,3,6,7,5,4,2] => [1,5,7,2,3,6,4]
[1,3,7,2,4,5,6] => [1,7,6,5,4,2,3]
[1,3,7,2,4,6,5] => [1,6,7,5,4,2,3]
[1,3,7,2,5,4,6] => [1,5,7,6,4,2,3]
[1,3,7,2,5,6,4] => [1,5,6,7,4,2,3]
[1,3,7,2,6,4,5] => [1,7,5,6,4,2,3]
[1,3,7,2,6,5,4] => [1,6,5,7,4,2,3]
[1,3,7,4,2,5,6] => [1,4,7,6,5,2,3]
[1,3,7,4,2,6,5] => [1,4,6,7,5,2,3]
[1,3,7,4,5,2,6] => [1,4,5,7,6,2,3]
[1,3,7,4,5,6,2] => [1,4,5,6,7,2,3]
[1,3,7,4,6,2,5] => [1,4,7,5,6,2,3]
[1,3,7,4,6,5,2] => [1,4,6,5,7,2,3]
[1,3,7,5,2,4,6] => [1,7,6,4,5,2,3]
[1,3,7,5,2,6,4] => [1,6,7,4,5,2,3]
[1,3,7,5,4,2,6] => [1,5,4,7,6,2,3]
[1,3,7,5,4,6,2] => [1,5,4,6,7,2,3]
[1,3,7,5,6,2,4] => [1,7,4,5,6,2,3]
[1,3,7,5,6,4,2] => [1,6,4,5,7,2,3]
[1,3,7,6,2,4,5] => [1,6,4,7,5,2,3]
[1,3,7,6,2,5,4] => [1,7,4,6,5,2,3]
[1,3,7,6,4,2,5] => [1,7,5,4,6,2,3]
[1,3,7,6,4,5,2] => [1,6,5,4,7,2,3]
[1,3,7,6,5,2,4] => [1,5,7,4,6,2,3]
[1,3,7,6,5,4,2] => [1,5,6,4,7,2,3]
[1,4,2,3,5,6,7] => [1,4,3,2,5,6,7]
[1,4,2,3,5,7,6] => [1,4,3,2,5,7,6]
[1,4,2,3,6,5,7] => [1,4,3,2,6,5,7]
[1,4,2,3,6,7,5] => [1,4,3,2,7,5,6]
[1,4,2,3,7,5,6] => [1,4,3,2,7,6,5]
[1,4,2,3,7,6,5] => [1,4,3,2,6,7,5]
[1,4,2,5,3,6,7] => [1,5,3,2,4,6,7]
[1,4,2,5,3,7,6] => [1,5,3,2,4,7,6]
[1,4,2,5,6,3,7] => [1,6,3,2,4,5,7]
[1,4,2,5,6,7,3] => [1,7,3,2,4,5,6]
[1,4,2,5,7,3,6] => [1,7,6,3,2,4,5]
[1,4,2,5,7,6,3] => [1,6,7,3,2,4,5]
[1,4,2,6,3,5,7] => [1,6,5,3,2,4,7]
[1,4,2,6,3,7,5] => [1,7,5,3,2,4,6]
[1,4,2,6,5,3,7] => [1,5,6,3,2,4,7]
[1,4,2,6,5,7,3] => [1,5,7,3,2,4,6]
[1,4,2,6,7,3,5] => [1,6,3,2,4,7,5]
[1,4,2,6,7,5,3] => [1,7,3,2,4,6,5]
[1,4,2,7,3,5,6] => [1,7,6,5,3,2,4]
[1,4,2,7,3,6,5] => [1,6,7,5,3,2,4]
[1,4,2,7,5,3,6] => [1,5,7,6,3,2,4]
[1,4,2,7,5,6,3] => [1,5,6,7,3,2,4]
[1,4,2,7,6,3,5] => [1,7,5,6,3,2,4]
[1,4,2,7,6,5,3] => [1,6,5,7,3,2,4]
[1,4,3,2,5,6,7] => [1,3,4,2,5,6,7]
[1,4,3,2,5,7,6] => [1,3,4,2,5,7,6]
[1,4,3,2,6,5,7] => [1,3,4,2,6,5,7]
[1,4,3,2,6,7,5] => [1,3,4,2,7,5,6]
[1,4,3,2,7,5,6] => [1,3,4,2,7,6,5]
[1,4,3,2,7,6,5] => [1,3,4,2,6,7,5]
[1,4,3,5,2,6,7] => [1,3,5,2,4,6,7]
[1,4,3,5,2,7,6] => [1,3,5,2,4,7,6]
[1,4,3,5,6,2,7] => [1,3,6,2,4,5,7]
[1,4,3,5,6,7,2] => [1,3,7,2,4,5,6]
[1,4,3,5,7,2,6] => [1,3,7,6,2,4,5]
[1,4,3,5,7,6,2] => [1,3,6,7,2,4,5]
[1,4,3,6,2,5,7] => [1,3,6,5,2,4,7]
[1,4,3,6,2,7,5] => [1,3,7,5,2,4,6]
[1,4,3,6,5,2,7] => [1,3,5,6,2,4,7]
[1,4,3,6,5,7,2] => [1,3,5,7,2,4,6]
[1,4,3,6,7,2,5] => [1,3,6,2,4,7,5]
[1,4,3,6,7,5,2] => [1,3,7,2,4,6,5]
[1,4,3,7,2,5,6] => [1,3,7,6,5,2,4]
[1,4,3,7,2,6,5] => [1,3,6,7,5,2,4]
[1,4,3,7,5,2,6] => [1,3,5,7,6,2,4]
[1,4,3,7,5,6,2] => [1,3,5,6,7,2,4]
[1,4,3,7,6,2,5] => [1,3,7,5,6,2,4]
[1,4,3,7,6,5,2] => [1,3,6,5,7,2,4]
[1,4,5,2,3,6,7] => [1,4,2,5,3,6,7]
[1,4,5,2,3,7,6] => [1,4,2,5,3,7,6]
[1,4,5,2,6,3,7] => [1,4,2,6,3,5,7]
[1,4,5,2,6,7,3] => [1,4,2,7,3,5,6]
[1,4,5,2,7,3,6] => [1,4,2,7,6,3,5]
[1,4,5,2,7,6,3] => [1,4,2,6,7,3,5]
[1,4,5,3,2,6,7] => [1,5,2,4,3,6,7]
[1,4,5,3,2,7,6] => [1,5,2,4,3,7,6]
[1,4,5,3,6,2,7] => [1,6,2,4,3,5,7]
[1,4,5,3,6,7,2] => [1,7,2,4,3,5,6]
[1,4,5,3,7,2,6] => [1,7,6,2,4,3,5]
[1,4,5,3,7,6,2] => [1,6,7,2,4,3,5]
[1,4,5,6,2,3,7] => [1,6,3,5,2,4,7]
[1,4,5,6,2,7,3] => [1,7,3,5,2,4,6]
[1,4,5,6,3,2,7] => [1,5,3,6,2,4,7]
[1,4,5,6,3,7,2] => [1,5,3,7,2,4,6]
[1,4,5,6,7,2,3] => [1,6,2,4,7,3,5]
[1,4,5,6,7,3,2] => [1,7,2,4,6,3,5]
[1,4,5,7,2,3,6] => [1,7,6,3,5,2,4]
[1,4,5,7,2,6,3] => [1,6,7,3,5,2,4]
[1,4,5,7,3,2,6] => [1,5,3,7,6,2,4]
[1,4,5,7,3,6,2] => [1,5,3,6,7,2,4]
[1,4,5,7,6,2,3] => [1,7,3,5,6,2,4]
[1,4,5,7,6,3,2] => [1,6,3,5,7,2,4]
[1,4,6,2,3,5,7] => [1,4,2,6,5,3,7]
[1,4,6,2,3,7,5] => [1,4,2,7,5,3,6]
[1,4,6,2,5,3,7] => [1,4,2,5,6,3,7]
[1,4,6,2,5,7,3] => [1,4,2,5,7,3,6]
[1,4,6,2,7,3,5] => [1,4,2,6,3,7,5]
[1,4,6,2,7,5,3] => [1,4,2,7,3,6,5]
[1,4,6,3,2,5,7] => [1,6,5,2,4,3,7]
[1,4,6,3,2,7,5] => [1,7,5,2,4,3,6]
[1,4,6,3,5,2,7] => [1,5,6,2,4,3,7]
[1,4,6,3,5,7,2] => [1,5,7,2,4,3,6]
[1,4,6,3,7,2,5] => [1,6,2,4,3,7,5]
[1,4,6,3,7,5,2] => [1,7,2,4,3,6,5]
[1,4,6,5,2,3,7] => [1,5,2,4,6,3,7]
[1,4,6,5,2,7,3] => [1,5,2,4,7,3,6]
[1,4,6,5,3,2,7] => [1,6,2,4,5,3,7]
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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.
Properties
bijectiveA map $\phi: A \rightarrow B$ is bijective if it is both injective and surjective. This is if (1) $\phi(a) = \phi(b)$ implies $a=b$, and (2) for any $b \in B$, there is an $a \in A$ such that $\phi(a) = b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if the $\operatorname{deg}(a) = \operatorname{deg}(\phi(a))$ for any $a \in A$.
Code
def fundamental_transformation_inverse(pi):
    """
    inverse of fundamental_bijection

    sage: all(pi == fundamental_bijection_inverse(fundamental_bijection(pi)) for pi in Permutations(6))
    """
    # rotate cycles such that maximum comes first
    def rotate(c):
        maximum = 0
        for i in range(1, len(c)):
            if c[i] > c[maximum]:
                maximum = i
        return c[maximum::] + c[:maximum]

    cycles = sorted([rotate(cycle) for cycle in pi.cycle_tuples()])
    return Permutation([e for c in cycles for e in c])