Identifier
-
Mp00087:
Permutations
—inverse first fundamental transformation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
St000470: Permutations ⟶ ℤ (values match St000021The number of descents of a permutation., St000325The width of the tree associated to a permutation.)
Values
[1] => [1] => [1] => 1
[1,2] => [1,2] => [2,1] => 2
[2,1] => [2,1] => [1,2] => 1
[1,2,3] => [1,2,3] => [3,2,1] => 3
[1,3,2] => [1,3,2] => [3,1,2] => 2
[2,1,3] => [2,1,3] => [2,3,1] => 2
[2,3,1] => [3,1,2] => [1,3,2] => 2
[3,1,2] => [3,2,1] => [1,2,3] => 1
[3,2,1] => [2,3,1] => [2,1,3] => 2
[1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 4
[1,2,4,3] => [1,2,4,3] => [4,3,1,2] => 3
[1,3,2,4] => [1,3,2,4] => [4,2,3,1] => 3
[1,3,4,2] => [1,4,2,3] => [4,1,3,2] => 3
[1,4,2,3] => [1,4,3,2] => [4,1,2,3] => 2
[1,4,3,2] => [1,3,4,2] => [4,2,1,3] => 3
[2,1,3,4] => [2,1,3,4] => [3,4,2,1] => 3
[2,1,4,3] => [2,1,4,3] => [3,4,1,2] => 2
[2,3,1,4] => [3,1,2,4] => [2,4,3,1] => 3
[2,3,4,1] => [4,1,2,3] => [1,4,3,2] => 3
[2,4,1,3] => [4,3,1,2] => [1,2,4,3] => 2
[2,4,3,1] => [3,4,1,2] => [2,1,4,3] => 3
[3,1,2,4] => [3,2,1,4] => [2,3,4,1] => 2
[3,1,4,2] => [4,2,1,3] => [1,3,4,2] => 2
[3,2,1,4] => [2,3,1,4] => [3,2,4,1] => 3
[3,2,4,1] => [2,4,1,3] => [3,1,4,2] => 3
[3,4,1,2] => [3,1,4,2] => [2,4,1,3] => 2
[3,4,2,1] => [4,1,3,2] => [1,4,2,3] => 2
[4,1,2,3] => [4,3,2,1] => [1,2,3,4] => 1
[4,1,3,2] => [3,4,2,1] => [2,1,3,4] => 2
[4,2,1,3] => [2,4,3,1] => [3,1,2,4] => 2
[4,2,3,1] => [2,3,4,1] => [3,2,1,4] => 3
[4,3,1,2] => [4,2,3,1] => [1,3,2,4] => 2
[4,3,2,1] => [3,2,4,1] => [2,3,1,4] => 2
[1,2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => 5
[1,2,3,5,4] => [1,2,3,5,4] => [5,4,3,1,2] => 4
[1,2,4,3,5] => [1,2,4,3,5] => [5,4,2,3,1] => 4
[1,2,4,5,3] => [1,2,5,3,4] => [5,4,1,3,2] => 4
[1,2,5,3,4] => [1,2,5,4,3] => [5,4,1,2,3] => 3
[1,2,5,4,3] => [1,2,4,5,3] => [5,4,2,1,3] => 4
[1,3,2,4,5] => [1,3,2,4,5] => [5,3,4,2,1] => 4
[1,3,2,5,4] => [1,3,2,5,4] => [5,3,4,1,2] => 3
[1,3,4,2,5] => [1,4,2,3,5] => [5,2,4,3,1] => 4
[1,3,4,5,2] => [1,5,2,3,4] => [5,1,4,3,2] => 4
[1,3,5,2,4] => [1,5,4,2,3] => [5,1,2,4,3] => 3
[1,3,5,4,2] => [1,4,5,2,3] => [5,2,1,4,3] => 4
[1,4,2,3,5] => [1,4,3,2,5] => [5,2,3,4,1] => 3
[1,4,2,5,3] => [1,5,3,2,4] => [5,1,3,4,2] => 3
[1,4,3,2,5] => [1,3,4,2,5] => [5,3,2,4,1] => 4
[1,4,3,5,2] => [1,3,5,2,4] => [5,3,1,4,2] => 4
[1,4,5,2,3] => [1,4,2,5,3] => [5,2,4,1,3] => 3
[1,4,5,3,2] => [1,5,2,4,3] => [5,1,4,2,3] => 3
[1,5,2,3,4] => [1,5,4,3,2] => [5,1,2,3,4] => 2
[1,5,2,4,3] => [1,4,5,3,2] => [5,2,1,3,4] => 3
[1,5,3,2,4] => [1,3,5,4,2] => [5,3,1,2,4] => 3
[1,5,3,4,2] => [1,3,4,5,2] => [5,3,2,1,4] => 4
[1,5,4,2,3] => [1,5,3,4,2] => [5,1,3,2,4] => 3
[1,5,4,3,2] => [1,4,3,5,2] => [5,2,3,1,4] => 3
[2,1,3,4,5] => [2,1,3,4,5] => [4,5,3,2,1] => 4
[2,1,3,5,4] => [2,1,3,5,4] => [4,5,3,1,2] => 3
[2,1,4,3,5] => [2,1,4,3,5] => [4,5,2,3,1] => 3
[2,1,4,5,3] => [2,1,5,3,4] => [4,5,1,3,2] => 3
[2,1,5,3,4] => [2,1,5,4,3] => [4,5,1,2,3] => 2
[2,1,5,4,3] => [2,1,4,5,3] => [4,5,2,1,3] => 3
[2,3,1,4,5] => [3,1,2,4,5] => [3,5,4,2,1] => 4
[2,3,1,5,4] => [3,1,2,5,4] => [3,5,4,1,2] => 3
[2,3,4,1,5] => [4,1,2,3,5] => [2,5,4,3,1] => 4
[2,3,4,5,1] => [5,1,2,3,4] => [1,5,4,3,2] => 4
[2,3,5,1,4] => [5,4,1,2,3] => [1,2,5,4,3] => 3
[2,3,5,4,1] => [4,5,1,2,3] => [2,1,5,4,3] => 4
[2,4,1,3,5] => [4,3,1,2,5] => [2,3,5,4,1] => 3
[2,4,1,5,3] => [5,3,1,2,4] => [1,3,5,4,2] => 3
[2,4,3,1,5] => [3,4,1,2,5] => [3,2,5,4,1] => 4
[2,4,3,5,1] => [3,5,1,2,4] => [3,1,5,4,2] => 4
[2,4,5,1,3] => [4,1,2,5,3] => [2,5,4,1,3] => 3
[2,4,5,3,1] => [5,1,2,4,3] => [1,5,4,2,3] => 3
[2,5,1,3,4] => [5,4,3,1,2] => [1,2,3,5,4] => 2
[2,5,1,4,3] => [4,5,3,1,2] => [2,1,3,5,4] => 3
[2,5,3,1,4] => [3,5,4,1,2] => [3,1,2,5,4] => 3
[2,5,3,4,1] => [3,4,5,1,2] => [3,2,1,5,4] => 4
[2,5,4,1,3] => [5,3,4,1,2] => [1,3,2,5,4] => 3
[2,5,4,3,1] => [4,3,5,1,2] => [2,3,1,5,4] => 3
[3,1,2,4,5] => [3,2,1,4,5] => [3,4,5,2,1] => 3
[3,1,2,5,4] => [3,2,1,5,4] => [3,4,5,1,2] => 2
[3,1,4,2,5] => [4,2,1,3,5] => [2,4,5,3,1] => 3
[3,1,4,5,2] => [5,2,1,3,4] => [1,4,5,3,2] => 3
[3,1,5,2,4] => [5,4,2,1,3] => [1,2,4,5,3] => 2
[3,1,5,4,2] => [4,5,2,1,3] => [2,1,4,5,3] => 3
[3,2,1,4,5] => [2,3,1,4,5] => [4,3,5,2,1] => 4
[3,2,1,5,4] => [2,3,1,5,4] => [4,3,5,1,2] => 3
[3,2,4,1,5] => [2,4,1,3,5] => [4,2,5,3,1] => 4
[3,2,4,5,1] => [2,5,1,3,4] => [4,1,5,3,2] => 4
[3,2,5,1,4] => [2,5,4,1,3] => [4,1,2,5,3] => 3
[3,2,5,4,1] => [2,4,5,1,3] => [4,2,1,5,3] => 4
[3,4,1,2,5] => [3,1,4,2,5] => [3,5,2,4,1] => 3
[3,4,1,5,2] => [3,1,5,2,4] => [3,5,1,4,2] => 3
[3,4,2,1,5] => [4,1,3,2,5] => [2,5,3,4,1] => 3
[3,4,2,5,1] => [5,1,3,2,4] => [1,5,3,4,2] => 3
[3,4,5,1,2] => [5,2,4,1,3] => [1,4,2,5,3] => 3
[3,4,5,2,1] => [4,2,5,1,3] => [2,4,1,5,3] => 3
[3,5,1,2,4] => [3,1,5,4,2] => [3,5,1,2,4] => 2
[3,5,1,4,2] => [3,1,4,5,2] => [3,5,2,1,4] => 3
>>> Load all 1201 entries. <<<[3,5,2,1,4] => [5,4,1,3,2] => [1,2,5,3,4] => 2
[3,5,2,4,1] => [4,5,1,3,2] => [2,1,5,3,4] => 3
[3,5,4,1,2] => [4,1,3,5,2] => [2,5,3,1,4] => 3
[3,5,4,2,1] => [5,1,3,4,2] => [1,5,3,2,4] => 3
[4,1,2,3,5] => [4,3,2,1,5] => [2,3,4,5,1] => 2
[4,1,2,5,3] => [5,3,2,1,4] => [1,3,4,5,2] => 2
[4,1,3,2,5] => [3,4,2,1,5] => [3,2,4,5,1] => 3
[4,1,3,5,2] => [3,5,2,1,4] => [3,1,4,5,2] => 3
[4,1,5,2,3] => [4,2,1,5,3] => [2,4,5,1,3] => 2
[4,1,5,3,2] => [5,2,1,4,3] => [1,4,5,2,3] => 2
[4,2,1,3,5] => [2,4,3,1,5] => [4,2,3,5,1] => 3
[4,2,1,5,3] => [2,5,3,1,4] => [4,1,3,5,2] => 3
[4,2,3,1,5] => [2,3,4,1,5] => [4,3,2,5,1] => 4
[4,2,3,5,1] => [2,3,5,1,4] => [4,3,1,5,2] => 4
[4,2,5,1,3] => [2,4,1,5,3] => [4,2,5,1,3] => 3
[4,2,5,3,1] => [2,5,1,4,3] => [4,1,5,2,3] => 3
[4,3,1,2,5] => [4,2,3,1,5] => [2,4,3,5,1] => 3
[4,3,1,5,2] => [5,2,3,1,4] => [1,4,3,5,2] => 3
[4,3,2,1,5] => [3,2,4,1,5] => [3,4,2,5,1] => 3
[4,3,2,5,1] => [3,2,5,1,4] => [3,4,1,5,2] => 3
[4,3,5,1,2] => [4,1,5,2,3] => [2,5,1,4,3] => 3
[4,3,5,2,1] => [5,1,4,2,3] => [1,5,2,4,3] => 3
[4,5,1,2,3] => [5,3,1,4,2] => [1,3,5,2,4] => 2
[4,5,1,3,2] => [4,3,1,5,2] => [2,3,5,1,4] => 2
[4,5,2,1,3] => [4,1,5,3,2] => [2,5,1,3,4] => 2
[4,5,2,3,1] => [5,1,4,3,2] => [1,5,2,3,4] => 2
[4,5,3,1,2] => [3,4,1,5,2] => [3,2,5,1,4] => 3
[4,5,3,2,1] => [3,5,1,4,2] => [3,1,5,2,4] => 3
[5,1,2,3,4] => [5,4,3,2,1] => [1,2,3,4,5] => 1
[5,1,2,4,3] => [4,5,3,2,1] => [2,1,3,4,5] => 2
[5,1,3,2,4] => [3,5,4,2,1] => [3,1,2,4,5] => 2
[5,1,3,4,2] => [3,4,5,2,1] => [3,2,1,4,5] => 3
[5,1,4,2,3] => [5,3,4,2,1] => [1,3,2,4,5] => 2
[5,1,4,3,2] => [4,3,5,2,1] => [2,3,1,4,5] => 2
[5,2,1,3,4] => [2,5,4,3,1] => [4,1,2,3,5] => 2
[5,2,1,4,3] => [2,4,5,3,1] => [4,2,1,3,5] => 3
[5,2,3,1,4] => [2,3,5,4,1] => [4,3,1,2,5] => 3
[5,2,3,4,1] => [2,3,4,5,1] => [4,3,2,1,5] => 4
[5,2,4,1,3] => [2,5,3,4,1] => [4,1,3,2,5] => 3
[5,2,4,3,1] => [2,4,3,5,1] => [4,2,3,1,5] => 3
[5,3,1,2,4] => [5,4,2,3,1] => [1,2,4,3,5] => 2
[5,3,1,4,2] => [4,5,2,3,1] => [2,1,4,3,5] => 3
[5,3,2,1,4] => [3,2,5,4,1] => [3,4,1,2,5] => 2
[5,3,2,4,1] => [3,2,4,5,1] => [3,4,2,1,5] => 3
[5,3,4,1,2] => [5,2,3,4,1] => [1,4,3,2,5] => 3
[5,3,4,2,1] => [4,2,3,5,1] => [2,4,3,1,5] => 3
[5,4,1,2,3] => [4,2,5,3,1] => [2,4,1,3,5] => 2
[5,4,1,3,2] => [5,2,4,3,1] => [1,4,2,3,5] => 2
[5,4,2,1,3] => [5,3,2,4,1] => [1,3,4,2,5] => 2
[5,4,2,3,1] => [4,3,2,5,1] => [2,3,4,1,5] => 2
[5,4,3,1,2] => [3,5,2,4,1] => [3,1,4,2,5] => 3
[5,4,3,2,1] => [3,4,2,5,1] => [3,2,4,1,5] => 3
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 6
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [6,5,4,3,1,2] => 5
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [6,5,4,2,3,1] => 5
[1,2,3,5,6,4] => [1,2,3,6,4,5] => [6,5,4,1,3,2] => 5
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [6,5,4,1,2,3] => 4
[1,2,3,6,5,4] => [1,2,3,5,6,4] => [6,5,4,2,1,3] => 5
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 5
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [6,5,3,4,1,2] => 4
[1,2,4,5,3,6] => [1,2,5,3,4,6] => [6,5,2,4,3,1] => 5
[1,2,4,5,6,3] => [1,2,6,3,4,5] => [6,5,1,4,3,2] => 5
[1,2,4,6,3,5] => [1,2,6,5,3,4] => [6,5,1,2,4,3] => 4
[1,2,4,6,5,3] => [1,2,5,6,3,4] => [6,5,2,1,4,3] => 5
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [6,5,2,3,4,1] => 4
[1,2,5,3,6,4] => [1,2,6,4,3,5] => [6,5,1,3,4,2] => 4
[1,2,5,4,3,6] => [1,2,4,5,3,6] => [6,5,3,2,4,1] => 5
[1,2,5,4,6,3] => [1,2,4,6,3,5] => [6,5,3,1,4,2] => 5
[1,2,5,6,3,4] => [1,2,5,3,6,4] => [6,5,2,4,1,3] => 4
[1,2,5,6,4,3] => [1,2,6,3,5,4] => [6,5,1,4,2,3] => 4
[1,2,6,3,4,5] => [1,2,6,5,4,3] => [6,5,1,2,3,4] => 3
[1,2,6,3,5,4] => [1,2,5,6,4,3] => [6,5,2,1,3,4] => 4
[1,2,6,4,3,5] => [1,2,4,6,5,3] => [6,5,3,1,2,4] => 4
[1,2,6,4,5,3] => [1,2,4,5,6,3] => [6,5,3,2,1,4] => 5
[1,2,6,5,3,4] => [1,2,6,4,5,3] => [6,5,1,3,2,4] => 4
[1,2,6,5,4,3] => [1,2,5,4,6,3] => [6,5,2,3,1,4] => 4
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [6,4,5,3,2,1] => 5
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [6,4,5,3,1,2] => 4
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 4
[1,3,2,5,6,4] => [1,3,2,6,4,5] => [6,4,5,1,3,2] => 4
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [6,4,5,1,2,3] => 3
[1,3,2,6,5,4] => [1,3,2,5,6,4] => [6,4,5,2,1,3] => 4
[1,3,4,2,5,6] => [1,4,2,3,5,6] => [6,3,5,4,2,1] => 5
[1,3,4,2,6,5] => [1,4,2,3,6,5] => [6,3,5,4,1,2] => 4
[1,3,4,5,2,6] => [1,5,2,3,4,6] => [6,2,5,4,3,1] => 5
[1,3,4,5,6,2] => [1,6,2,3,4,5] => [6,1,5,4,3,2] => 5
[1,3,4,6,2,5] => [1,6,5,2,3,4] => [6,1,2,5,4,3] => 4
[1,3,4,6,5,2] => [1,5,6,2,3,4] => [6,2,1,5,4,3] => 5
[1,3,5,2,4,6] => [1,5,4,2,3,6] => [6,2,3,5,4,1] => 4
[1,3,5,2,6,4] => [1,6,4,2,3,5] => [6,1,3,5,4,2] => 4
[1,3,5,4,2,6] => [1,4,5,2,3,6] => [6,3,2,5,4,1] => 5
[1,3,5,4,6,2] => [1,4,6,2,3,5] => [6,3,1,5,4,2] => 5
[1,3,5,6,2,4] => [1,5,2,3,6,4] => [6,2,5,4,1,3] => 4
[1,3,5,6,4,2] => [1,6,2,3,5,4] => [6,1,5,4,2,3] => 4
[1,3,6,2,4,5] => [1,6,5,4,2,3] => [6,1,2,3,5,4] => 3
[1,3,6,2,5,4] => [1,5,6,4,2,3] => [6,2,1,3,5,4] => 4
[1,3,6,4,2,5] => [1,4,6,5,2,3] => [6,3,1,2,5,4] => 4
[1,3,6,4,5,2] => [1,4,5,6,2,3] => [6,3,2,1,5,4] => 5
[1,3,6,5,2,4] => [1,6,4,5,2,3] => [6,1,3,2,5,4] => 4
[1,3,6,5,4,2] => [1,5,4,6,2,3] => [6,2,3,1,5,4] => 4
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [6,3,4,5,2,1] => 4
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [6,3,4,5,1,2] => 3
[1,4,2,5,3,6] => [1,5,3,2,4,6] => [6,2,4,5,3,1] => 4
[1,4,2,5,6,3] => [1,6,3,2,4,5] => [6,1,4,5,3,2] => 4
[1,4,2,6,3,5] => [1,6,5,3,2,4] => [6,1,2,4,5,3] => 3
[1,4,2,6,5,3] => [1,5,6,3,2,4] => [6,2,1,4,5,3] => 4
[1,4,3,2,5,6] => [1,3,4,2,5,6] => [6,4,3,5,2,1] => 5
[1,4,3,2,6,5] => [1,3,4,2,6,5] => [6,4,3,5,1,2] => 4
[1,4,3,5,2,6] => [1,3,5,2,4,6] => [6,4,2,5,3,1] => 5
[1,4,3,5,6,2] => [1,3,6,2,4,5] => [6,4,1,5,3,2] => 5
[1,4,3,6,2,5] => [1,3,6,5,2,4] => [6,4,1,2,5,3] => 4
[1,4,3,6,5,2] => [1,3,5,6,2,4] => [6,4,2,1,5,3] => 5
[1,4,5,2,3,6] => [1,4,2,5,3,6] => [6,3,5,2,4,1] => 4
[1,4,5,2,6,3] => [1,4,2,6,3,5] => [6,3,5,1,4,2] => 4
[1,4,5,3,2,6] => [1,5,2,4,3,6] => [6,2,5,3,4,1] => 4
[1,4,5,3,6,2] => [1,6,2,4,3,5] => [6,1,5,3,4,2] => 4
[1,4,5,6,2,3] => [1,6,3,5,2,4] => [6,1,4,2,5,3] => 4
[1,4,5,6,3,2] => [1,5,3,6,2,4] => [6,2,4,1,5,3] => 4
[1,4,6,2,3,5] => [1,4,2,6,5,3] => [6,3,5,1,2,4] => 3
[1,4,6,2,5,3] => [1,4,2,5,6,3] => [6,3,5,2,1,4] => 4
[1,4,6,3,2,5] => [1,6,5,2,4,3] => [6,1,2,5,3,4] => 3
[1,4,6,3,5,2] => [1,5,6,2,4,3] => [6,2,1,5,3,4] => 4
[1,4,6,5,2,3] => [1,5,2,4,6,3] => [6,2,5,3,1,4] => 4
[1,4,6,5,3,2] => [1,6,2,4,5,3] => [6,1,5,3,2,4] => 4
[1,5,2,3,4,6] => [1,5,4,3,2,6] => [6,2,3,4,5,1] => 3
[1,5,2,3,6,4] => [1,6,4,3,2,5] => [6,1,3,4,5,2] => 3
[1,5,2,4,3,6] => [1,4,5,3,2,6] => [6,3,2,4,5,1] => 4
[1,5,2,4,6,3] => [1,4,6,3,2,5] => [6,3,1,4,5,2] => 4
[1,5,2,6,3,4] => [1,5,3,2,6,4] => [6,2,4,5,1,3] => 3
[1,5,2,6,4,3] => [1,6,3,2,5,4] => [6,1,4,5,2,3] => 3
[1,5,3,2,4,6] => [1,3,5,4,2,6] => [6,4,2,3,5,1] => 4
[1,5,3,2,6,4] => [1,3,6,4,2,5] => [6,4,1,3,5,2] => 4
[1,5,3,4,2,6] => [1,3,4,5,2,6] => [6,4,3,2,5,1] => 5
[1,5,3,4,6,2] => [1,3,4,6,2,5] => [6,4,3,1,5,2] => 5
[1,5,3,6,2,4] => [1,3,5,2,6,4] => [6,4,2,5,1,3] => 4
[1,5,3,6,4,2] => [1,3,6,2,5,4] => [6,4,1,5,2,3] => 4
[1,5,4,2,3,6] => [1,5,3,4,2,6] => [6,2,4,3,5,1] => 4
[1,5,4,2,6,3] => [1,6,3,4,2,5] => [6,1,4,3,5,2] => 4
[1,5,4,3,2,6] => [1,4,3,5,2,6] => [6,3,4,2,5,1] => 4
[1,5,4,3,6,2] => [1,4,3,6,2,5] => [6,3,4,1,5,2] => 4
[1,5,4,6,2,3] => [1,5,2,6,3,4] => [6,2,5,1,4,3] => 4
[1,5,4,6,3,2] => [1,6,2,5,3,4] => [6,1,5,2,4,3] => 4
[1,5,6,2,3,4] => [1,6,4,2,5,3] => [6,1,3,5,2,4] => 3
[1,5,6,2,4,3] => [1,5,4,2,6,3] => [6,2,3,5,1,4] => 3
[1,5,6,3,2,4] => [1,5,2,6,4,3] => [6,2,5,1,3,4] => 3
[1,5,6,3,4,2] => [1,6,2,5,4,3] => [6,1,5,2,3,4] => 3
[1,5,6,4,2,3] => [1,4,5,2,6,3] => [6,3,2,5,1,4] => 4
[1,5,6,4,3,2] => [1,4,6,2,5,3] => [6,3,1,5,2,4] => 4
[1,6,2,3,4,5] => [1,6,5,4,3,2] => [6,1,2,3,4,5] => 2
[1,6,2,3,5,4] => [1,5,6,4,3,2] => [6,2,1,3,4,5] => 3
[1,6,2,4,3,5] => [1,4,6,5,3,2] => [6,3,1,2,4,5] => 3
[1,6,2,4,5,3] => [1,4,5,6,3,2] => [6,3,2,1,4,5] => 4
[1,6,2,5,3,4] => [1,6,4,5,3,2] => [6,1,3,2,4,5] => 3
[1,6,2,5,4,3] => [1,5,4,6,3,2] => [6,2,3,1,4,5] => 3
[1,6,3,2,4,5] => [1,3,6,5,4,2] => [6,4,1,2,3,5] => 3
[1,6,3,2,5,4] => [1,3,5,6,4,2] => [6,4,2,1,3,5] => 4
[1,6,3,4,2,5] => [1,3,4,6,5,2] => [6,4,3,1,2,5] => 4
[1,6,3,4,5,2] => [1,3,4,5,6,2] => [6,4,3,2,1,5] => 5
[1,6,3,5,2,4] => [1,3,6,4,5,2] => [6,4,1,3,2,5] => 4
[1,6,3,5,4,2] => [1,3,5,4,6,2] => [6,4,2,3,1,5] => 4
[1,6,4,2,3,5] => [1,6,5,3,4,2] => [6,1,2,4,3,5] => 3
[1,6,4,2,5,3] => [1,5,6,3,4,2] => [6,2,1,4,3,5] => 4
[1,6,4,3,2,5] => [1,4,3,6,5,2] => [6,3,4,1,2,5] => 3
[1,6,4,3,5,2] => [1,4,3,5,6,2] => [6,3,4,2,1,5] => 4
[1,6,4,5,2,3] => [1,6,3,4,5,2] => [6,1,4,3,2,5] => 4
[1,6,4,5,3,2] => [1,5,3,4,6,2] => [6,2,4,3,1,5] => 4
[1,6,5,2,3,4] => [1,5,3,6,4,2] => [6,2,4,1,3,5] => 3
[1,6,5,2,4,3] => [1,6,3,5,4,2] => [6,1,4,2,3,5] => 3
[1,6,5,3,2,4] => [1,6,4,3,5,2] => [6,1,3,4,2,5] => 3
[1,6,5,3,4,2] => [1,5,4,3,6,2] => [6,2,3,4,1,5] => 3
[1,6,5,4,2,3] => [1,4,6,3,5,2] => [6,3,1,4,2,5] => 4
[1,6,5,4,3,2] => [1,4,5,3,6,2] => [6,3,2,4,1,5] => 4
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [5,6,4,3,2,1] => 5
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 4
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [5,6,4,2,3,1] => 4
[2,1,3,5,6,4] => [2,1,3,6,4,5] => [5,6,4,1,3,2] => 4
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [5,6,4,1,2,3] => 3
[2,1,3,6,5,4] => [2,1,3,5,6,4] => [5,6,4,2,1,3] => 4
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [5,6,3,4,2,1] => 4
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 3
[2,1,4,5,3,6] => [2,1,5,3,4,6] => [5,6,2,4,3,1] => 4
[2,1,4,5,6,3] => [2,1,6,3,4,5] => [5,6,1,4,3,2] => 4
[2,1,4,6,3,5] => [2,1,6,5,3,4] => [5,6,1,2,4,3] => 3
[2,1,4,6,5,3] => [2,1,5,6,3,4] => [5,6,2,1,4,3] => 4
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [5,6,2,3,4,1] => 3
[2,1,5,3,6,4] => [2,1,6,4,3,5] => [5,6,1,3,4,2] => 3
[2,1,5,4,3,6] => [2,1,4,5,3,6] => [5,6,3,2,4,1] => 4
[2,1,5,4,6,3] => [2,1,4,6,3,5] => [5,6,3,1,4,2] => 4
[2,1,5,6,3,4] => [2,1,5,3,6,4] => [5,6,2,4,1,3] => 3
[2,1,5,6,4,3] => [2,1,6,3,5,4] => [5,6,1,4,2,3] => 3
[2,1,6,3,4,5] => [2,1,6,5,4,3] => [5,6,1,2,3,4] => 2
[2,1,6,3,5,4] => [2,1,5,6,4,3] => [5,6,2,1,3,4] => 3
[2,1,6,4,3,5] => [2,1,4,6,5,3] => [5,6,3,1,2,4] => 3
[2,1,6,4,5,3] => [2,1,4,5,6,3] => [5,6,3,2,1,4] => 4
[2,1,6,5,3,4] => [2,1,6,4,5,3] => [5,6,1,3,2,4] => 3
[2,1,6,5,4,3] => [2,1,5,4,6,3] => [5,6,2,3,1,4] => 3
[2,3,1,4,5,6] => [3,1,2,4,5,6] => [4,6,5,3,2,1] => 5
[2,3,1,4,6,5] => [3,1,2,4,6,5] => [4,6,5,3,1,2] => 4
[2,3,1,5,4,6] => [3,1,2,5,4,6] => [4,6,5,2,3,1] => 4
[2,3,1,5,6,4] => [3,1,2,6,4,5] => [4,6,5,1,3,2] => 4
[2,3,1,6,4,5] => [3,1,2,6,5,4] => [4,6,5,1,2,3] => 3
[2,3,1,6,5,4] => [3,1,2,5,6,4] => [4,6,5,2,1,3] => 4
[2,3,4,1,5,6] => [4,1,2,3,5,6] => [3,6,5,4,2,1] => 5
[2,3,4,1,6,5] => [4,1,2,3,6,5] => [3,6,5,4,1,2] => 4
[2,3,4,5,1,6] => [5,1,2,3,4,6] => [2,6,5,4,3,1] => 5
[2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 5
[2,3,4,6,1,5] => [6,5,1,2,3,4] => [1,2,6,5,4,3] => 4
[2,3,4,6,5,1] => [5,6,1,2,3,4] => [2,1,6,5,4,3] => 5
[2,3,5,1,4,6] => [5,4,1,2,3,6] => [2,3,6,5,4,1] => 4
[2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,3,6,5,4,2] => 4
[2,3,5,4,1,6] => [4,5,1,2,3,6] => [3,2,6,5,4,1] => 5
[2,3,5,4,6,1] => [4,6,1,2,3,5] => [3,1,6,5,4,2] => 5
[2,3,5,6,1,4] => [5,1,2,3,6,4] => [2,6,5,4,1,3] => 4
[2,3,5,6,4,1] => [6,1,2,3,5,4] => [1,6,5,4,2,3] => 4
[2,3,6,1,4,5] => [6,5,4,1,2,3] => [1,2,3,6,5,4] => 3
[2,3,6,1,5,4] => [5,6,4,1,2,3] => [2,1,3,6,5,4] => 4
[2,3,6,4,1,5] => [4,6,5,1,2,3] => [3,1,2,6,5,4] => 4
[2,3,6,4,5,1] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 5
[2,3,6,5,1,4] => [6,4,5,1,2,3] => [1,3,2,6,5,4] => 4
[2,3,6,5,4,1] => [5,4,6,1,2,3] => [2,3,1,6,5,4] => 4
[2,4,1,3,5,6] => [4,3,1,2,5,6] => [3,4,6,5,2,1] => 4
[2,4,1,3,6,5] => [4,3,1,2,6,5] => [3,4,6,5,1,2] => 3
[2,4,1,5,3,6] => [5,3,1,2,4,6] => [2,4,6,5,3,1] => 4
[2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,4,6,5,3,2] => 4
[2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,2,4,6,5,3] => 3
[2,4,1,6,5,3] => [5,6,3,1,2,4] => [2,1,4,6,5,3] => 4
[2,4,3,1,5,6] => [3,4,1,2,5,6] => [4,3,6,5,2,1] => 5
[2,4,3,1,6,5] => [3,4,1,2,6,5] => [4,3,6,5,1,2] => 4
[2,4,3,5,1,6] => [3,5,1,2,4,6] => [4,2,6,5,3,1] => 5
[2,4,3,5,6,1] => [3,6,1,2,4,5] => [4,1,6,5,3,2] => 5
[2,4,3,6,1,5] => [3,6,5,1,2,4] => [4,1,2,6,5,3] => 4
[2,4,3,6,5,1] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => 5
[2,4,5,1,3,6] => [4,1,2,5,3,6] => [3,6,5,2,4,1] => 4
[2,4,5,1,6,3] => [4,1,2,6,3,5] => [3,6,5,1,4,2] => 4
[2,4,5,3,1,6] => [5,1,2,4,3,6] => [2,6,5,3,4,1] => 4
[2,4,5,3,6,1] => [6,1,2,4,3,5] => [1,6,5,3,4,2] => 4
[2,4,5,6,1,3] => [6,3,5,1,2,4] => [1,4,2,6,5,3] => 4
[2,4,5,6,3,1] => [5,3,6,1,2,4] => [2,4,1,6,5,3] => 4
[2,4,6,1,3,5] => [4,1,2,6,5,3] => [3,6,5,1,2,4] => 3
[2,4,6,1,5,3] => [4,1,2,5,6,3] => [3,6,5,2,1,4] => 4
[2,4,6,3,1,5] => [6,5,1,2,4,3] => [1,2,6,5,3,4] => 3
[2,4,6,3,5,1] => [5,6,1,2,4,3] => [2,1,6,5,3,4] => 4
[2,4,6,5,1,3] => [5,1,2,4,6,3] => [2,6,5,3,1,4] => 4
[2,4,6,5,3,1] => [6,1,2,4,5,3] => [1,6,5,3,2,4] => 4
[2,5,1,3,4,6] => [5,4,3,1,2,6] => [2,3,4,6,5,1] => 3
[2,5,1,3,6,4] => [6,4,3,1,2,5] => [1,3,4,6,5,2] => 3
[2,5,1,4,3,6] => [4,5,3,1,2,6] => [3,2,4,6,5,1] => 4
[2,5,1,4,6,3] => [4,6,3,1,2,5] => [3,1,4,6,5,2] => 4
[2,5,1,6,3,4] => [5,3,1,2,6,4] => [2,4,6,5,1,3] => 3
[2,5,1,6,4,3] => [6,3,1,2,5,4] => [1,4,6,5,2,3] => 3
[2,5,3,1,4,6] => [3,5,4,1,2,6] => [4,2,3,6,5,1] => 4
[2,5,3,1,6,4] => [3,6,4,1,2,5] => [4,1,3,6,5,2] => 4
[2,5,3,4,1,6] => [3,4,5,1,2,6] => [4,3,2,6,5,1] => 5
[2,5,3,4,6,1] => [3,4,6,1,2,5] => [4,3,1,6,5,2] => 5
[2,5,3,6,1,4] => [3,5,1,2,6,4] => [4,2,6,5,1,3] => 4
[2,5,3,6,4,1] => [3,6,1,2,5,4] => [4,1,6,5,2,3] => 4
[2,5,4,1,3,6] => [5,3,4,1,2,6] => [2,4,3,6,5,1] => 4
[2,5,4,1,6,3] => [6,3,4,1,2,5] => [1,4,3,6,5,2] => 4
[2,5,4,3,1,6] => [4,3,5,1,2,6] => [3,4,2,6,5,1] => 4
[2,5,4,3,6,1] => [4,3,6,1,2,5] => [3,4,1,6,5,2] => 4
[2,5,4,6,1,3] => [5,1,2,6,3,4] => [2,6,5,1,4,3] => 4
[2,5,4,6,3,1] => [6,1,2,5,3,4] => [1,6,5,2,4,3] => 4
[2,5,6,1,3,4] => [6,4,1,2,5,3] => [1,3,6,5,2,4] => 3
[2,5,6,1,4,3] => [5,4,1,2,6,3] => [2,3,6,5,1,4] => 3
[2,5,6,3,1,4] => [5,1,2,6,4,3] => [2,6,5,1,3,4] => 3
[2,5,6,3,4,1] => [6,1,2,5,4,3] => [1,6,5,2,3,4] => 3
[2,5,6,4,1,3] => [4,5,1,2,6,3] => [3,2,6,5,1,4] => 4
[2,5,6,4,3,1] => [4,6,1,2,5,3] => [3,1,6,5,2,4] => 4
[2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,2,3,4,6,5] => 2
[2,6,1,3,5,4] => [5,6,4,3,1,2] => [2,1,3,4,6,5] => 3
[2,6,1,4,3,5] => [4,6,5,3,1,2] => [3,1,2,4,6,5] => 3
[2,6,1,4,5,3] => [4,5,6,3,1,2] => [3,2,1,4,6,5] => 4
[2,6,1,5,3,4] => [6,4,5,3,1,2] => [1,3,2,4,6,5] => 3
[2,6,1,5,4,3] => [5,4,6,3,1,2] => [2,3,1,4,6,5] => 3
[2,6,3,1,4,5] => [3,6,5,4,1,2] => [4,1,2,3,6,5] => 3
[2,6,3,1,5,4] => [3,5,6,4,1,2] => [4,2,1,3,6,5] => 4
[2,6,3,4,1,5] => [3,4,6,5,1,2] => [4,3,1,2,6,5] => 4
[2,6,3,4,5,1] => [3,4,5,6,1,2] => [4,3,2,1,6,5] => 5
[2,6,3,5,1,4] => [3,6,4,5,1,2] => [4,1,3,2,6,5] => 4
[2,6,3,5,4,1] => [3,5,4,6,1,2] => [4,2,3,1,6,5] => 4
[2,6,4,1,3,5] => [6,5,3,4,1,2] => [1,2,4,3,6,5] => 3
[2,6,4,1,5,3] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => 4
[2,6,4,3,1,5] => [4,3,6,5,1,2] => [3,4,1,2,6,5] => 3
[2,6,4,3,5,1] => [4,3,5,6,1,2] => [3,4,2,1,6,5] => 4
[2,6,4,5,1,3] => [6,3,4,5,1,2] => [1,4,3,2,6,5] => 4
[2,6,4,5,3,1] => [5,3,4,6,1,2] => [2,4,3,1,6,5] => 4
[2,6,5,1,3,4] => [5,3,6,4,1,2] => [2,4,1,3,6,5] => 3
[2,6,5,1,4,3] => [6,3,5,4,1,2] => [1,4,2,3,6,5] => 3
[2,6,5,3,1,4] => [6,4,3,5,1,2] => [1,3,4,2,6,5] => 3
[2,6,5,3,4,1] => [5,4,3,6,1,2] => [2,3,4,1,6,5] => 3
[2,6,5,4,1,3] => [4,6,3,5,1,2] => [3,1,4,2,6,5] => 4
[2,6,5,4,3,1] => [4,5,3,6,1,2] => [3,2,4,1,6,5] => 4
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [4,5,6,3,2,1] => 4
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [4,5,6,3,1,2] => 3
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [4,5,6,2,3,1] => 3
[3,1,2,5,6,4] => [3,2,1,6,4,5] => [4,5,6,1,3,2] => 3
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => 2
[3,1,2,6,5,4] => [3,2,1,5,6,4] => [4,5,6,2,1,3] => 3
[3,1,4,2,5,6] => [4,2,1,3,5,6] => [3,5,6,4,2,1] => 4
[3,1,4,2,6,5] => [4,2,1,3,6,5] => [3,5,6,4,1,2] => 3
[3,1,4,5,2,6] => [5,2,1,3,4,6] => [2,5,6,4,3,1] => 4
[3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,5,6,4,3,2] => 4
[3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,2,5,6,4,3] => 3
[3,1,4,6,5,2] => [5,6,2,1,3,4] => [2,1,5,6,4,3] => 4
[3,1,5,2,4,6] => [5,4,2,1,3,6] => [2,3,5,6,4,1] => 3
[3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,3,5,6,4,2] => 3
[3,1,5,4,2,6] => [4,5,2,1,3,6] => [3,2,5,6,4,1] => 4
[3,1,5,4,6,2] => [4,6,2,1,3,5] => [3,1,5,6,4,2] => 4
[3,1,5,6,2,4] => [5,2,1,3,6,4] => [2,5,6,4,1,3] => 3
[3,1,5,6,4,2] => [6,2,1,3,5,4] => [1,5,6,4,2,3] => 3
[3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,2,3,5,6,4] => 2
[3,1,6,2,5,4] => [5,6,4,2,1,3] => [2,1,3,5,6,4] => 3
[3,1,6,4,2,5] => [4,6,5,2,1,3] => [3,1,2,5,6,4] => 3
[3,1,6,4,5,2] => [4,5,6,2,1,3] => [3,2,1,5,6,4] => 4
[3,1,6,5,2,4] => [6,4,5,2,1,3] => [1,3,2,5,6,4] => 3
[3,1,6,5,4,2] => [5,4,6,2,1,3] => [2,3,1,5,6,4] => 3
[3,2,1,4,5,6] => [2,3,1,4,5,6] => [5,4,6,3,2,1] => 5
[3,2,1,4,6,5] => [2,3,1,4,6,5] => [5,4,6,3,1,2] => 4
[3,2,1,5,4,6] => [2,3,1,5,4,6] => [5,4,6,2,3,1] => 4
[3,2,1,5,6,4] => [2,3,1,6,4,5] => [5,4,6,1,3,2] => 4
[3,2,1,6,4,5] => [2,3,1,6,5,4] => [5,4,6,1,2,3] => 3
[3,2,1,6,5,4] => [2,3,1,5,6,4] => [5,4,6,2,1,3] => 4
[3,2,4,1,5,6] => [2,4,1,3,5,6] => [5,3,6,4,2,1] => 5
[3,2,4,1,6,5] => [2,4,1,3,6,5] => [5,3,6,4,1,2] => 4
[3,2,4,5,1,6] => [2,5,1,3,4,6] => [5,2,6,4,3,1] => 5
[3,2,4,5,6,1] => [2,6,1,3,4,5] => [5,1,6,4,3,2] => 5
[3,2,4,6,1,5] => [2,6,5,1,3,4] => [5,1,2,6,4,3] => 4
[3,2,4,6,5,1] => [2,5,6,1,3,4] => [5,2,1,6,4,3] => 5
[3,2,5,1,4,6] => [2,5,4,1,3,6] => [5,2,3,6,4,1] => 4
[3,2,5,1,6,4] => [2,6,4,1,3,5] => [5,1,3,6,4,2] => 4
[3,2,5,4,1,6] => [2,4,5,1,3,6] => [5,3,2,6,4,1] => 5
[3,2,5,4,6,1] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => 5
[3,2,5,6,1,4] => [2,5,1,3,6,4] => [5,2,6,4,1,3] => 4
[3,2,5,6,4,1] => [2,6,1,3,5,4] => [5,1,6,4,2,3] => 4
[3,2,6,1,4,5] => [2,6,5,4,1,3] => [5,1,2,3,6,4] => 3
[3,2,6,1,5,4] => [2,5,6,4,1,3] => [5,2,1,3,6,4] => 4
[3,2,6,4,1,5] => [2,4,6,5,1,3] => [5,3,1,2,6,4] => 4
[3,2,6,4,5,1] => [2,4,5,6,1,3] => [5,3,2,1,6,4] => 5
[3,2,6,5,1,4] => [2,6,4,5,1,3] => [5,1,3,2,6,4] => 4
[3,2,6,5,4,1] => [2,5,4,6,1,3] => [5,2,3,1,6,4] => 4
[3,4,1,2,5,6] => [3,1,4,2,5,6] => [4,6,3,5,2,1] => 4
[3,4,1,2,6,5] => [3,1,4,2,6,5] => [4,6,3,5,1,2] => 3
[3,4,1,5,2,6] => [3,1,5,2,4,6] => [4,6,2,5,3,1] => 4
[3,4,1,5,6,2] => [3,1,6,2,4,5] => [4,6,1,5,3,2] => 4
[3,4,1,6,2,5] => [3,1,6,5,2,4] => [4,6,1,2,5,3] => 3
[3,4,1,6,5,2] => [3,1,5,6,2,4] => [4,6,2,1,5,3] => 4
[3,4,2,1,5,6] => [4,1,3,2,5,6] => [3,6,4,5,2,1] => 4
[3,4,2,1,6,5] => [4,1,3,2,6,5] => [3,6,4,5,1,2] => 3
[3,4,2,5,1,6] => [5,1,3,2,4,6] => [2,6,4,5,3,1] => 4
[3,4,2,5,6,1] => [6,1,3,2,4,5] => [1,6,4,5,3,2] => 4
[3,4,2,6,1,5] => [6,5,1,3,2,4] => [1,2,6,4,5,3] => 3
[3,4,2,6,5,1] => [5,6,1,3,2,4] => [2,1,6,4,5,3] => 4
[3,4,5,1,2,6] => [5,2,4,1,3,6] => [2,5,3,6,4,1] => 4
[3,4,5,1,6,2] => [6,2,4,1,3,5] => [1,5,3,6,4,2] => 4
[3,4,5,2,1,6] => [4,2,5,1,3,6] => [3,5,2,6,4,1] => 4
[3,4,5,2,6,1] => [4,2,6,1,3,5] => [3,5,1,6,4,2] => 4
[3,4,5,6,1,2] => [5,1,3,6,2,4] => [2,6,4,1,5,3] => 4
[3,4,5,6,2,1] => [6,1,3,5,2,4] => [1,6,4,2,5,3] => 4
[3,4,6,1,2,5] => [6,5,2,4,1,3] => [1,2,5,3,6,4] => 3
[3,4,6,1,5,2] => [5,6,2,4,1,3] => [2,1,5,3,6,4] => 4
[3,4,6,2,1,5] => [4,2,6,5,1,3] => [3,5,1,2,6,4] => 3
[3,4,6,2,5,1] => [4,2,5,6,1,3] => [3,5,2,1,6,4] => 4
[3,4,6,5,1,2] => [6,2,4,5,1,3] => [1,5,3,2,6,4] => 4
[3,4,6,5,2,1] => [5,2,4,6,1,3] => [2,5,3,1,6,4] => 4
[3,5,1,2,4,6] => [3,1,5,4,2,6] => [4,6,2,3,5,1] => 3
[3,5,1,2,6,4] => [3,1,6,4,2,5] => [4,6,1,3,5,2] => 3
[3,5,1,4,2,6] => [3,1,4,5,2,6] => [4,6,3,2,5,1] => 4
[3,5,1,4,6,2] => [3,1,4,6,2,5] => [4,6,3,1,5,2] => 4
[3,5,1,6,2,4] => [3,1,5,2,6,4] => [4,6,2,5,1,3] => 3
[3,5,1,6,4,2] => [3,1,6,2,5,4] => [4,6,1,5,2,3] => 3
[3,5,2,1,4,6] => [5,4,1,3,2,6] => [2,3,6,4,5,1] => 3
[3,5,2,1,6,4] => [6,4,1,3,2,5] => [1,3,6,4,5,2] => 3
[3,5,2,4,1,6] => [4,5,1,3,2,6] => [3,2,6,4,5,1] => 4
[3,5,2,4,6,1] => [4,6,1,3,2,5] => [3,1,6,4,5,2] => 4
[3,5,2,6,1,4] => [5,1,3,2,6,4] => [2,6,4,5,1,3] => 3
[3,5,2,6,4,1] => [6,1,3,2,5,4] => [1,6,4,5,2,3] => 3
[3,5,4,1,2,6] => [4,1,3,5,2,6] => [3,6,4,2,5,1] => 4
[3,5,4,1,6,2] => [4,1,3,6,2,5] => [3,6,4,1,5,2] => 4
[3,5,4,2,1,6] => [5,1,3,4,2,6] => [2,6,4,3,5,1] => 4
[3,5,4,2,6,1] => [6,1,3,4,2,5] => [1,6,4,3,5,2] => 4
[3,5,4,6,1,2] => [6,2,5,1,3,4] => [1,5,2,6,4,3] => 4
[3,5,4,6,2,1] => [5,2,6,1,3,4] => [2,5,1,6,4,3] => 4
[3,5,6,1,2,4] => [5,2,6,4,1,3] => [2,5,1,3,6,4] => 3
[3,5,6,1,4,2] => [6,2,5,4,1,3] => [1,5,2,3,6,4] => 3
[3,5,6,2,1,4] => [6,4,2,5,1,3] => [1,3,5,2,6,4] => 3
[3,5,6,2,4,1] => [5,4,2,6,1,3] => [2,3,5,1,6,4] => 3
[3,5,6,4,1,2] => [4,6,2,5,1,3] => [3,1,5,2,6,4] => 4
[3,5,6,4,2,1] => [4,5,2,6,1,3] => [3,2,5,1,6,4] => 4
[3,6,1,2,4,5] => [3,1,6,5,4,2] => [4,6,1,2,3,5] => 2
[3,6,1,2,5,4] => [3,1,5,6,4,2] => [4,6,2,1,3,5] => 3
[3,6,1,4,2,5] => [3,1,4,6,5,2] => [4,6,3,1,2,5] => 3
[3,6,1,4,5,2] => [3,1,4,5,6,2] => [4,6,3,2,1,5] => 4
[3,6,1,5,2,4] => [3,1,6,4,5,2] => [4,6,1,3,2,5] => 3
[3,6,1,5,4,2] => [3,1,5,4,6,2] => [4,6,2,3,1,5] => 3
[3,6,2,1,4,5] => [6,5,4,1,3,2] => [1,2,3,6,4,5] => 2
[3,6,2,1,5,4] => [5,6,4,1,3,2] => [2,1,3,6,4,5] => 3
[3,6,2,4,1,5] => [4,6,5,1,3,2] => [3,1,2,6,4,5] => 3
[3,6,2,4,5,1] => [4,5,6,1,3,2] => [3,2,1,6,4,5] => 4
[3,6,2,5,1,4] => [6,4,5,1,3,2] => [1,3,2,6,4,5] => 3
[3,6,2,5,4,1] => [5,4,6,1,3,2] => [2,3,1,6,4,5] => 3
[3,6,4,1,2,5] => [4,1,3,6,5,2] => [3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => [4,1,3,5,6,2] => [3,6,4,2,1,5] => 4
[3,6,4,2,1,5] => [6,5,1,3,4,2] => [1,2,6,4,3,5] => 3
[3,6,4,2,5,1] => [5,6,1,3,4,2] => [2,1,6,4,3,5] => 4
[3,6,4,5,1,2] => [5,1,3,4,6,2] => [2,6,4,3,1,5] => 4
[3,6,4,5,2,1] => [6,1,3,4,5,2] => [1,6,4,3,2,5] => 4
[3,6,5,1,2,4] => [6,4,1,3,5,2] => [1,3,6,4,2,5] => 3
[3,6,5,1,4,2] => [5,4,1,3,6,2] => [2,3,6,4,1,5] => 3
[3,6,5,2,1,4] => [5,1,3,6,4,2] => [2,6,4,1,3,5] => 3
[3,6,5,2,4,1] => [6,1,3,5,4,2] => [1,6,4,2,3,5] => 3
[3,6,5,4,1,2] => [4,5,1,3,6,2] => [3,2,6,4,1,5] => 4
[3,6,5,4,2,1] => [4,6,1,3,5,2] => [3,1,6,4,2,5] => 4
[4,1,2,3,5,6] => [4,3,2,1,5,6] => [3,4,5,6,2,1] => 3
[4,1,2,3,6,5] => [4,3,2,1,6,5] => [3,4,5,6,1,2] => 2
[4,1,2,5,3,6] => [5,3,2,1,4,6] => [2,4,5,6,3,1] => 3
[4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,4,5,6,3,2] => 3
[4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,2,4,5,6,3] => 2
[4,1,2,6,5,3] => [5,6,3,2,1,4] => [2,1,4,5,6,3] => 3
[4,1,3,2,5,6] => [3,4,2,1,5,6] => [4,3,5,6,2,1] => 4
[4,1,3,2,6,5] => [3,4,2,1,6,5] => [4,3,5,6,1,2] => 3
[4,1,3,5,2,6] => [3,5,2,1,4,6] => [4,2,5,6,3,1] => 4
[4,1,3,5,6,2] => [3,6,2,1,4,5] => [4,1,5,6,3,2] => 4
[4,1,3,6,2,5] => [3,6,5,2,1,4] => [4,1,2,5,6,3] => 3
[4,1,3,6,5,2] => [3,5,6,2,1,4] => [4,2,1,5,6,3] => 4
[4,1,5,2,3,6] => [4,2,1,5,3,6] => [3,5,6,2,4,1] => 3
[4,1,5,2,6,3] => [4,2,1,6,3,5] => [3,5,6,1,4,2] => 3
[4,1,5,3,2,6] => [5,2,1,4,3,6] => [2,5,6,3,4,1] => 3
[4,1,5,3,6,2] => [6,2,1,4,3,5] => [1,5,6,3,4,2] => 3
[4,1,5,6,2,3] => [6,3,5,2,1,4] => [1,4,2,5,6,3] => 3
[4,1,5,6,3,2] => [5,3,6,2,1,4] => [2,4,1,5,6,3] => 3
[4,1,6,2,3,5] => [4,2,1,6,5,3] => [3,5,6,1,2,4] => 2
[4,1,6,2,5,3] => [4,2,1,5,6,3] => [3,5,6,2,1,4] => 3
[4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,2,5,6,3,4] => 2
[4,1,6,3,5,2] => [5,6,2,1,4,3] => [2,1,5,6,3,4] => 3
[4,1,6,5,2,3] => [5,2,1,4,6,3] => [2,5,6,3,1,4] => 3
[4,1,6,5,3,2] => [6,2,1,4,5,3] => [1,5,6,3,2,4] => 3
[4,2,1,3,5,6] => [2,4,3,1,5,6] => [5,3,4,6,2,1] => 4
[4,2,1,3,6,5] => [2,4,3,1,6,5] => [5,3,4,6,1,2] => 3
[4,2,1,5,3,6] => [2,5,3,1,4,6] => [5,2,4,6,3,1] => 4
[4,2,1,5,6,3] => [2,6,3,1,4,5] => [5,1,4,6,3,2] => 4
[4,2,1,6,3,5] => [2,6,5,3,1,4] => [5,1,2,4,6,3] => 3
[4,2,1,6,5,3] => [2,5,6,3,1,4] => [5,2,1,4,6,3] => 4
[4,2,3,1,5,6] => [2,3,4,1,5,6] => [5,4,3,6,2,1] => 5
[4,2,3,1,6,5] => [2,3,4,1,6,5] => [5,4,3,6,1,2] => 4
[4,2,3,5,1,6] => [2,3,5,1,4,6] => [5,4,2,6,3,1] => 5
[4,2,3,5,6,1] => [2,3,6,1,4,5] => [5,4,1,6,3,2] => 5
[4,2,3,6,1,5] => [2,3,6,5,1,4] => [5,4,1,2,6,3] => 4
[4,2,3,6,5,1] => [2,3,5,6,1,4] => [5,4,2,1,6,3] => 5
[4,2,5,1,3,6] => [2,4,1,5,3,6] => [5,3,6,2,4,1] => 4
[4,2,5,1,6,3] => [2,4,1,6,3,5] => [5,3,6,1,4,2] => 4
[4,2,5,3,1,6] => [2,5,1,4,3,6] => [5,2,6,3,4,1] => 4
[4,2,5,3,6,1] => [2,6,1,4,3,5] => [5,1,6,3,4,2] => 4
[4,2,5,6,1,3] => [2,6,3,5,1,4] => [5,1,4,2,6,3] => 4
[4,2,5,6,3,1] => [2,5,3,6,1,4] => [5,2,4,1,6,3] => 4
[4,2,6,1,3,5] => [2,4,1,6,5,3] => [5,3,6,1,2,4] => 3
[4,2,6,1,5,3] => [2,4,1,5,6,3] => [5,3,6,2,1,4] => 4
[4,2,6,3,1,5] => [2,6,5,1,4,3] => [5,1,2,6,3,4] => 3
[4,2,6,3,5,1] => [2,5,6,1,4,3] => [5,2,1,6,3,4] => 4
[4,2,6,5,1,3] => [2,5,1,4,6,3] => [5,2,6,3,1,4] => 4
[4,2,6,5,3,1] => [2,6,1,4,5,3] => [5,1,6,3,2,4] => 4
[4,3,1,2,5,6] => [4,2,3,1,5,6] => [3,5,4,6,2,1] => 4
[4,3,1,2,6,5] => [4,2,3,1,6,5] => [3,5,4,6,1,2] => 3
[4,3,1,5,2,6] => [5,2,3,1,4,6] => [2,5,4,6,3,1] => 4
[4,3,1,5,6,2] => [6,2,3,1,4,5] => [1,5,4,6,3,2] => 4
[4,3,1,6,2,5] => [6,5,2,3,1,4] => [1,2,5,4,6,3] => 3
[4,3,1,6,5,2] => [5,6,2,3,1,4] => [2,1,5,4,6,3] => 4
[4,3,2,1,5,6] => [3,2,4,1,5,6] => [4,5,3,6,2,1] => 4
[4,3,2,1,6,5] => [3,2,4,1,6,5] => [4,5,3,6,1,2] => 3
[4,3,2,5,1,6] => [3,2,5,1,4,6] => [4,5,2,6,3,1] => 4
[4,3,2,5,6,1] => [3,2,6,1,4,5] => [4,5,1,6,3,2] => 4
[4,3,2,6,1,5] => [3,2,6,5,1,4] => [4,5,1,2,6,3] => 3
[4,3,2,6,5,1] => [3,2,5,6,1,4] => [4,5,2,1,6,3] => 4
[4,3,5,1,2,6] => [4,1,5,2,3,6] => [3,6,2,5,4,1] => 4
[4,3,5,1,6,2] => [4,1,6,2,3,5] => [3,6,1,5,4,2] => 4
[4,3,5,2,1,6] => [5,1,4,2,3,6] => [2,6,3,5,4,1] => 4
[4,3,5,2,6,1] => [6,1,4,2,3,5] => [1,6,3,5,4,2] => 4
[4,3,5,6,1,2] => [6,2,3,5,1,4] => [1,5,4,2,6,3] => 4
[4,3,5,6,2,1] => [5,2,3,6,1,4] => [2,5,4,1,6,3] => 4
[4,3,6,1,2,5] => [4,1,6,5,2,3] => [3,6,1,2,5,4] => 3
[4,3,6,1,5,2] => [4,1,5,6,2,3] => [3,6,2,1,5,4] => 4
[4,3,6,2,1,5] => [6,5,1,4,2,3] => [1,2,6,3,5,4] => 3
[4,3,6,2,5,1] => [5,6,1,4,2,3] => [2,1,6,3,5,4] => 4
[4,3,6,5,1,2] => [5,1,4,6,2,3] => [2,6,3,1,5,4] => 4
[4,3,6,5,2,1] => [6,1,4,5,2,3] => [1,6,3,2,5,4] => 4
[4,5,1,2,3,6] => [5,3,1,4,2,6] => [2,4,6,3,5,1] => 3
[4,5,1,2,6,3] => [6,3,1,4,2,5] => [1,4,6,3,5,2] => 3
[4,5,1,3,2,6] => [4,3,1,5,2,6] => [3,4,6,2,5,1] => 3
[4,5,1,3,6,2] => [4,3,1,6,2,5] => [3,4,6,1,5,2] => 3
[4,5,1,6,2,3] => [5,2,6,3,1,4] => [2,5,1,4,6,3] => 3
[4,5,1,6,3,2] => [6,2,5,3,1,4] => [1,5,2,4,6,3] => 3
[4,5,2,1,3,6] => [4,1,5,3,2,6] => [3,6,2,4,5,1] => 3
[4,5,2,1,6,3] => [4,1,6,3,2,5] => [3,6,1,4,5,2] => 3
[4,5,2,3,1,6] => [5,1,4,3,2,6] => [2,6,3,4,5,1] => 3
[4,5,2,3,6,1] => [6,1,4,3,2,5] => [1,6,3,4,5,2] => 3
[4,5,2,6,1,3] => [6,3,2,5,1,4] => [1,4,5,2,6,3] => 3
[4,5,2,6,3,1] => [5,3,2,6,1,4] => [2,4,5,1,6,3] => 3
[4,5,3,1,2,6] => [3,4,1,5,2,6] => [4,3,6,2,5,1] => 4
[4,5,3,1,6,2] => [3,4,1,6,2,5] => [4,3,6,1,5,2] => 4
[4,5,3,2,1,6] => [3,5,1,4,2,6] => [4,2,6,3,5,1] => 4
[4,5,3,2,6,1] => [3,6,1,4,2,5] => [4,1,6,3,5,2] => 4
[4,5,3,6,1,2] => [3,6,2,5,1,4] => [4,1,5,2,6,3] => 4
[4,5,3,6,2,1] => [3,5,2,6,1,4] => [4,2,5,1,6,3] => 4
[4,5,6,1,2,3] => [4,1,5,2,6,3] => [3,6,2,5,1,4] => 3
[4,5,6,1,3,2] => [4,1,6,2,5,3] => [3,6,1,5,2,4] => 3
[4,5,6,2,1,3] => [5,1,4,2,6,3] => [2,6,3,5,1,4] => 3
[4,5,6,2,3,1] => [6,1,4,2,5,3] => [1,6,3,5,2,4] => 3
[4,5,6,3,1,2] => [6,2,5,1,4,3] => [1,5,2,6,3,4] => 3
[4,5,6,3,2,1] => [5,2,6,1,4,3] => [2,5,1,6,3,4] => 3
[4,6,1,2,3,5] => [6,5,3,1,4,2] => [1,2,4,6,3,5] => 2
[4,6,1,2,5,3] => [5,6,3,1,4,2] => [2,1,4,6,3,5] => 3
[4,6,1,3,2,5] => [4,3,1,6,5,2] => [3,4,6,1,2,5] => 2
[4,6,1,3,5,2] => [4,3,1,5,6,2] => [3,4,6,2,1,5] => 3
[4,6,1,5,2,3] => [6,3,1,4,5,2] => [1,4,6,3,2,5] => 3
[4,6,1,5,3,2] => [5,3,1,4,6,2] => [2,4,6,3,1,5] => 3
[4,6,2,1,3,5] => [4,1,6,5,3,2] => [3,6,1,2,4,5] => 2
[4,6,2,1,5,3] => [4,1,5,6,3,2] => [3,6,2,1,4,5] => 3
[4,6,2,3,1,5] => [6,5,1,4,3,2] => [1,2,6,3,4,5] => 2
[4,6,2,3,5,1] => [5,6,1,4,3,2] => [2,1,6,3,4,5] => 3
[4,6,2,5,1,3] => [5,1,4,6,3,2] => [2,6,3,1,4,5] => 3
[4,6,2,5,3,1] => [6,1,4,5,3,2] => [1,6,3,2,4,5] => 3
[4,6,3,1,2,5] => [3,4,1,6,5,2] => [4,3,6,1,2,5] => 3
[4,6,3,1,5,2] => [3,4,1,5,6,2] => [4,3,6,2,1,5] => 4
[4,6,3,2,1,5] => [3,6,5,1,4,2] => [4,1,2,6,3,5] => 3
[4,6,3,2,5,1] => [3,5,6,1,4,2] => [4,2,1,6,3,5] => 4
[4,6,3,5,1,2] => [3,5,1,4,6,2] => [4,2,6,3,1,5] => 4
[4,6,3,5,2,1] => [3,6,1,4,5,2] => [4,1,6,3,2,5] => 4
[4,6,5,1,2,3] => [4,1,6,3,5,2] => [3,6,1,4,2,5] => 3
[4,6,5,1,3,2] => [4,1,5,3,6,2] => [3,6,2,4,1,5] => 3
[4,6,5,2,1,3] => [6,3,5,1,4,2] => [1,4,2,6,3,5] => 3
[4,6,5,2,3,1] => [5,3,6,1,4,2] => [2,4,1,6,3,5] => 3
[4,6,5,3,1,2] => [5,1,4,3,6,2] => [2,6,3,4,1,5] => 3
[4,6,5,3,2,1] => [6,1,4,3,5,2] => [1,6,3,4,2,5] => 3
[5,1,2,3,4,6] => [5,4,3,2,1,6] => [2,3,4,5,6,1] => 2
[5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,3,4,5,6,2] => 2
[5,1,2,4,3,6] => [4,5,3,2,1,6] => [3,2,4,5,6,1] => 3
[5,1,2,4,6,3] => [4,6,3,2,1,5] => [3,1,4,5,6,2] => 3
[5,1,2,6,3,4] => [5,3,2,1,6,4] => [2,4,5,6,1,3] => 2
[5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,4,5,6,2,3] => 2
[5,1,3,2,4,6] => [3,5,4,2,1,6] => [4,2,3,5,6,1] => 3
[5,1,3,2,6,4] => [3,6,4,2,1,5] => [4,1,3,5,6,2] => 3
[5,1,3,4,2,6] => [3,4,5,2,1,6] => [4,3,2,5,6,1] => 4
[5,1,3,4,6,2] => [3,4,6,2,1,5] => [4,3,1,5,6,2] => 4
[5,1,3,6,2,4] => [3,5,2,1,6,4] => [4,2,5,6,1,3] => 3
[5,1,3,6,4,2] => [3,6,2,1,5,4] => [4,1,5,6,2,3] => 3
[5,1,4,2,3,6] => [5,3,4,2,1,6] => [2,4,3,5,6,1] => 3
[5,1,4,2,6,3] => [6,3,4,2,1,5] => [1,4,3,5,6,2] => 3
[5,1,4,3,2,6] => [4,3,5,2,1,6] => [3,4,2,5,6,1] => 3
[5,1,4,3,6,2] => [4,3,6,2,1,5] => [3,4,1,5,6,2] => 3
[5,1,4,6,2,3] => [5,2,1,6,3,4] => [2,5,6,1,4,3] => 3
[5,1,4,6,3,2] => [6,2,1,5,3,4] => [1,5,6,2,4,3] => 3
[5,1,6,2,3,4] => [6,4,2,1,5,3] => [1,3,5,6,2,4] => 2
[5,1,6,2,4,3] => [5,4,2,1,6,3] => [2,3,5,6,1,4] => 2
[5,1,6,3,2,4] => [5,2,1,6,4,3] => [2,5,6,1,3,4] => 2
[5,1,6,3,4,2] => [6,2,1,5,4,3] => [1,5,6,2,3,4] => 2
[5,1,6,4,2,3] => [4,5,2,1,6,3] => [3,2,5,6,1,4] => 3
[5,1,6,4,3,2] => [4,6,2,1,5,3] => [3,1,5,6,2,4] => 3
[5,2,1,3,4,6] => [2,5,4,3,1,6] => [5,2,3,4,6,1] => 3
[5,2,1,3,6,4] => [2,6,4,3,1,5] => [5,1,3,4,6,2] => 3
[5,2,1,4,3,6] => [2,4,5,3,1,6] => [5,3,2,4,6,1] => 4
[5,2,1,4,6,3] => [2,4,6,3,1,5] => [5,3,1,4,6,2] => 4
[5,2,1,6,3,4] => [2,5,3,1,6,4] => [5,2,4,6,1,3] => 3
[5,2,1,6,4,3] => [2,6,3,1,5,4] => [5,1,4,6,2,3] => 3
[5,2,3,1,4,6] => [2,3,5,4,1,6] => [5,4,2,3,6,1] => 4
[5,2,3,1,6,4] => [2,3,6,4,1,5] => [5,4,1,3,6,2] => 4
[5,2,3,4,1,6] => [2,3,4,5,1,6] => [5,4,3,2,6,1] => 5
[5,2,3,4,6,1] => [2,3,4,6,1,5] => [5,4,3,1,6,2] => 5
[5,2,3,6,1,4] => [2,3,5,1,6,4] => [5,4,2,6,1,3] => 4
[5,2,3,6,4,1] => [2,3,6,1,5,4] => [5,4,1,6,2,3] => 4
[5,2,4,1,3,6] => [2,5,3,4,1,6] => [5,2,4,3,6,1] => 4
[5,2,4,1,6,3] => [2,6,3,4,1,5] => [5,1,4,3,6,2] => 4
[5,2,4,3,1,6] => [2,4,3,5,1,6] => [5,3,4,2,6,1] => 4
[5,2,4,3,6,1] => [2,4,3,6,1,5] => [5,3,4,1,6,2] => 4
[5,2,4,6,1,3] => [2,5,1,6,3,4] => [5,2,6,1,4,3] => 4
[5,2,4,6,3,1] => [2,6,1,5,3,4] => [5,1,6,2,4,3] => 4
[5,2,6,1,3,4] => [2,6,4,1,5,3] => [5,1,3,6,2,4] => 3
[5,2,6,1,4,3] => [2,5,4,1,6,3] => [5,2,3,6,1,4] => 3
[5,2,6,3,1,4] => [2,5,1,6,4,3] => [5,2,6,1,3,4] => 3
[5,2,6,3,4,1] => [2,6,1,5,4,3] => [5,1,6,2,3,4] => 3
[5,2,6,4,1,3] => [2,4,5,1,6,3] => [5,3,2,6,1,4] => 4
[5,2,6,4,3,1] => [2,4,6,1,5,3] => [5,3,1,6,2,4] => 4
[5,3,1,2,4,6] => [5,4,2,3,1,6] => [2,3,5,4,6,1] => 3
[5,3,1,2,6,4] => [6,4,2,3,1,5] => [1,3,5,4,6,2] => 3
[5,3,1,4,2,6] => [4,5,2,3,1,6] => [3,2,5,4,6,1] => 4
[5,3,1,4,6,2] => [4,6,2,3,1,5] => [3,1,5,4,6,2] => 4
[5,3,1,6,2,4] => [5,2,3,1,6,4] => [2,5,4,6,1,3] => 3
[5,3,1,6,4,2] => [6,2,3,1,5,4] => [1,5,4,6,2,3] => 3
[5,3,2,1,4,6] => [3,2,5,4,1,6] => [4,5,2,3,6,1] => 3
[5,3,2,1,6,4] => [3,2,6,4,1,5] => [4,5,1,3,6,2] => 3
[5,3,2,4,1,6] => [3,2,4,5,1,6] => [4,5,3,2,6,1] => 4
[5,3,2,4,6,1] => [3,2,4,6,1,5] => [4,5,3,1,6,2] => 4
[5,3,2,6,1,4] => [3,2,5,1,6,4] => [4,5,2,6,1,3] => 3
[5,3,2,6,4,1] => [3,2,6,1,5,4] => [4,5,1,6,2,3] => 3
[5,3,4,1,2,6] => [5,2,3,4,1,6] => [2,5,4,3,6,1] => 4
[5,3,4,1,6,2] => [6,2,3,4,1,5] => [1,5,4,3,6,2] => 4
[5,3,4,2,1,6] => [4,2,3,5,1,6] => [3,5,4,2,6,1] => 4
[5,3,4,2,6,1] => [4,2,3,6,1,5] => [3,5,4,1,6,2] => 4
[5,3,4,6,1,2] => [5,1,6,2,3,4] => [2,6,1,5,4,3] => 4
[5,3,4,6,2,1] => [6,1,5,2,3,4] => [1,6,2,5,4,3] => 4
[5,3,6,1,2,4] => [6,4,1,5,2,3] => [1,3,6,2,5,4] => 3
[5,3,6,1,4,2] => [5,4,1,6,2,3] => [2,3,6,1,5,4] => 3
[5,3,6,2,1,4] => [5,1,6,4,2,3] => [2,6,1,3,5,4] => 3
[5,3,6,2,4,1] => [6,1,5,4,2,3] => [1,6,2,3,5,4] => 3
[5,3,6,4,1,2] => [4,5,1,6,2,3] => [3,2,6,1,5,4] => 4
[5,3,6,4,2,1] => [4,6,1,5,2,3] => [3,1,6,2,5,4] => 4
[5,4,1,2,3,6] => [4,2,5,3,1,6] => [3,5,2,4,6,1] => 3
[5,4,1,2,6,3] => [4,2,6,3,1,5] => [3,5,1,4,6,2] => 3
[5,4,1,3,2,6] => [5,2,4,3,1,6] => [2,5,3,4,6,1] => 3
[5,4,1,3,6,2] => [6,2,4,3,1,5] => [1,5,3,4,6,2] => 3
[5,4,1,6,2,3] => [6,3,1,5,2,4] => [1,4,6,2,5,3] => 3
[5,4,1,6,3,2] => [5,3,1,6,2,4] => [2,4,6,1,5,3] => 3
[5,4,2,1,3,6] => [5,3,2,4,1,6] => [2,4,5,3,6,1] => 3
[5,4,2,1,6,3] => [6,3,2,4,1,5] => [1,4,5,3,6,2] => 3
[5,4,2,3,1,6] => [4,3,2,5,1,6] => [3,4,5,2,6,1] => 3
[5,4,2,3,6,1] => [4,3,2,6,1,5] => [3,4,5,1,6,2] => 3
[5,4,2,6,1,3] => [5,1,6,3,2,4] => [2,6,1,4,5,3] => 3
[5,4,2,6,3,1] => [6,1,5,3,2,4] => [1,6,2,4,5,3] => 3
[5,4,3,1,2,6] => [3,5,2,4,1,6] => [4,2,5,3,6,1] => 4
[5,4,3,1,6,2] => [3,6,2,4,1,5] => [4,1,5,3,6,2] => 4
[5,4,3,2,1,6] => [3,4,2,5,1,6] => [4,3,5,2,6,1] => 4
[5,4,3,2,6,1] => [3,4,2,6,1,5] => [4,3,5,1,6,2] => 4
[5,4,3,6,1,2] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => 4
[5,4,3,6,2,1] => [3,6,1,5,2,4] => [4,1,6,2,5,3] => 4
[5,4,6,1,2,3] => [5,2,4,1,6,3] => [2,5,3,6,1,4] => 3
[5,4,6,1,3,2] => [6,2,4,1,5,3] => [1,5,3,6,2,4] => 3
[5,4,6,2,1,3] => [4,2,5,1,6,3] => [3,5,2,6,1,4] => 3
[5,4,6,2,3,1] => [4,2,6,1,5,3] => [3,5,1,6,2,4] => 3
[5,4,6,3,1,2] => [5,1,6,2,4,3] => [2,6,1,5,3,4] => 3
[5,4,6,3,2,1] => [6,1,5,2,4,3] => [1,6,2,5,3,4] => 3
[5,6,1,2,3,4] => [5,3,1,6,4,2] => [2,4,6,1,3,5] => 2
[5,6,1,2,4,3] => [6,3,1,5,4,2] => [1,4,6,2,3,5] => 2
[5,6,1,3,2,4] => [6,4,3,1,5,2] => [1,3,4,6,2,5] => 2
[5,6,1,3,4,2] => [5,4,3,1,6,2] => [2,3,4,6,1,5] => 2
[5,6,1,4,2,3] => [4,6,3,1,5,2] => [3,1,4,6,2,5] => 3
[5,6,1,4,3,2] => [4,5,3,1,6,2] => [3,2,4,6,1,5] => 3
[5,6,2,1,3,4] => [6,4,1,5,3,2] => [1,3,6,2,4,5] => 2
[5,6,2,1,4,3] => [5,4,1,6,3,2] => [2,3,6,1,4,5] => 2
[5,6,2,3,1,4] => [5,1,6,4,3,2] => [2,6,1,3,4,5] => 2
[5,6,2,3,4,1] => [6,1,5,4,3,2] => [1,6,2,3,4,5] => 2
[5,6,2,4,1,3] => [4,5,1,6,3,2] => [3,2,6,1,4,5] => 3
[5,6,2,4,3,1] => [4,6,1,5,3,2] => [3,1,6,2,4,5] => 3
[5,6,3,1,2,4] => [3,6,4,1,5,2] => [4,1,3,6,2,5] => 3
[5,6,3,1,4,2] => [3,5,4,1,6,2] => [4,2,3,6,1,5] => 3
[5,6,3,2,1,4] => [3,5,1,6,4,2] => [4,2,6,1,3,5] => 3
[5,6,3,2,4,1] => [3,6,1,5,4,2] => [4,1,6,2,3,5] => 3
[5,6,3,4,1,2] => [3,4,5,1,6,2] => [4,3,2,6,1,5] => 4
[5,6,3,4,2,1] => [3,4,6,1,5,2] => [4,3,1,6,2,5] => 4
[5,6,4,1,2,3] => [6,3,4,1,5,2] => [1,4,3,6,2,5] => 3
[5,6,4,1,3,2] => [5,3,4,1,6,2] => [2,4,3,6,1,5] => 3
[5,6,4,2,1,3] => [5,1,6,3,4,2] => [2,6,1,4,3,5] => 3
[5,6,4,2,3,1] => [6,1,5,3,4,2] => [1,6,2,4,3,5] => 3
[5,6,4,3,1,2] => [4,3,5,1,6,2] => [3,4,2,6,1,5] => 3
[5,6,4,3,2,1] => [4,3,6,1,5,2] => [3,4,1,6,2,5] => 3
[6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 1
[6,1,2,3,5,4] => [5,6,4,3,2,1] => [2,1,3,4,5,6] => 2
[6,1,2,4,3,5] => [4,6,5,3,2,1] => [3,1,2,4,5,6] => 2
[6,1,2,4,5,3] => [4,5,6,3,2,1] => [3,2,1,4,5,6] => 3
[6,1,2,5,3,4] => [6,4,5,3,2,1] => [1,3,2,4,5,6] => 2
[6,1,2,5,4,3] => [5,4,6,3,2,1] => [2,3,1,4,5,6] => 2
[6,1,3,2,4,5] => [3,6,5,4,2,1] => [4,1,2,3,5,6] => 2
[6,1,3,2,5,4] => [3,5,6,4,2,1] => [4,2,1,3,5,6] => 3
[6,1,3,4,2,5] => [3,4,6,5,2,1] => [4,3,1,2,5,6] => 3
[6,1,3,4,5,2] => [3,4,5,6,2,1] => [4,3,2,1,5,6] => 4
[6,1,3,5,2,4] => [3,6,4,5,2,1] => [4,1,3,2,5,6] => 3
[6,1,3,5,4,2] => [3,5,4,6,2,1] => [4,2,3,1,5,6] => 3
[6,1,4,2,3,5] => [6,5,3,4,2,1] => [1,2,4,3,5,6] => 2
[6,1,4,2,5,3] => [5,6,3,4,2,1] => [2,1,4,3,5,6] => 3
[6,1,4,3,2,5] => [4,3,6,5,2,1] => [3,4,1,2,5,6] => 2
[6,1,4,3,5,2] => [4,3,5,6,2,1] => [3,4,2,1,5,6] => 3
[6,1,4,5,2,3] => [6,3,4,5,2,1] => [1,4,3,2,5,6] => 3
[6,1,4,5,3,2] => [5,3,4,6,2,1] => [2,4,3,1,5,6] => 3
[6,1,5,2,3,4] => [5,3,6,4,2,1] => [2,4,1,3,5,6] => 2
[6,1,5,2,4,3] => [6,3,5,4,2,1] => [1,4,2,3,5,6] => 2
[6,1,5,3,2,4] => [6,4,3,5,2,1] => [1,3,4,2,5,6] => 2
[6,1,5,3,4,2] => [5,4,3,6,2,1] => [2,3,4,1,5,6] => 2
[6,1,5,4,2,3] => [4,6,3,5,2,1] => [3,1,4,2,5,6] => 3
[6,1,5,4,3,2] => [4,5,3,6,2,1] => [3,2,4,1,5,6] => 3
[6,2,1,3,4,5] => [2,6,5,4,3,1] => [5,1,2,3,4,6] => 2
[6,2,1,3,5,4] => [2,5,6,4,3,1] => [5,2,1,3,4,6] => 3
[6,2,1,4,3,5] => [2,4,6,5,3,1] => [5,3,1,2,4,6] => 3
[6,2,1,4,5,3] => [2,4,5,6,3,1] => [5,3,2,1,4,6] => 4
[6,2,1,5,3,4] => [2,6,4,5,3,1] => [5,1,3,2,4,6] => 3
[6,2,1,5,4,3] => [2,5,4,6,3,1] => [5,2,3,1,4,6] => 3
[6,2,3,1,4,5] => [2,3,6,5,4,1] => [5,4,1,2,3,6] => 3
[6,2,3,1,5,4] => [2,3,5,6,4,1] => [5,4,2,1,3,6] => 4
[6,2,3,4,1,5] => [2,3,4,6,5,1] => [5,4,3,1,2,6] => 4
[6,2,3,4,5,1] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => 5
[6,2,3,5,1,4] => [2,3,6,4,5,1] => [5,4,1,3,2,6] => 4
[6,2,3,5,4,1] => [2,3,5,4,6,1] => [5,4,2,3,1,6] => 4
[6,2,4,1,3,5] => [2,6,5,3,4,1] => [5,1,2,4,3,6] => 3
[6,2,4,1,5,3] => [2,5,6,3,4,1] => [5,2,1,4,3,6] => 4
[6,2,4,3,1,5] => [2,4,3,6,5,1] => [5,3,4,1,2,6] => 3
[6,2,4,3,5,1] => [2,4,3,5,6,1] => [5,3,4,2,1,6] => 4
[6,2,4,5,1,3] => [2,6,3,4,5,1] => [5,1,4,3,2,6] => 4
[6,2,4,5,3,1] => [2,5,3,4,6,1] => [5,2,4,3,1,6] => 4
[6,2,5,1,3,4] => [2,5,3,6,4,1] => [5,2,4,1,3,6] => 3
[6,2,5,1,4,3] => [2,6,3,5,4,1] => [5,1,4,2,3,6] => 3
[6,2,5,3,1,4] => [2,6,4,3,5,1] => [5,1,3,4,2,6] => 3
[6,2,5,3,4,1] => [2,5,4,3,6,1] => [5,2,3,4,1,6] => 3
[6,2,5,4,1,3] => [2,4,6,3,5,1] => [5,3,1,4,2,6] => 4
[6,2,5,4,3,1] => [2,4,5,3,6,1] => [5,3,2,4,1,6] => 4
[6,3,1,2,4,5] => [6,5,4,2,3,1] => [1,2,3,5,4,6] => 2
[6,3,1,2,5,4] => [5,6,4,2,3,1] => [2,1,3,5,4,6] => 3
[6,3,1,4,2,5] => [4,6,5,2,3,1] => [3,1,2,5,4,6] => 3
[6,3,1,4,5,2] => [4,5,6,2,3,1] => [3,2,1,5,4,6] => 4
[6,3,1,5,2,4] => [6,4,5,2,3,1] => [1,3,2,5,4,6] => 3
[6,3,1,5,4,2] => [5,4,6,2,3,1] => [2,3,1,5,4,6] => 3
[6,3,2,1,4,5] => [3,2,6,5,4,1] => [4,5,1,2,3,6] => 2
[6,3,2,1,5,4] => [3,2,5,6,4,1] => [4,5,2,1,3,6] => 3
[6,3,2,4,1,5] => [3,2,4,6,5,1] => [4,5,3,1,2,6] => 3
[6,3,2,4,5,1] => [3,2,4,5,6,1] => [4,5,3,2,1,6] => 4
[6,3,2,5,1,4] => [3,2,6,4,5,1] => [4,5,1,3,2,6] => 3
[6,3,2,5,4,1] => [3,2,5,4,6,1] => [4,5,2,3,1,6] => 3
[6,3,4,1,2,5] => [6,5,2,3,4,1] => [1,2,5,4,3,6] => 3
[6,3,4,1,5,2] => [5,6,2,3,4,1] => [2,1,5,4,3,6] => 4
[6,3,4,2,1,5] => [4,2,3,6,5,1] => [3,5,4,1,2,6] => 3
[6,3,4,2,5,1] => [4,2,3,5,6,1] => [3,5,4,2,1,6] => 4
[6,3,4,5,1,2] => [6,2,3,4,5,1] => [1,5,4,3,2,6] => 4
[6,3,4,5,2,1] => [5,2,3,4,6,1] => [2,5,4,3,1,6] => 4
[6,3,5,1,2,4] => [5,2,3,6,4,1] => [2,5,4,1,3,6] => 3
[6,3,5,1,4,2] => [6,2,3,5,4,1] => [1,5,4,2,3,6] => 3
[6,3,5,2,1,4] => [6,4,2,3,5,1] => [1,3,5,4,2,6] => 3
[6,3,5,2,4,1] => [5,4,2,3,6,1] => [2,3,5,4,1,6] => 3
[6,3,5,4,1,2] => [4,6,2,3,5,1] => [3,1,5,4,2,6] => 4
[6,3,5,4,2,1] => [4,5,2,3,6,1] => [3,2,5,4,1,6] => 4
[6,4,1,2,3,5] => [4,2,6,5,3,1] => [3,5,1,2,4,6] => 2
[6,4,1,2,5,3] => [4,2,5,6,3,1] => [3,5,2,1,4,6] => 3
[6,4,1,3,2,5] => [6,5,2,4,3,1] => [1,2,5,3,4,6] => 2
[6,4,1,3,5,2] => [5,6,2,4,3,1] => [2,1,5,3,4,6] => 3
[6,4,1,5,2,3] => [5,2,4,6,3,1] => [2,5,3,1,4,6] => 3
[6,4,1,5,3,2] => [6,2,4,5,3,1] => [1,5,3,2,4,6] => 3
[6,4,2,1,3,5] => [6,5,3,2,4,1] => [1,2,4,5,3,6] => 2
[6,4,2,1,5,3] => [5,6,3,2,4,1] => [2,1,4,5,3,6] => 3
[6,4,2,3,1,5] => [4,3,2,6,5,1] => [3,4,5,1,2,6] => 2
[6,4,2,3,5,1] => [4,3,2,5,6,1] => [3,4,5,2,1,6] => 3
[6,4,2,5,1,3] => [6,3,2,4,5,1] => [1,4,5,3,2,6] => 3
[6,4,2,5,3,1] => [5,3,2,4,6,1] => [2,4,5,3,1,6] => 3
[6,4,3,1,2,5] => [3,6,5,2,4,1] => [4,1,2,5,3,6] => 3
[6,4,3,1,5,2] => [3,5,6,2,4,1] => [4,2,1,5,3,6] => 4
[6,4,3,2,1,5] => [3,4,2,6,5,1] => [4,3,5,1,2,6] => 3
[6,4,3,2,5,1] => [3,4,2,5,6,1] => [4,3,5,2,1,6] => 4
[6,4,3,5,1,2] => [3,6,2,4,5,1] => [4,1,5,3,2,6] => 4
[6,4,3,5,2,1] => [3,5,2,4,6,1] => [4,2,5,3,1,6] => 4
[6,4,5,1,2,3] => [6,3,5,2,4,1] => [1,4,2,5,3,6] => 3
[6,4,5,1,3,2] => [5,3,6,2,4,1] => [2,4,1,5,3,6] => 3
[6,4,5,2,1,3] => [4,2,6,3,5,1] => [3,5,1,4,2,6] => 3
[6,4,5,2,3,1] => [4,2,5,3,6,1] => [3,5,2,4,1,6] => 3
[6,4,5,3,1,2] => [6,2,4,3,5,1] => [1,5,3,4,2,6] => 3
[6,4,5,3,2,1] => [5,2,4,3,6,1] => [2,5,3,4,1,6] => 3
[6,5,1,2,3,4] => [6,4,2,5,3,1] => [1,3,5,2,4,6] => 2
[6,5,1,2,4,3] => [5,4,2,6,3,1] => [2,3,5,1,4,6] => 2
[6,5,1,3,2,4] => [5,2,6,4,3,1] => [2,5,1,3,4,6] => 2
[6,5,1,3,4,2] => [6,2,5,4,3,1] => [1,5,2,3,4,6] => 2
[6,5,1,4,2,3] => [4,5,2,6,3,1] => [3,2,5,1,4,6] => 3
[6,5,1,4,3,2] => [4,6,2,5,3,1] => [3,1,5,2,4,6] => 3
[6,5,2,1,3,4] => [5,3,2,6,4,1] => [2,4,5,1,3,6] => 2
[6,5,2,1,4,3] => [6,3,2,5,4,1] => [1,4,5,2,3,6] => 2
[6,5,2,3,1,4] => [6,4,3,2,5,1] => [1,3,4,5,2,6] => 2
[6,5,2,3,4,1] => [5,4,3,2,6,1] => [2,3,4,5,1,6] => 2
[6,5,2,4,1,3] => [4,6,3,2,5,1] => [3,1,4,5,2,6] => 3
[6,5,2,4,3,1] => [4,5,3,2,6,1] => [3,2,4,5,1,6] => 3
[6,5,3,1,2,4] => [3,5,2,6,4,1] => [4,2,5,1,3,6] => 3
[6,5,3,1,4,2] => [3,6,2,5,4,1] => [4,1,5,2,3,6] => 3
[6,5,3,2,1,4] => [3,6,4,2,5,1] => [4,1,3,5,2,6] => 3
[6,5,3,2,4,1] => [3,5,4,2,6,1] => [4,2,3,5,1,6] => 3
[6,5,3,4,1,2] => [3,4,6,2,5,1] => [4,3,1,5,2,6] => 4
[6,5,3,4,2,1] => [3,4,5,2,6,1] => [4,3,2,5,1,6] => 4
[6,5,4,1,2,3] => [5,2,6,3,4,1] => [2,5,1,4,3,6] => 3
[6,5,4,1,3,2] => [6,2,5,3,4,1] => [1,5,2,4,3,6] => 3
[6,5,4,2,1,3] => [6,3,4,2,5,1] => [1,4,3,5,2,6] => 3
[6,5,4,2,3,1] => [5,3,4,2,6,1] => [2,4,3,5,1,6] => 3
[6,5,4,3,1,2] => [4,3,6,2,5,1] => [3,4,1,5,2,6] => 3
[6,5,4,3,2,1] => [4,3,5,2,6,1] => [3,4,2,5,1,6] => 3
[2,3,4,5,7,1,6] => [7,6,1,2,3,4,5] => [1,2,7,6,5,4,3] => 5
[2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => [1,3,7,6,5,4,2] => 5
[2,3,4,7,1,5,6] => [7,6,5,1,2,3,4] => [1,2,3,7,6,5,4] => 4
[2,3,4,7,6,1,5] => [7,5,6,1,2,3,4] => [1,3,2,7,6,5,4] => 5
[2,3,5,1,7,4,6] => [7,6,4,1,2,3,5] => [1,2,4,7,6,5,3] => 4
[2,3,5,6,7,1,4] => [7,4,6,1,2,3,5] => [1,4,2,7,6,5,3] => 5
[2,3,5,7,4,1,6] => [7,6,1,2,3,5,4] => [1,2,7,6,5,3,4] => 4
[2,3,6,1,4,7,5] => [7,5,4,1,2,3,6] => [1,3,4,7,6,5,2] => 4
[2,3,6,5,1,7,4] => [7,4,5,1,2,3,6] => [1,4,3,7,6,5,2] => 5
[2,3,6,7,1,4,5] => [7,5,1,2,3,6,4] => [1,3,7,6,5,2,4] => 4
[2,3,7,1,4,5,6] => [7,6,5,4,1,2,3] => [1,2,3,4,7,6,5] => 3
[2,3,7,1,6,4,5] => [7,5,6,4,1,2,3] => [1,3,2,4,7,6,5] => 4
[2,3,7,5,1,4,6] => [7,6,4,5,1,2,3] => [1,2,4,3,7,6,5] => 4
[2,3,7,5,6,1,4] => [7,4,5,6,1,2,3] => [1,4,3,2,7,6,5] => 5
[2,3,7,6,1,5,4] => [7,4,6,5,1,2,3] => [1,4,2,3,7,6,5] => 4
[2,3,7,6,4,1,5] => [7,5,4,6,1,2,3] => [1,3,4,2,7,6,5] => 4
[2,4,1,5,7,3,6] => [7,6,3,1,2,4,5] => [1,2,5,7,6,4,3] => 4
[2,4,1,6,3,7,5] => [7,5,3,1,2,4,6] => [1,3,5,7,6,4,2] => 4
[2,4,1,7,3,5,6] => [7,6,5,3,1,2,4] => [1,2,3,5,7,6,4] => 3
[2,4,1,7,6,3,5] => [7,5,6,3,1,2,4] => [1,3,2,5,7,6,4] => 4
[2,4,5,3,7,1,6] => [7,6,1,2,4,3,5] => [1,2,7,6,4,5,3] => 4
[2,4,5,7,1,3,6] => [7,6,3,5,1,2,4] => [1,2,5,3,7,6,4] => 4
[2,4,6,3,1,7,5] => [7,5,1,2,4,3,6] => [1,3,7,6,4,5,2] => 4
[2,4,6,7,3,1,5] => [7,5,3,6,1,2,4] => [1,3,5,2,7,6,4] => 4
[2,4,7,3,1,5,6] => [7,6,5,1,2,4,3] => [1,2,3,7,6,4,5] => 3
[2,4,7,3,6,1,5] => [7,5,6,1,2,4,3] => [1,3,2,7,6,4,5] => 4
[2,4,7,5,3,1,6] => [7,6,1,2,4,5,3] => [1,2,7,6,4,3,5] => 4
[2,4,7,6,1,3,5] => [7,5,1,2,4,6,3] => [1,3,7,6,4,2,5] => 4
[2,5,1,3,6,7,4] => [7,4,3,1,2,5,6] => [1,4,5,7,6,3,2] => 4
[2,5,1,3,7,4,6] => [7,6,4,3,1,2,5] => [1,2,4,5,7,6,3] => 3
[2,5,1,6,7,3,4] => [7,4,6,3,1,2,5] => [1,4,2,5,7,6,3] => 4
[2,5,1,7,4,3,6] => [7,6,3,1,2,5,4] => [1,2,5,7,6,3,4] => 3
[2,5,4,1,7,3,6] => [7,6,3,4,1,2,5] => [1,2,5,4,7,6,3] => 4
[2,5,4,7,3,1,6] => [7,6,1,2,5,3,4] => [1,2,7,6,3,5,4] => 4
[2,5,6,3,7,1,4] => [7,4,3,6,1,2,5] => [1,4,5,2,7,6,3] => 4
[2,5,7,1,3,4,6] => [7,6,4,1,2,5,3] => [1,2,4,7,6,3,5] => 3
[2,5,7,3,4,1,6] => [7,6,1,2,5,4,3] => [1,2,7,6,3,4,5] => 3
[2,5,7,6,3,1,4] => [7,4,6,1,2,5,3] => [1,4,2,7,6,3,5] => 4
[2,6,1,3,4,7,5] => [7,5,4,3,1,2,6] => [1,3,4,5,7,6,2] => 3
[2,6,1,3,7,5,4] => [7,4,3,1,2,6,5] => [1,4,5,7,6,2,3] => 3
[2,6,1,5,3,7,4] => [7,4,5,3,1,2,6] => [1,4,3,5,7,6,2] => 4
[2,6,1,7,3,4,5] => [7,5,3,1,2,6,4] => [1,3,5,7,6,2,4] => 3
[2,6,4,1,3,7,5] => [7,5,3,4,1,2,6] => [1,3,5,4,7,6,2] => 4
[2,6,4,7,1,3,5] => [7,5,1,2,6,3,4] => [1,3,7,6,2,5,4] => 4
[2,6,5,3,1,7,4] => [7,4,3,5,1,2,6] => [1,4,5,3,7,6,2] => 4
[2,6,7,1,4,3,5] => [7,5,4,1,2,6,3] => [1,3,4,7,6,2,5] => 3
[2,6,7,3,1,4,5] => [7,5,1,2,6,4,3] => [1,3,7,6,2,4,5] => 3
[2,6,7,5,1,3,4] => [7,4,5,1,2,6,3] => [1,4,3,7,6,2,5] => 4
[2,7,1,3,4,5,6] => [7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => 2
[2,7,1,3,6,4,5] => [7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => 3
[2,7,1,5,3,4,6] => [7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => 3
[2,7,1,5,6,3,4] => [7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => 4
[2,7,1,6,3,5,4] => [7,4,6,5,3,1,2] => [1,4,2,3,5,7,6] => 3
[2,7,1,6,4,3,5] => [7,5,4,6,3,1,2] => [1,3,4,2,5,7,6] => 3
[2,7,4,1,3,5,6] => [7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => 3
[2,7,4,1,6,3,5] => [7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => 4
[2,7,4,5,1,3,6] => [7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => 4
[2,7,4,6,3,1,5] => [7,5,3,4,6,1,2] => [1,3,5,4,2,7,6] => 4
[2,7,5,1,4,3,6] => [7,6,3,5,4,1,2] => [1,2,5,3,4,7,6] => 3
[2,7,5,3,1,4,6] => [7,6,4,3,5,1,2] => [1,2,4,5,3,7,6] => 3
[2,7,5,3,6,1,4] => [7,4,3,5,6,1,2] => [1,4,5,3,2,7,6] => 4
[2,7,5,6,1,3,4] => [7,4,6,3,5,1,2] => [1,4,2,5,3,7,6] => 4
[2,7,6,1,3,4,5] => [7,5,3,6,4,1,2] => [1,3,5,2,4,7,6] => 3
[2,7,6,3,1,5,4] => [7,4,3,6,5,1,2] => [1,4,5,2,3,7,6] => 3
[2,7,6,3,4,1,5] => [7,5,4,3,6,1,2] => [1,3,4,5,2,7,6] => 3
[2,7,6,5,3,1,4] => [7,4,5,3,6,1,2] => [1,4,3,5,2,7,6] => 4
[3,1,4,5,7,2,6] => [7,6,2,1,3,4,5] => [1,2,6,7,5,4,3] => 4
[3,1,4,6,2,7,5] => [7,5,2,1,3,4,6] => [1,3,6,7,5,4,2] => 4
[3,1,4,7,2,5,6] => [7,6,5,2,1,3,4] => [1,2,3,6,7,5,4] => 3
[3,1,4,7,6,2,5] => [7,5,6,2,1,3,4] => [1,3,2,6,7,5,4] => 4
[3,1,5,2,7,4,6] => [7,6,4,2,1,3,5] => [1,2,4,6,7,5,3] => 3
[3,1,5,6,7,2,4] => [7,4,6,2,1,3,5] => [1,4,2,6,7,5,3] => 4
[3,1,5,7,4,2,6] => [7,6,2,1,3,5,4] => [1,2,6,7,5,3,4] => 3
[3,1,6,2,4,7,5] => [7,5,4,2,1,3,6] => [1,3,4,6,7,5,2] => 3
[3,1,6,5,2,7,4] => [7,4,5,2,1,3,6] => [1,4,3,6,7,5,2] => 4
[3,1,6,7,2,4,5] => [7,5,2,1,3,6,4] => [1,3,6,7,5,2,4] => 3
[3,1,7,2,4,5,6] => [7,6,5,4,2,1,3] => [1,2,3,4,6,7,5] => 2
[3,1,7,2,6,4,5] => [7,5,6,4,2,1,3] => [1,3,2,4,6,7,5] => 3
[3,1,7,5,2,4,6] => [7,6,4,5,2,1,3] => [1,2,4,3,6,7,5] => 3
[3,1,7,5,6,2,4] => [7,4,5,6,2,1,3] => [1,4,3,2,6,7,5] => 4
[3,1,7,6,2,5,4] => [7,4,6,5,2,1,3] => [1,4,2,3,6,7,5] => 3
[3,1,7,6,4,2,5] => [7,5,4,6,2,1,3] => [1,3,4,2,6,7,5] => 3
[3,4,2,5,7,1,6] => [7,6,1,3,2,4,5] => [1,2,7,5,6,4,3] => 4
[3,4,2,6,1,7,5] => [7,5,1,3,2,4,6] => [1,3,7,5,6,4,2] => 4
[3,4,2,7,1,5,6] => [7,6,5,1,3,2,4] => [1,2,3,7,5,6,4] => 3
[3,4,2,7,6,1,5] => [7,5,6,1,3,2,4] => [1,3,2,7,5,6,4] => 4
[3,4,5,1,7,2,6] => [7,6,2,4,1,3,5] => [1,2,6,4,7,5,3] => 4
[3,4,5,7,2,1,6] => [7,6,1,3,5,2,4] => [1,2,7,5,3,6,4] => 4
[3,4,6,1,2,7,5] => [7,5,2,4,1,3,6] => [1,3,6,4,7,5,2] => 4
[3,4,6,7,1,2,5] => [7,5,1,3,6,2,4] => [1,3,7,5,2,6,4] => 4
[3,4,7,1,2,5,6] => [7,6,5,2,4,1,3] => [1,2,3,6,4,7,5] => 3
[3,4,7,1,6,2,5] => [7,5,6,2,4,1,3] => [1,3,2,6,4,7,5] => 4
[3,4,7,5,1,2,6] => [7,6,2,4,5,1,3] => [1,2,6,4,3,7,5] => 4
[3,4,7,6,2,1,5] => [7,5,2,4,6,1,3] => [1,3,6,4,2,7,5] => 4
[3,5,2,1,7,4,6] => [7,6,4,1,3,2,5] => [1,2,4,7,5,6,3] => 3
[3,5,2,6,7,1,4] => [7,4,6,1,3,2,5] => [1,4,2,7,5,6,3] => 4
[3,5,2,7,4,1,6] => [7,6,1,3,2,5,4] => [1,2,7,5,6,3,4] => 3
[3,5,4,2,7,1,6] => [7,6,1,3,4,2,5] => [1,2,7,5,4,6,3] => 4
[3,5,4,7,1,2,6] => [7,6,2,5,1,3,4] => [1,2,6,3,7,5,4] => 4
[3,5,6,2,1,7,4] => [7,4,2,5,1,3,6] => [1,4,6,3,7,5,2] => 4
[3,5,7,1,4,2,6] => [7,6,2,5,4,1,3] => [1,2,6,3,4,7,5] => 3
[3,5,7,2,1,4,6] => [7,6,4,2,5,1,3] => [1,2,4,6,3,7,5] => 3
[3,5,7,2,6,1,4] => [7,4,2,5,6,1,3] => [1,4,6,3,2,7,5] => 4
[3,5,7,6,1,2,4] => [7,4,6,2,5,1,3] => [1,4,2,6,3,7,5] => 4
[3,6,2,1,4,7,5] => [7,5,4,1,3,2,6] => [1,3,4,7,5,6,2] => 3
[3,6,2,5,1,7,4] => [7,4,5,1,3,2,6] => [1,4,3,7,5,6,2] => 4
[3,6,2,7,1,4,5] => [7,5,1,3,2,6,4] => [1,3,7,5,6,2,4] => 3
[3,6,4,2,1,7,5] => [7,5,1,3,4,2,6] => [1,3,7,5,4,6,2] => 4
[3,6,4,7,2,1,5] => [7,5,2,6,1,3,4] => [1,3,6,2,7,5,4] => 4
[3,6,5,2,7,1,4] => [7,4,2,6,1,3,5] => [1,4,6,2,7,5,3] => 4
[3,6,7,1,2,4,5] => [7,5,2,6,4,1,3] => [1,3,6,2,4,7,5] => 3
[3,6,7,2,1,5,4] => [7,4,2,6,5,1,3] => [1,4,6,2,3,7,5] => 3
[3,6,7,2,4,1,5] => [7,5,4,2,6,1,3] => [1,3,4,6,2,7,5] => 3
[3,6,7,5,2,1,4] => [7,4,5,2,6,1,3] => [1,4,3,6,2,7,5] => 4
[3,7,2,1,4,5,6] => [7,6,5,4,1,3,2] => [1,2,3,4,7,5,6] => 2
[3,7,2,1,6,4,5] => [7,5,6,4,1,3,2] => [1,3,2,4,7,5,6] => 3
[3,7,2,5,1,4,6] => [7,6,4,5,1,3,2] => [1,2,4,3,7,5,6] => 3
[3,7,2,5,6,1,4] => [7,4,5,6,1,3,2] => [1,4,3,2,7,5,6] => 4
[3,7,2,6,1,5,4] => [7,4,6,5,1,3,2] => [1,4,2,3,7,5,6] => 3
[3,7,2,6,4,1,5] => [7,5,4,6,1,3,2] => [1,3,4,2,7,5,6] => 3
[3,7,4,2,1,5,6] => [7,6,5,1,3,4,2] => [1,2,3,7,5,4,6] => 3
[3,7,4,2,6,1,5] => [7,5,6,1,3,4,2] => [1,3,2,7,5,4,6] => 4
[3,7,4,5,2,1,6] => [7,6,1,3,4,5,2] => [1,2,7,5,4,3,6] => 4
[3,7,4,6,1,2,5] => [7,5,1,3,4,6,2] => [1,3,7,5,4,2,6] => 4
[3,7,5,1,2,4,6] => [7,6,4,1,3,5,2] => [1,2,4,7,5,3,6] => 3
[3,7,5,2,4,1,6] => [7,6,1,3,5,4,2] => [1,2,7,5,3,4,6] => 3
[3,7,5,6,2,1,4] => [7,4,6,1,3,5,2] => [1,4,2,7,5,3,6] => 4
[3,7,6,1,4,2,5] => [7,5,4,1,3,6,2] => [1,3,4,7,5,2,6] => 3
[3,7,6,2,1,4,5] => [7,5,1,3,6,4,2] => [1,3,7,5,2,4,6] => 3
[3,7,6,5,1,2,4] => [7,4,5,1,3,6,2] => [1,4,3,7,5,2,6] => 4
[4,1,2,5,7,3,6] => [7,6,3,2,1,4,5] => [1,2,5,6,7,4,3] => 3
[4,1,2,6,3,7,5] => [7,5,3,2,1,4,6] => [1,3,5,6,7,4,2] => 3
[4,1,2,7,3,5,6] => [7,6,5,3,2,1,4] => [1,2,3,5,6,7,4] => 2
[4,1,2,7,6,3,5] => [7,5,6,3,2,1,4] => [1,3,2,5,6,7,4] => 3
[4,1,5,3,7,2,6] => [7,6,2,1,4,3,5] => [1,2,6,7,4,5,3] => 3
[4,1,5,7,2,3,6] => [7,6,3,5,2,1,4] => [1,2,5,3,6,7,4] => 3
[4,1,6,3,2,7,5] => [7,5,2,1,4,3,6] => [1,3,6,7,4,5,2] => 3
[4,1,6,7,3,2,5] => [7,5,3,6,2,1,4] => [1,3,5,2,6,7,4] => 3
[4,1,7,3,2,5,6] => [7,6,5,2,1,4,3] => [1,2,3,6,7,4,5] => 2
[4,1,7,3,6,2,5] => [7,5,6,2,1,4,3] => [1,3,2,6,7,4,5] => 3
[4,1,7,5,3,2,6] => [7,6,2,1,4,5,3] => [1,2,6,7,4,3,5] => 3
[4,1,7,6,2,3,5] => [7,5,2,1,4,6,3] => [1,3,6,7,4,2,5] => 3
[4,3,1,5,7,2,6] => [7,6,2,3,1,4,5] => [1,2,6,5,7,4,3] => 4
[4,3,1,6,2,7,5] => [7,5,2,3,1,4,6] => [1,3,6,5,7,4,2] => 4
[4,3,1,7,2,5,6] => [7,6,5,2,3,1,4] => [1,2,3,6,5,7,4] => 3
[4,3,1,7,6,2,5] => [7,5,6,2,3,1,4] => [1,3,2,6,5,7,4] => 4
[4,3,5,2,7,1,6] => [7,6,1,4,2,3,5] => [1,2,7,4,6,5,3] => 4
[4,3,5,7,1,2,6] => [7,6,2,3,5,1,4] => [1,2,6,5,3,7,4] => 4
[4,3,6,2,1,7,5] => [7,5,1,4,2,3,6] => [1,3,7,4,6,5,2] => 4
[4,3,6,7,2,1,5] => [7,5,2,3,6,1,4] => [1,3,6,5,2,7,4] => 4
[4,3,7,2,1,5,6] => [7,6,5,1,4,2,3] => [1,2,3,7,4,6,5] => 3
[4,3,7,2,6,1,5] => [7,5,6,1,4,2,3] => [1,3,2,7,4,6,5] => 4
[4,3,7,5,2,1,6] => [7,6,1,4,5,2,3] => [1,2,7,4,3,6,5] => 4
[4,3,7,6,1,2,5] => [7,5,1,4,6,2,3] => [1,3,7,4,2,6,5] => 4
[4,5,1,2,7,3,6] => [7,6,3,1,4,2,5] => [1,2,5,7,4,6,3] => 3
[4,5,1,7,3,2,6] => [7,6,2,5,3,1,4] => [1,2,6,3,5,7,4] => 3
[4,5,2,3,7,1,6] => [7,6,1,4,3,2,5] => [1,2,7,4,5,6,3] => 3
[4,5,2,7,1,3,6] => [7,6,3,2,5,1,4] => [1,2,5,6,3,7,4] => 3
[4,5,7,2,3,1,6] => [7,6,1,4,2,5,3] => [1,2,7,4,6,3,5] => 3
[4,5,7,3,1,2,6] => [7,6,2,5,1,4,3] => [1,2,6,3,7,4,5] => 3
[4,6,1,2,3,7,5] => [7,5,3,1,4,2,6] => [1,3,5,7,4,6,2] => 3
[4,6,1,7,2,3,5] => [7,5,2,6,3,1,4] => [1,3,6,2,5,7,4] => 3
[4,6,2,3,1,7,5] => [7,5,1,4,3,2,6] => [1,3,7,4,5,6,2] => 3
[4,6,2,7,3,1,5] => [7,5,3,2,6,1,4] => [1,3,5,6,2,7,4] => 3
[4,6,7,2,1,3,5] => [7,5,1,4,2,6,3] => [1,3,7,4,6,2,5] => 3
[4,6,7,3,2,1,5] => [7,5,2,6,1,4,3] => [1,3,6,2,7,4,5] => 3
[4,7,1,2,3,5,6] => [7,6,5,3,1,4,2] => [1,2,3,5,7,4,6] => 2
[4,7,1,2,6,3,5] => [7,5,6,3,1,4,2] => [1,3,2,5,7,4,6] => 3
[4,7,1,5,2,3,6] => [7,6,3,1,4,5,2] => [1,2,5,7,4,3,6] => 3
[4,7,1,6,3,2,5] => [7,5,3,1,4,6,2] => [1,3,5,7,4,2,6] => 3
[4,7,2,3,1,5,6] => [7,6,5,1,4,3,2] => [1,2,3,7,4,5,6] => 2
[4,7,2,3,6,1,5] => [7,5,6,1,4,3,2] => [1,3,2,7,4,5,6] => 3
[4,7,2,5,3,1,6] => [7,6,1,4,5,3,2] => [1,2,7,4,3,5,6] => 3
[4,7,2,6,1,3,5] => [7,5,1,4,6,3,2] => [1,3,7,4,2,5,6] => 3
[4,7,5,2,1,3,6] => [7,6,3,5,1,4,2] => [1,2,5,3,7,4,6] => 3
[4,7,5,3,2,1,6] => [7,6,1,4,3,5,2] => [1,2,7,4,5,3,6] => 3
[4,7,6,2,3,1,5] => [7,5,3,6,1,4,2] => [1,3,5,2,7,4,6] => 3
[4,7,6,3,1,2,5] => [7,5,1,4,3,6,2] => [1,3,7,4,5,2,6] => 3
[5,1,2,3,6,7,4] => [7,4,3,2,1,5,6] => [1,4,5,6,7,3,2] => 3
[5,1,2,3,7,4,6] => [7,6,4,3,2,1,5] => [1,2,4,5,6,7,3] => 2
[5,1,2,6,7,3,4] => [7,4,6,3,2,1,5] => [1,4,2,5,6,7,3] => 3
[5,1,2,7,4,3,6] => [7,6,3,2,1,5,4] => [1,2,5,6,7,3,4] => 2
[5,1,4,2,7,3,6] => [7,6,3,4,2,1,5] => [1,2,5,4,6,7,3] => 3
[5,1,4,7,3,2,6] => [7,6,2,1,5,3,4] => [1,2,6,7,3,5,4] => 3
[5,1,6,3,7,2,4] => [7,4,3,6,2,1,5] => [1,4,5,2,6,7,3] => 3
[5,1,7,2,3,4,6] => [7,6,4,2,1,5,3] => [1,2,4,6,7,3,5] => 2
[5,1,7,3,4,2,6] => [7,6,2,1,5,4,3] => [1,2,6,7,3,4,5] => 2
[5,1,7,6,3,2,4] => [7,4,6,2,1,5,3] => [1,4,2,6,7,3,5] => 3
[5,3,1,2,7,4,6] => [7,6,4,2,3,1,5] => [1,2,4,6,5,7,3] => 3
[5,3,1,6,7,2,4] => [7,4,6,2,3,1,5] => [1,4,2,6,5,7,3] => 4
[5,3,1,7,4,2,6] => [7,6,2,3,1,5,4] => [1,2,6,5,7,3,4] => 3
[5,3,4,1,7,2,6] => [7,6,2,3,4,1,5] => [1,2,6,5,4,7,3] => 4
[5,3,4,7,2,1,6] => [7,6,1,5,2,3,4] => [1,2,7,3,6,5,4] => 4
[5,3,6,2,7,1,4] => [7,4,2,3,6,1,5] => [1,4,6,5,2,7,3] => 4
[5,3,7,1,2,4,6] => [7,6,4,1,5,2,3] => [1,2,4,7,3,6,5] => 3
[5,3,7,2,4,1,6] => [7,6,1,5,4,2,3] => [1,2,7,3,4,6,5] => 3
[5,3,7,6,2,1,4] => [7,4,6,1,5,2,3] => [1,4,2,7,3,6,5] => 4
[5,4,1,3,7,2,6] => [7,6,2,4,3,1,5] => [1,2,6,4,5,7,3] => 3
[5,4,1,7,2,3,6] => [7,6,3,1,5,2,4] => [1,2,5,7,3,6,4] => 3
[5,4,2,1,7,3,6] => [7,6,3,2,4,1,5] => [1,2,5,6,4,7,3] => 3
[5,4,2,7,3,1,6] => [7,6,1,5,3,2,4] => [1,2,7,3,5,6,4] => 3
[5,4,7,1,3,2,6] => [7,6,2,4,1,5,3] => [1,2,6,4,7,3,5] => 3
[5,4,7,3,2,1,6] => [7,6,1,5,2,4,3] => [1,2,7,3,6,4,5] => 3
[5,6,1,2,7,3,4] => [7,4,2,6,3,1,5] => [1,4,6,2,5,7,3] => 3
[5,6,1,3,2,7,4] => [7,4,3,1,5,2,6] => [1,4,5,7,3,6,2] => 3
[5,6,2,3,7,1,4] => [7,4,3,2,6,1,5] => [1,4,5,6,2,7,3] => 3
[5,6,7,2,3,1,4] => [7,4,2,6,1,5,3] => [1,4,6,2,7,3,5] => 3
[5,7,1,2,4,3,6] => [7,6,3,1,5,4,2] => [1,2,5,7,3,4,6] => 2
[5,7,1,3,2,4,6] => [7,6,4,3,1,5,2] => [1,2,4,5,7,3,6] => 2
[5,7,1,3,6,2,4] => [7,4,3,1,5,6,2] => [1,4,5,7,3,2,6] => 3
[5,7,1,6,2,3,4] => [7,4,6,3,1,5,2] => [1,4,2,5,7,3,6] => 3
[5,7,2,1,3,4,6] => [7,6,4,1,5,3,2] => [1,2,4,7,3,5,6] => 2
[5,7,2,3,4,1,6] => [7,6,1,5,4,3,2] => [1,2,7,3,4,5,6] => 2
[5,7,2,6,3,1,4] => [7,4,6,1,5,3,2] => [1,4,2,7,3,5,6] => 3
[5,7,4,1,2,3,6] => [7,6,3,4,1,5,2] => [1,2,5,4,7,3,6] => 3
[5,7,4,2,3,1,6] => [7,6,1,5,3,4,2] => [1,2,7,3,5,4,6] => 3
[5,7,6,3,2,1,4] => [7,4,3,6,1,5,2] => [1,4,5,2,7,3,6] => 3
[6,1,2,3,4,7,5] => [7,5,4,3,2,1,6] => [1,3,4,5,6,7,2] => 2
[6,1,2,3,7,5,4] => [7,4,3,2,1,6,5] => [1,4,5,6,7,2,3] => 2
[6,1,2,5,3,7,4] => [7,4,5,3,2,1,6] => [1,4,3,5,6,7,2] => 3
[6,1,2,7,3,4,5] => [7,5,3,2,1,6,4] => [1,3,5,6,7,2,4] => 2
[6,1,4,2,3,7,5] => [7,5,3,4,2,1,6] => [1,3,5,4,6,7,2] => 3
[6,1,4,7,2,3,5] => [7,5,2,1,6,3,4] => [1,3,6,7,2,5,4] => 3
[6,1,5,3,2,7,4] => [7,4,3,5,2,1,6] => [1,4,5,3,6,7,2] => 3
[6,1,7,2,4,3,5] => [7,5,4,2,1,6,3] => [1,3,4,6,7,2,5] => 2
[6,1,7,3,2,4,5] => [7,5,2,1,6,4,3] => [1,3,6,7,2,4,5] => 2
[6,1,7,5,2,3,4] => [7,4,5,2,1,6,3] => [1,4,3,6,7,2,5] => 3
[6,3,1,2,4,7,5] => [7,5,4,2,3,1,6] => [1,3,4,6,5,7,2] => 3
[6,3,1,5,2,7,4] => [7,4,5,2,3,1,6] => [1,4,3,6,5,7,2] => 4
[6,3,1,7,2,4,5] => [7,5,2,3,1,6,4] => [1,3,6,5,7,2,4] => 3
[6,3,4,1,2,7,5] => [7,5,2,3,4,1,6] => [1,3,6,5,4,7,2] => 4
[6,3,4,7,1,2,5] => [7,5,1,6,2,3,4] => [1,3,7,2,6,5,4] => 4
[6,3,5,2,1,7,4] => [7,4,2,3,5,1,6] => [1,4,6,5,3,7,2] => 4
[6,3,7,1,4,2,5] => [7,5,4,1,6,2,3] => [1,3,4,7,2,6,5] => 3
[6,3,7,2,1,4,5] => [7,5,1,6,4,2,3] => [1,3,7,2,4,6,5] => 3
[6,3,7,5,1,2,4] => [7,4,5,1,6,2,3] => [1,4,3,7,2,6,5] => 4
[6,4,1,3,2,7,5] => [7,5,2,4,3,1,6] => [1,3,6,4,5,7,2] => 3
[6,4,1,7,3,2,5] => [7,5,3,1,6,2,4] => [1,3,5,7,2,6,4] => 3
[6,4,2,1,3,7,5] => [7,5,3,2,4,1,6] => [1,3,5,6,4,7,2] => 3
[6,4,2,7,1,3,5] => [7,5,1,6,3,2,4] => [1,3,7,2,5,6,4] => 3
[6,4,7,1,2,3,5] => [7,5,2,4,1,6,3] => [1,3,6,4,7,2,5] => 3
[6,4,7,3,1,2,5] => [7,5,1,6,2,4,3] => [1,3,7,2,6,4,5] => 3
[6,5,1,2,3,7,4] => [7,4,2,5,3,1,6] => [1,4,6,3,5,7,2] => 3
[6,5,1,3,7,2,4] => [7,4,3,1,6,2,5] => [1,4,5,7,2,6,3] => 3
[6,5,2,3,1,7,4] => [7,4,3,2,5,1,6] => [1,4,5,6,3,7,2] => 3
[6,5,7,2,1,3,4] => [7,4,2,5,1,6,3] => [1,4,6,3,7,2,5] => 3
[6,7,1,2,3,4,5] => [7,5,3,1,6,4,2] => [1,3,5,7,2,4,6] => 2
[6,7,1,3,2,5,4] => [7,4,3,1,6,5,2] => [1,4,5,7,2,3,6] => 2
[6,7,1,3,4,2,5] => [7,5,4,3,1,6,2] => [1,3,4,5,7,2,6] => 2
[6,7,1,5,3,2,4] => [7,4,5,3,1,6,2] => [1,4,3,5,7,2,6] => 3
[6,7,2,1,4,3,5] => [7,5,4,1,6,3,2] => [1,3,4,7,2,5,6] => 2
[6,7,2,3,1,4,5] => [7,5,1,6,4,3,2] => [1,3,7,2,4,5,6] => 2
[6,7,2,5,1,3,4] => [7,4,5,1,6,3,2] => [1,4,3,7,2,5,6] => 3
[6,7,4,1,3,2,5] => [7,5,3,4,1,6,2] => [1,3,5,4,7,2,6] => 3
[6,7,4,2,1,3,5] => [7,5,1,6,3,4,2] => [1,3,7,2,5,4,6] => 3
[6,7,5,3,1,2,4] => [7,4,3,5,1,6,2] => [1,4,5,3,7,2,6] => 3
[7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 1
[7,1,2,3,6,4,5] => [7,5,6,4,3,2,1] => [1,3,2,4,5,6,7] => 2
[7,1,2,5,3,4,6] => [7,6,4,5,3,2,1] => [1,2,4,3,5,6,7] => 2
[7,1,2,5,6,3,4] => [7,4,5,6,3,2,1] => [1,4,3,2,5,6,7] => 3
[7,1,2,6,3,5,4] => [7,4,6,5,3,2,1] => [1,4,2,3,5,6,7] => 2
[7,1,2,6,4,3,5] => [7,5,4,6,3,2,1] => [1,3,4,2,5,6,7] => 2
[7,1,4,2,3,5,6] => [7,6,5,3,4,2,1] => [1,2,3,5,4,6,7] => 2
[7,1,4,2,6,3,5] => [7,5,6,3,4,2,1] => [1,3,2,5,4,6,7] => 3
[7,1,4,5,2,3,6] => [7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => 3
[7,1,4,6,3,2,5] => [7,5,3,4,6,2,1] => [1,3,5,4,2,6,7] => 3
[7,1,5,2,4,3,6] => [7,6,3,5,4,2,1] => [1,2,5,3,4,6,7] => 2
[7,1,5,3,2,4,6] => [7,6,4,3,5,2,1] => [1,2,4,5,3,6,7] => 2
[7,1,5,3,6,2,4] => [7,4,3,5,6,2,1] => [1,4,5,3,2,6,7] => 3
[7,1,5,6,2,3,4] => [7,4,6,3,5,2,1] => [1,4,2,5,3,6,7] => 3
[7,1,6,2,3,4,5] => [7,5,3,6,4,2,1] => [1,3,5,2,4,6,7] => 2
[7,1,6,3,2,5,4] => [7,4,3,6,5,2,1] => [1,4,5,2,3,6,7] => 2
[7,1,6,3,4,2,5] => [7,5,4,3,6,2,1] => [1,3,4,5,2,6,7] => 2
[7,1,6,5,3,2,4] => [7,4,5,3,6,2,1] => [1,4,3,5,2,6,7] => 3
[7,3,1,2,4,5,6] => [7,6,5,4,2,3,1] => [1,2,3,4,6,5,7] => 2
[7,3,1,2,6,4,5] => [7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => 3
[7,3,1,5,2,4,6] => [7,6,4,5,2,3,1] => [1,2,4,3,6,5,7] => 3
[7,3,1,5,6,2,4] => [7,4,5,6,2,3,1] => [1,4,3,2,6,5,7] => 4
[7,3,1,6,2,5,4] => [7,4,6,5,2,3,1] => [1,4,2,3,6,5,7] => 3
[7,3,1,6,4,2,5] => [7,5,4,6,2,3,1] => [1,3,4,2,6,5,7] => 3
[7,3,4,1,2,5,6] => [7,6,5,2,3,4,1] => [1,2,3,6,5,4,7] => 3
[7,3,4,1,6,2,5] => [7,5,6,2,3,4,1] => [1,3,2,6,5,4,7] => 4
[7,3,4,5,1,2,6] => [7,6,2,3,4,5,1] => [1,2,6,5,4,3,7] => 4
[7,3,4,6,2,1,5] => [7,5,2,3,4,6,1] => [1,3,6,5,4,2,7] => 4
[7,3,5,1,4,2,6] => [7,6,2,3,5,4,1] => [1,2,6,5,3,4,7] => 3
[7,3,5,2,1,4,6] => [7,6,4,2,3,5,1] => [1,2,4,6,5,3,7] => 3
[7,3,5,2,6,1,4] => [7,4,2,3,5,6,1] => [1,4,6,5,3,2,7] => 4
[7,3,5,6,1,2,4] => [7,4,6,2,3,5,1] => [1,4,2,6,5,3,7] => 4
[7,3,6,1,2,4,5] => [7,5,2,3,6,4,1] => [1,3,6,5,2,4,7] => 3
[7,3,6,2,1,5,4] => [7,4,2,3,6,5,1] => [1,4,6,5,2,3,7] => 3
[7,3,6,2,4,1,5] => [7,5,4,2,3,6,1] => [1,3,4,6,5,2,7] => 3
[7,3,6,5,2,1,4] => [7,4,5,2,3,6,1] => [1,4,3,6,5,2,7] => 4
[7,4,1,3,2,5,6] => [7,6,5,2,4,3,1] => [1,2,3,6,4,5,7] => 2
[7,4,1,3,6,2,5] => [7,5,6,2,4,3,1] => [1,3,2,6,4,5,7] => 3
[7,4,1,5,3,2,6] => [7,6,2,4,5,3,1] => [1,2,6,4,3,5,7] => 3
[7,4,1,6,2,3,5] => [7,5,2,4,6,3,1] => [1,3,6,4,2,5,7] => 3
[7,4,2,1,3,5,6] => [7,6,5,3,2,4,1] => [1,2,3,5,6,4,7] => 2
[7,4,2,1,6,3,5] => [7,5,6,3,2,4,1] => [1,3,2,5,6,4,7] => 3
[7,4,2,5,1,3,6] => [7,6,3,2,4,5,1] => [1,2,5,6,4,3,7] => 3
[7,4,2,6,3,1,5] => [7,5,3,2,4,6,1] => [1,3,5,6,4,2,7] => 3
[7,4,5,1,2,3,6] => [7,6,3,5,2,4,1] => [1,2,5,3,6,4,7] => 3
[7,4,5,3,1,2,6] => [7,6,2,4,3,5,1] => [1,2,6,4,5,3,7] => 3
[7,4,6,1,3,2,5] => [7,5,3,6,2,4,1] => [1,3,5,2,6,4,7] => 3
[7,4,6,3,2,1,5] => [7,5,2,4,3,6,1] => [1,3,6,4,5,2,7] => 3
[7,5,1,2,3,4,6] => [7,6,4,2,5,3,1] => [1,2,4,6,3,5,7] => 2
[7,5,1,2,6,3,4] => [7,4,2,5,6,3,1] => [1,4,6,3,2,5,7] => 3
[7,5,1,3,4,2,6] => [7,6,2,5,4,3,1] => [1,2,6,3,4,5,7] => 2
[7,5,1,6,3,2,4] => [7,4,6,2,5,3,1] => [1,4,2,6,3,5,7] => 3
[7,5,2,1,4,3,6] => [7,6,3,2,5,4,1] => [1,2,5,6,3,4,7] => 2
[7,5,2,3,1,4,6] => [7,6,4,3,2,5,1] => [1,2,4,5,6,3,7] => 2
[7,5,2,3,6,1,4] => [7,4,3,2,5,6,1] => [1,4,5,6,3,2,7] => 3
[7,5,2,6,1,3,4] => [7,4,6,3,2,5,1] => [1,4,2,5,6,3,7] => 3
[7,5,4,1,3,2,6] => [7,6,2,5,3,4,1] => [1,2,6,3,5,4,7] => 3
[7,5,4,2,1,3,6] => [7,6,3,4,2,5,1] => [1,2,5,4,6,3,7] => 3
[7,5,6,2,3,1,4] => [7,4,2,5,3,6,1] => [1,4,6,3,5,2,7] => 3
[7,5,6,3,1,2,4] => [7,4,3,6,2,5,1] => [1,4,5,2,6,3,7] => 3
[7,6,1,2,3,5,4] => [7,4,2,6,5,3,1] => [1,4,6,2,3,5,7] => 2
[7,6,1,2,4,3,5] => [7,5,4,2,6,3,1] => [1,3,4,6,2,5,7] => 2
[7,6,1,3,2,4,5] => [7,5,2,6,4,3,1] => [1,3,6,2,4,5,7] => 2
[7,6,1,5,2,3,4] => [7,4,5,2,6,3,1] => [1,4,3,6,2,5,7] => 3
[7,6,2,1,3,4,5] => [7,5,3,2,6,4,1] => [1,3,5,6,2,4,7] => 2
[7,6,2,3,1,5,4] => [7,4,3,2,6,5,1] => [1,4,5,6,2,3,7] => 2
[7,6,2,3,4,1,5] => [7,5,4,3,2,6,1] => [1,3,4,5,6,2,7] => 2
[7,6,2,5,3,1,4] => [7,4,5,3,2,6,1] => [1,4,3,5,6,2,7] => 3
[7,6,4,1,2,3,5] => [7,5,2,6,3,4,1] => [1,3,6,2,5,4,7] => 3
[7,6,4,2,3,1,5] => [7,5,3,4,2,6,1] => [1,3,5,4,6,2,7] => 3
[7,6,5,2,1,3,4] => [7,4,2,6,3,5,1] => [1,4,6,2,5,3,7] => 3
[7,6,5,3,2,1,4] => [7,4,3,5,2,6,1] => [1,4,5,3,6,2,7] => 3
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,4,1 1,11,11,1 1,26,66,26,1 1,57,302,302,57,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 4\ q^{2} + q^{3}$
$F_{4} = q + 11\ q^{2} + 11\ q^{3} + q^{4}$
$F_{5} = q + 26\ q^{2} + 66\ q^{3} + 26\ q^{4} + q^{5}$
$F_{6} = q + 57\ q^{2} + 302\ q^{3} + 302\ q^{4} + 57\ q^{5} + q^{6}$
Description
The number of runs in a permutation.
A run in a permutation is an inclusion-wise maximal increasing substring, i.e., a contiguous subsequence.
This is the same as the number of descents plus 1.
A run in a permutation is an inclusion-wise maximal increasing substring, i.e., a contiguous subsequence.
This is the same as the number of descents plus 1.
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.
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
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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