Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
St000021: Permutations ⟶ ℤ (values match St000325The width of the tree associated to a permutation., St000470The number of runs in a permutation.)
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 1
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[2,3,1] => [3,2,1] => [3,2,1] => [3,2,1] => 2
[3,1,2] => [3,2,1] => [3,2,1] => [3,2,1] => 2
[3,2,1] => [3,2,1] => [3,2,1] => [3,2,1] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 2
[1,4,2,3] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 2
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
[2,3,1,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 2
[2,3,4,1] => [4,2,3,1] => [4,3,2,1] => [4,3,2,1] => 3
[2,4,1,3] => [3,4,1,2] => [4,3,2,1] => [4,3,2,1] => 3
[2,4,3,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[3,1,2,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 2
[3,1,4,2] => [4,2,3,1] => [4,3,2,1] => [4,3,2,1] => 3
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 2
[3,2,4,1] => [4,2,3,1] => [4,3,2,1] => [4,3,2,1] => 3
[3,4,1,2] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[3,4,2,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[4,1,2,3] => [4,2,3,1] => [4,3,2,1] => [4,3,2,1] => 3
[4,1,3,2] => [4,2,3,1] => [4,3,2,1] => [4,3,2,1] => 3
[4,2,1,3] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[4,2,3,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[4,3,1,2] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,3,5,2,4] => [1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,3,5,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,4,5,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,5,2,3,4] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,5,2,4,3] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,5,3,2,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,5,4,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 2
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 3
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 3
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 3
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 2
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 3
[2,3,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[2,3,4,5,1] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,3,5,1,4] => [4,2,5,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,3,5,4,1] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,4,1,3,5] => [3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[2,4,1,5,3] => [3,5,1,4,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,4,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[2,4,3,5,1] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,4,5,1,3] => [4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,4,5,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,5,1,3,4] => [3,5,1,4,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,5,1,4,3] => [3,5,1,4,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,5,3,1,4] => [4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,5,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,5,4,1,3] => [4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[2,5,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 2
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 3
[3,1,4,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[3,1,4,5,2] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,1,5,2,4] => [4,2,5,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,1,5,4,2] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 2
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 3
[3,2,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[3,2,4,5,1] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,2,5,1,4] => [4,2,5,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,2,5,4,1] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[3,4,1,5,2] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,4,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[3,4,2,5,1] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,4,5,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,4,5,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,5,1,2,4] => [4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,5,1,4,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
>>> Load all 874 entries. <<<[3,5,2,1,4] => [4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,5,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,5,4,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[3,5,4,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,1,2,3,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[4,1,2,5,3] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,1,3,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[4,1,3,5,2] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,1,5,2,3] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,1,5,3,2] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,2,1,3,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[4,2,1,5,3] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[4,2,3,5,1] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,2,5,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,2,5,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,3,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[4,3,1,5,2] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[4,3,2,5,1] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,3,5,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,3,5,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,5,1,2,3] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,5,1,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,5,2,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,5,2,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,5,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[4,5,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,1,2,3,4] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,1,2,4,3] => [5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,1,3,2,4] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,1,3,4,2] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,1,4,2,3] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,1,4,3,2] => [5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,2,1,3,4] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,2,1,4,3] => [5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,2,3,1,4] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,2,3,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,2,4,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,2,4,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,3,1,2,4] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,3,1,4,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,3,2,1,4] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,3,2,4,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,3,4,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,3,4,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,4,1,2,3] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,4,1,3,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,4,2,1,3] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,4,2,3,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,4,3,1,2] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 4
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 2
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 2
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 2
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 2
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 2
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => 2
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 3
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 3
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 3
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => [1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 2
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 3
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,3,5,2,6,4] => [1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,6,2,4,5] => [1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,6,2,5,4] => [1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 2
[1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 3
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => [1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => [1,4,3,2,6,5] => 3
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,3,6,5,2] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,5,2,3,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,4,5,2,6,3] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,5,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,4,5,3,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,6,2,3,5] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,6,3,2,5] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,4,6,5,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,5,2,3,6,4] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,5,2,4,6,3] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,2,6,3,4] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,2,6,4,3] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,5,3,2,6,4] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,5,3,4,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,5,4,2,6,3] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => [1,5,4,3,2,6] => 3
[1,5,4,3,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,4,6,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,6,3,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,6,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,5,6,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,2,3,4,5] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,2,3,5,4] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,2,4,3,5] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,2,4,5,3] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,2,5,3,4] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,2,5,4,3] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,3,2,4,5] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,3,2,5,4] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,3,4,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,3,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,4,2,3,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,4,3,2,5] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,4,3,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,4,5,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,4,5,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,5,2,4,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,5,3,2,4] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,5,3,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,5,4,2,3] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 3
[2,1,3,6,4,5] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 3
[2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => [2,1,3,6,5,4] => 3
[2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 3
[2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,5,3,4,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 3
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => [2,1,5,4,3,6] => 3
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,6,3,4,5] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 2
[2,3,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 3
[2,3,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 3
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[2,3,4,1,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[2,3,4,1,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[2,3,4,5,1,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,3,4,5,6,1] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,3,4,6,1,5] => [5,2,3,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,3,4,6,5,1] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,3,5,1,4,6] => [4,2,5,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,3,5,1,6,4] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[2,3,5,4,1,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,3,5,4,6,1] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,3,5,6,4,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,3,6,1,4,5] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[2,3,6,1,5,4] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,3,6,4,5,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,3,6,5,4,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,1,3,5,6] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[2,4,1,5,3,6] => [3,5,1,4,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,4,1,5,6,3] => [3,6,1,4,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => 5
[2,4,1,6,5,3] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,4,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[2,4,3,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,4,3,5,6,1] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,4,3,6,1,5] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,4,3,6,5,1] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,4,5,1,3,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,4,5,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,5,6,1,3] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,5,6,3,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,6,1,3,5] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,6,1,5,3] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,6,3,1,5] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,6,3,5,1] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,6,5,1,3] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,4,6,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,1,3,4,6] => [3,5,1,4,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,5,1,3,6,4] => [3,6,1,4,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,5,1,4,3,6] => [3,5,1,4,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,5,1,4,6,3] => [3,6,1,4,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,5,1,6,3,4] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,5,1,6,4,3] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,5,3,1,4,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,5,3,1,6,4] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,5,3,4,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,3,6,1,4] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,3,6,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,4,1,3,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,5,4,1,6,3] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[2,5,4,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,4,6,1,3] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,4,6,3,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,6,1,3,4] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,6,1,4,3] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,6,3,1,4] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,6,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,6,4,1,3] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,5,6,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,1,3,4,5] => [3,6,1,4,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,6,1,3,5,4] => [3,6,1,4,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,6,1,4,3,5] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,6,1,4,5,3] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,6,1,5,3,4] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,6,1,5,4,3] => [3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[2,6,3,1,4,5] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,3,1,5,4] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,3,4,1,5] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,3,5,1,4] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,4,1,3,5] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,4,1,5,3] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,4,3,1,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,4,5,1,3] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,4,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,5,1,3,4] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,5,1,4,3] => [4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,5,3,1,4] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,5,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,5,4,1,3] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[2,6,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,1,2,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 2
[3,1,2,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 3
[3,1,2,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 3
[3,1,2,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,1,2,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,1,2,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,1,4,2,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[3,1,4,2,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[3,1,4,5,2,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,1,4,5,6,2] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,1,4,6,2,5] => [5,2,3,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,1,4,6,5,2] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,1,5,2,4,6] => [4,2,5,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,1,5,2,6,4] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[3,1,5,4,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,1,5,4,6,2] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,1,5,6,2,4] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,1,5,6,4,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,1,6,2,4,5] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[3,1,6,2,5,4] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[3,1,6,4,2,5] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,1,6,4,5,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,1,6,5,2,4] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,1,6,5,4,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 2
[3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => [3,2,1,4,6,5] => 3
[3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => [3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,2,1,6,4,5] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => [3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[3,2,4,1,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[3,2,4,5,1,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,2,4,5,6,1] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,2,4,6,1,5] => [5,2,3,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,2,4,6,5,1] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,2,5,1,4,6] => [4,2,5,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,2,5,1,6,4] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[3,2,5,4,1,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,2,5,4,6,1] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,2,5,6,1,4] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,2,5,6,4,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,2,6,1,4,5] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[3,2,6,1,5,4] => [4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 5
[3,2,6,4,1,5] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,2,6,4,5,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,2,6,5,1,4] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,2,6,5,4,1] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[3,4,1,5,2,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,4,1,5,6,2] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,4,1,6,2,5] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,4,1,6,5,2] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,4,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[3,4,2,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,4,2,5,6,1] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,4,2,6,1,5] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,4,2,6,5,1] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[3,4,5,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,4,5,1,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,5,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,4,5,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,5,6,1,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,5,6,2,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,6,1,2,5] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,6,1,5,2] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,6,2,1,5] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,6,2,5,1] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,6,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,4,6,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,1,2,4,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,5,1,2,6,4] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,5,1,4,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,1,6,2,4] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,1,6,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,2,1,4,6] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,5,2,1,6,4] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,5,2,4,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,2,6,1,4] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,2,6,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,5,4,1,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[3,5,4,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,4,6,1,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,4,6,2,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,6,1,2,4] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,6,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,6,2,1,4] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,6,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,6,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,5,6,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,1,2,4,5] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,1,2,5,4] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,1,4,2,5] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,1,4,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,1,5,2,4] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,2,1,4,5] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,2,1,5,4] => [4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,2,4,1,5] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,2,5,1,4] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,4,1,2,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,4,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,4,2,1,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,4,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,4,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,4,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,5,1,2,4] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,5,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,5,2,1,4] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,5,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,5,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[3,6,5,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,2,3,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[4,1,2,3,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[4,1,2,5,3,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,1,2,5,6,3] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,1,2,6,3,5] => [5,2,3,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,1,2,6,5,3] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,1,3,2,5,6] => [4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[4,1,3,2,6,5] => [4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[4,1,3,5,2,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,1,3,5,6,2] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,1,3,6,2,5] => [5,2,3,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,1,3,6,5,2] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,1,5,2,3,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,1,5,2,6,3] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,5,3,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,1,5,3,6,2] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,5,6,2,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,5,6,3,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,6,2,3,5] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,6,2,5,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,6,3,2,5] => [5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,6,3,5,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,6,5,2,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,1,6,5,3,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,1,3,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[4,2,1,5,3,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,2,1,5,6,3] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,2,1,6,3,5] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,2,1,6,5,3] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,2,3,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[4,2,3,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,2,3,5,6,1] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,2,3,6,1,5] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,2,3,6,5,1] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,2,5,1,6,3] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,2,5,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,5,6,1,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,5,6,3,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,6,1,3,5] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,6,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,6,3,1,5] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,6,3,5,1] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,6,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,2,6,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,1,2,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[4,3,1,5,2,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,3,1,5,6,2] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,3,1,6,2,5] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,3,1,6,5,2] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => [4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,3,2,5,6,1] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,3,2,6,1,5] => [5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,3,2,6,5,1] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,3,5,1,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,3,5,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,5,6,1,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,5,6,2,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,6,1,2,5] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,6,1,5,2] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,6,2,1,5] => [5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,6,2,5,1] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,6,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,3,6,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,5,1,2,6,3] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,5,1,3,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,1,6,2,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,1,6,3,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,5,2,1,6,3] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,5,2,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,2,6,1,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,2,6,3,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,5,3,1,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[4,5,3,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,3,6,1,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,3,6,2,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,6,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,6,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,6,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,6,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,5,6,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,1,2,3,5] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,1,2,5,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,1,3,2,5] => [5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,1,3,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,1,5,2,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,1,5,3,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,2,1,3,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,2,1,5,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,2,3,1,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,2,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,2,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,2,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,3,1,2,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,3,2,1,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,3,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,3,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,5,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,5,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,5,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[4,6,5,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,2,3,4,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,1,2,3,6,4] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,1,2,4,3,6] => [5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,1,2,4,6,3] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,1,2,6,3,4] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,1,2,6,4,3] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,1,3,2,4,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,1,3,2,6,4] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,3,4,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,1,3,4,6,2] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,3,6,2,4] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,3,6,4,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,4,2,3,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,1,4,2,6,3] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,4,3,2,6] => [5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,1,4,3,6,2] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,4,6,2,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,4,6,3,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,6,2,3,4] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,6,2,4,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,6,3,2,4] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,6,3,4,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,6,4,2,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,1,6,4,3,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,1,3,4,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,2,1,3,6,4] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,2,1,4,3,6] => [5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,2,1,4,6,3] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,2,1,6,3,4] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,2,1,6,4,3] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,2,3,1,6,4] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,2,3,4,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,3,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,3,6,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,2,4,1,6,3] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,2,4,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,4,6,1,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,4,6,3,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,6,1,3,4] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,6,1,4,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,6,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,6,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,6,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,2,6,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,3,1,2,6,4] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,3,1,4,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,1,6,2,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,1,6,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,3,2,1,6,4] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,3,2,4,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,2,6,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,2,6,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,3,4,1,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,3,4,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,4,6,1,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,4,6,2,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,6,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,6,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,6,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,6,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,6,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,3,6,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,4,1,2,6,3] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,4,1,3,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,1,6,2,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,1,6,3,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,4,2,1,6,3] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,4,2,3,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,2,6,1,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,2,6,3,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,4,3,1,6,2] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,3,6,1,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,3,6,2,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,6,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,6,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,6,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,6,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,6,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,4,6,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,1,2,3,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,1,2,4,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,1,3,2,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,1,3,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,1,4,2,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,1,4,3,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,2,1,3,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,2,1,4,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,2,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,2,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,2,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,2,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,3,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,3,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,3,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,3,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,4,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,4,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,4,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,4,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[5,6,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,2,3,4,5] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,1,2,3,5,4] => [6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,1,2,4,3,5] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,1,2,4,5,3] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,1,2,5,3,4] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,1,2,5,4,3] => [6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,1,3,2,4,5] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,3,2,5,4] => [6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,3,4,2,5] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,3,4,5,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,3,5,2,4] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,3,5,4,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,4,2,3,5] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,4,2,5,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,4,3,2,5] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,4,3,5,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,4,5,2,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,4,5,3,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,5,2,3,4] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,5,2,4,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,5,3,2,4] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,5,3,4,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,5,4,2,3] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,1,5,4,3,2] => [6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,1,3,4,5] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,2,1,3,5,4] => [6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,2,1,4,3,5] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,2,1,4,5,3] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,2,1,5,3,4] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,2,1,5,4,3] => [6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => 5
[6,2,3,1,4,5] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,3,1,5,4] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,3,4,1,5] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,3,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,3,5,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,3,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,4,1,3,5] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,4,1,5,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,4,3,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,4,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,4,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,4,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,5,1,3,4] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,5,1,4,3] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,5,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,5,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,5,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,2,5,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,1,2,4,5] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,1,2,5,4] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,1,4,2,5] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,1,4,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,1,5,2,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,1,5,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,2,1,4,5] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,2,1,5,4] => [6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,2,4,1,5] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,2,4,5,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,2,5,1,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,2,5,4,1] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,4,1,2,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,4,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,4,2,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,4,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,4,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,4,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,5,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,5,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,5,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,5,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,5,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,3,5,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,1,2,3,5] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,1,2,5,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,1,3,2,5] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,1,3,5,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,1,5,2,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,1,5,3,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,2,1,3,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,2,1,5,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,2,3,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,2,3,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,2,5,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,2,5,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,3,1,2,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,3,1,5,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,3,2,1,5] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,3,2,5,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,3,5,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,3,5,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,5,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,5,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,5,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,5,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,5,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,4,5,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,1,2,3,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,1,2,4,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,1,3,2,4] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,1,3,4,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,1,4,2,3] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,1,4,3,2] => [6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,2,1,3,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,2,1,4,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,2,3,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,2,3,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,2,4,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,2,4,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,3,1,2,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,3,1,4,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,3,2,1,4] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,3,2,4,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,3,4,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,3,4,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,4,1,2,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,4,1,3,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,4,2,1,3] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,4,2,3,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,4,3,1,2] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 5
[] => [] => [] => [] => 0
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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 1,2,3 1,3,7,13 1,4,12,32,71 1,5,18,58,177,461
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 3\ q^{2}$
$F_{4} = 1 + 3\ q + 7\ q^{2} + 13\ q^{3}$
$F_{5} = 1 + 4\ q + 12\ q^{2} + 32\ q^{3} + 71\ q^{4}$
$F_{6} = 1 + 5\ q + 18\ q^{2} + 58\ q^{3} + 177\ q^{4} + 461\ q^{5}$
Description
The number of descents of a permutation.
This can be described as an occurrence of the vincular mesh pattern ([2,1], {(1,0),(1,1),(1,2)}), i.e., the middle column is shaded, see [3].
This can be described as an occurrence of the vincular mesh pattern ([2,1], {(1,0),(1,1),(1,2)}), i.e., the middle column is shaded, see [3].
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
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