Identifier
-
Mp00089:
Permutations
—Inverse Kreweras complement⟶
Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001223: Dyck paths ⟶ ℤ (values match St000932The number of occurrences of the pattern UDU in a Dyck path., St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra.)
Values
[1] => [1] => [1] => [1,0] => 0
[1,2] => [2,1] => [2,1] => [1,1,0,0] => 0
[2,1] => [1,2] => [1,2] => [1,0,1,0] => 1
[1,2,3] => [2,3,1] => [3,1,2] => [1,1,1,0,0,0] => 0
[1,3,2] => [3,2,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[2,1,3] => [1,3,2] => [1,3,2] => [1,0,1,1,0,0] => 1
[2,3,1] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 2
[3,1,2] => [3,1,2] => [3,2,1] => [1,1,1,0,0,0] => 0
[3,2,1] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 0
[1,2,3,4] => [2,3,4,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 0
[1,2,4,3] => [2,4,3,1] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 1
[1,3,2,4] => [3,2,4,1] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => 1
[1,3,4,2] => [4,2,3,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[1,4,2,3] => [3,4,2,1] => [4,1,3,2] => [1,1,1,1,0,0,0,0] => 0
[1,4,3,2] => [4,3,2,1] => [3,2,4,1] => [1,1,1,0,0,1,0,0] => 0
[2,1,3,4] => [1,3,4,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 1
[2,1,4,3] => [1,4,3,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[2,3,1,4] => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 2
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[2,4,1,3] => [1,4,2,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0] => 1
[2,4,3,1] => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 1
[3,1,2,4] => [3,1,4,2] => [4,2,1,3] => [1,1,1,1,0,0,0,0] => 0
[3,1,4,2] => [4,1,3,2] => [3,4,2,1] => [1,1,1,0,1,0,0,0] => 1
[3,2,1,4] => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 0
[3,2,4,1] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 1
[3,4,1,2] => [4,1,2,3] => [4,3,2,1] => [1,1,1,1,0,0,0,0] => 0
[3,4,2,1] => [3,1,2,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0] => 0
[4,1,2,3] => [3,4,1,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 0
[4,1,3,2] => [4,3,1,2] => [4,2,3,1] => [1,1,1,1,0,0,0,0] => 0
[4,2,1,3] => [2,4,1,3] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => 0
[4,2,3,1] => [2,3,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 0
[4,3,1,2] => [4,2,1,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0] => 1
[4,3,2,1] => [3,2,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 1
[1,2,3,4,5] => [2,3,4,5,1] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,2,3,5,4] => [2,3,5,4,1] => [4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,2,4,3,5] => [2,4,3,5,1] => [3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,4,5,3] => [2,5,3,4,1] => [3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => 2
[1,2,5,3,4] => [2,4,5,3,1] => [5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,2,5,4,3] => [2,5,4,3,1] => [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => 0
[1,3,2,4,5] => [3,2,4,5,1] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,2,5,4] => [3,2,5,4,1] => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => 2
[1,3,4,2,5] => [4,2,3,5,1] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,3,4,5,2] => [5,2,3,4,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[1,3,5,2,4] => [4,2,5,3,1] => [2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,5,4,2] => [5,2,4,3,1] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => 1
[1,4,2,3,5] => [3,4,2,5,1] => [5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,4,2,5,3] => [3,5,2,4,1] => [4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,4,3,2,5] => [4,3,2,5,1] => [3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => 0
[1,4,3,5,2] => [5,3,2,4,1] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,4,5,2,3] => [4,5,2,3,1] => [5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,4,5,3,2] => [5,4,2,3,1] => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,5,2,3,4] => [3,4,5,2,1] => [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => 0
[1,5,2,4,3] => [3,5,4,2,1] => [5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,5,3,2,4] => [4,3,5,2,1] => [5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,5,3,4,2] => [5,3,4,2,1] => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,5,4,2,3] => [4,5,3,2,1] => [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,5,4,3,2] => [5,4,3,2,1] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => 1
[2,1,3,4,5] => [1,3,4,5,2] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,5,4] => [1,3,5,4,2] => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => 2
[2,1,4,3,5] => [1,4,3,5,2] => [1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,1,4,5,3] => [1,5,3,4,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,1,5,3,4] => [1,4,5,3,2] => [1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,5,4,3] => [1,5,4,3,2] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => 1
[2,3,1,4,5] => [1,2,4,5,3] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,3,1,5,4] => [1,2,5,4,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,3,4,1,5] => [1,2,3,5,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 3
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[2,3,5,1,4] => [1,2,5,3,4] => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,3,5,4,1] => [1,2,4,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,4,1,3,5] => [1,4,2,5,3] => [1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,4,1,5,3] => [1,5,2,4,3] => [1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => 2
[2,4,3,1,5] => [1,3,2,5,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 1
[2,4,3,5,1] => [1,3,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 2
[2,4,5,1,3] => [1,5,2,3,4] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,4,5,3,1] => [1,4,2,3,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,5,1,3,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 1
[2,5,1,4,3] => [1,5,4,2,3] => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,5,3,1,4] => [1,3,5,2,4] => [1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,5,3,4,1] => [1,3,4,2,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,5,4,1,3] => [1,5,3,2,4] => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,5,4,3,1] => [1,4,3,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 2
[3,1,2,4,5] => [3,1,4,5,2] => [5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[3,1,2,5,4] => [3,1,5,4,2] => [4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,1,4,2,5] => [4,1,3,5,2] => [3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,1,4,5,2] => [5,1,3,4,2] => [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => 2
[3,1,5,2,4] => [4,1,5,3,2] => [5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[3,1,5,4,2] => [5,1,4,3,2] => [4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => 0
[3,2,1,4,5] => [2,1,4,5,3] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => 0
[3,2,1,5,4] => [2,1,5,4,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 1
[3,2,4,1,5] => [2,1,3,5,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 1
[3,2,4,5,1] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 2
[3,2,5,1,4] => [2,1,5,3,4] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => 0
[3,2,5,4,1] => [2,1,4,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 0
[3,4,1,2,5] => [4,1,2,5,3] => [5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[3,4,1,5,2] => [5,1,2,4,3] => [4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,4,2,1,5] => [3,1,2,5,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => 0
[3,4,2,5,1] => [3,1,2,4,5] => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => 1
[3,4,5,1,2] => [5,1,2,3,4] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[3,4,5,2,1] => [4,1,2,3,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[3,5,1,2,4] => [4,1,5,2,3] => [4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => 0
[3,5,1,4,2] => [5,1,4,2,3] => [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => 0
>>> Load all 873 entries. <<<[3,5,2,1,4] => [3,1,5,2,4] => [5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[3,5,2,4,1] => [3,1,4,2,5] => [4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[3,5,4,1,2] => [5,1,3,2,4] => [3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,5,4,2,1] => [4,1,3,2,5] => [3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => 1
[4,1,2,3,5] => [3,4,1,5,2] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => 0
[4,1,2,5,3] => [3,5,1,4,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 1
[4,1,3,2,5] => [4,3,1,5,2] => [5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[4,1,3,5,2] => [5,3,1,4,2] => [4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => 1
[4,1,5,2,3] => [4,5,1,3,2] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => 0
[4,1,5,3,2] => [5,4,1,3,2] => [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[4,2,1,3,5] => [2,4,1,5,3] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => 0
[4,2,1,5,3] => [2,5,1,4,3] => [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => 1
[4,2,3,1,5] => [2,3,1,5,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 0
[4,2,3,5,1] => [2,3,1,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 1
[4,2,5,1,3] => [2,5,1,3,4] => [5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[4,2,5,3,1] => [2,4,1,3,5] => [4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[4,3,1,2,5] => [4,2,1,5,3] => [2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => 1
[4,3,1,5,2] => [5,2,1,4,3] => [2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => 2
[4,3,2,1,5] => [3,2,1,5,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 1
[4,3,2,5,1] => [3,2,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 2
[4,3,5,1,2] => [5,2,1,3,4] => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => 1
[4,3,5,2,1] => [4,2,1,3,5] => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => 1
[4,5,1,2,3] => [4,5,1,2,3] => [5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[4,5,1,3,2] => [5,4,1,2,3] => [4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => 0
[4,5,2,1,3] => [3,5,1,2,4] => [3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => 0
[4,5,2,3,1] => [3,4,1,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 0
[4,5,3,1,2] => [5,3,1,2,4] => [5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[4,5,3,2,1] => [4,3,1,2,5] => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[5,1,2,3,4] => [3,4,5,1,2] => [5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[5,1,2,4,3] => [3,5,4,1,2] => [4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => 0
[5,1,3,2,4] => [4,3,5,1,2] => [4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => 0
[5,1,3,4,2] => [5,3,4,1,2] => [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[5,1,4,2,3] => [4,5,3,1,2] => [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => 1
[5,1,4,3,2] => [5,4,3,1,2] => [3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => 1
[5,2,1,3,4] => [2,4,5,1,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 0
[5,2,1,4,3] => [2,5,4,1,3] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[5,2,3,1,4] => [2,3,5,1,4] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => 0
[5,2,3,4,1] => [2,3,4,1,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[5,2,4,1,3] => [2,5,3,1,4] => [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => 1
[5,2,4,3,1] => [2,4,3,1,5] => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => 1
[5,3,1,2,4] => [4,2,5,1,3] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => 1
[5,3,1,4,2] => [5,2,4,1,3] => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => 1
[5,3,2,1,4] => [3,2,5,1,4] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => 1
[5,3,2,4,1] => [3,2,4,1,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => 1
[5,3,4,1,2] => [5,2,3,1,4] => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => 2
[5,3,4,2,1] => [4,2,3,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 2
[5,4,1,2,3] => [4,5,2,1,3] => [4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => 0
[5,4,1,3,2] => [5,4,2,1,3] => [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => 0
[5,4,2,1,3] => [3,5,2,1,4] => [5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => 0
[5,4,2,3,1] => [3,4,2,1,5] => [4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => 0
[5,4,3,1,2] => [5,3,2,1,4] => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => 0
[5,4,3,2,1] => [4,3,2,1,5] => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,2,3,4,5,6] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,3,4,6,5] => [2,3,4,6,5,1] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,2,3,5,4,6] => [2,3,5,4,6,1] => [4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,3,5,6,4] => [2,3,6,4,5,1] => [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,2,3,6,4,5] => [2,3,5,6,4,1] => [6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,3,6,5,4] => [2,3,6,5,4,1] => [5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,2,4,3,5,6] => [2,4,3,5,6,1] => [3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,4,3,6,5] => [2,4,3,6,5,1] => [3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,2,4,5,3,6] => [2,5,3,4,6,1] => [3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,2,4,5,6,3] => [2,6,3,4,5,1] => [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,2,4,6,3,5] => [2,5,3,6,4,1] => [3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,5,3] => [2,6,3,5,4,1] => [3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,2,5,3,4,6] => [2,4,5,3,6,1] => [6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,5,3,6,4] => [2,4,6,3,5,1] => [5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,2,5,4,3,6] => [2,5,4,3,6,1] => [4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,2,5,4,6,3] => [2,6,4,3,5,1] => [4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,2,5,6,3,4] => [2,5,6,3,4,1] => [6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,5,6,4,3] => [2,6,5,3,4,1] => [5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,2,6,3,4,5] => [2,4,5,6,3,1] => [5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,2,6,3,5,4] => [2,4,6,5,3,1] => [6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,6,4,3,5] => [2,5,4,6,3,1] => [6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,6,4,5,3] => [2,6,4,5,3,1] => [5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,2,6,5,3,4] => [2,5,6,4,3,1] => [4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,6,5,4,3] => [2,6,5,4,3,1] => [4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,3,2,4,5,6] => [3,2,4,5,6,1] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,4,6,5] => [3,2,4,6,5,1] => [2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,3,2,5,4,6] => [3,2,5,4,6,1] => [2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,3,2,5,6,4] => [3,2,6,4,5,1] => [2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => 3
[1,3,2,6,4,5] => [3,2,5,6,4,1] => [2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,2,6,5,4] => [3,2,6,5,4,1] => [2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,3,4,2,5,6] => [4,2,3,5,6,1] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,3,4,2,6,5] => [4,2,3,6,5,1] => [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,3,4,5,2,6] => [5,2,3,4,6,1] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,3,4,5,6,2] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 4
[1,3,4,6,2,5] => [5,2,3,6,4,1] => [2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,3,4,6,5,2] => [6,2,3,5,4,1] => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,3,5,2,4,6] => [4,2,5,3,6,1] => [2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,5,2,6,4] => [4,2,6,3,5,1] => [2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,3,5,4,2,6] => [5,2,4,3,6,1] => [2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,3,5,4,6,2] => [6,2,4,3,5,1] => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,3,5,6,2,4] => [5,2,6,3,4,1] => [2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,5,6,4,2] => [6,2,5,3,4,1] => [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,3,6,2,4,5] => [4,2,5,6,3,1] => [2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,3,6,2,5,4] => [4,2,6,5,3,1] => [2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,4,2,5] => [5,2,4,6,3,1] => [2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,6,4,5,2] => [6,2,4,5,3,1] => [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,3,6,5,2,4] => [5,2,6,4,3,1] => [2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,3,6,5,4,2] => [6,2,5,4,3,1] => [2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,4,2,3,5,6] => [3,4,2,5,6,1] => [6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,4,2,3,6,5] => [3,4,2,6,5,1] => [5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,4,2,5,3,6] => [3,5,2,4,6,1] => [4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,4,2,5,6,3] => [3,6,2,4,5,1] => [4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,4,2,6,3,5] => [3,5,2,6,4,1] => [6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,4,2,6,5,3] => [3,6,2,5,4,1] => [5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,4,3,2,5,6] => [4,3,2,5,6,1] => [3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,4,3,2,6,5] => [4,3,2,6,5,1] => [3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,4,3,5,2,6] => [5,3,2,4,6,1] => [3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,4,3,5,6,2] => [6,3,2,4,5,1] => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,4,3,6,2,5] => [5,3,2,6,4,1] => [3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,4,3,6,5,2] => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,4,5,2,3,6] => [4,5,2,3,6,1] => [6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,4,5,2,6,3] => [4,6,2,3,5,1] => [5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,4,5,3,2,6] => [5,4,2,3,6,1] => [4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,4,5,3,6,2] => [6,4,2,3,5,1] => [4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,4,5,6,2,3] => [5,6,2,3,4,1] => [6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,4,5,6,3,2] => [6,5,2,3,4,1] => [5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,4,6,2,3,5] => [4,5,2,6,3,1] => [5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,4,6,2,5,3] => [4,6,2,5,3,1] => [6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,4,6,3,2,5] => [5,4,2,6,3,1] => [6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,4,6,3,5,2] => [6,4,2,5,3,1] => [5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,4,6,5,2,3] => [5,6,2,4,3,1] => [4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,4,6,5,3,2] => [6,5,2,4,3,1] => [4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,5,2,3,4,6] => [3,4,5,2,6,1] => [4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,5,2,3,6,4] => [3,4,6,2,5,1] => [4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,5,2,4,3,6] => [3,5,4,2,6,1] => [6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,5,2,4,6,3] => [3,6,4,2,5,1] => [5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,5,2,6,3,4] => [3,5,6,2,4,1] => [5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,5,2,6,4,3] => [3,6,5,2,4,1] => [6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,5,3,2,4,6] => [4,3,5,2,6,1] => [6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,5,3,2,6,4] => [4,3,6,2,5,1] => [5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,5,3,4,2,6] => [5,3,4,2,6,1] => [4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,5,3,4,6,2] => [6,3,4,2,5,1] => [4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,5,3,6,2,4] => [5,3,6,2,4,1] => [6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,5,3,6,4,2] => [6,3,5,2,4,1] => [5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,5,4,2,3,6] => [4,5,3,2,6,1] => [3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,5,4,2,6,3] => [4,6,3,2,5,1] => [3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,5,4,3,2,6] => [5,4,3,2,6,1] => [3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,5,4,3,6,2] => [6,4,3,2,5,1] => [3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,5,4,6,2,3] => [5,6,3,2,4,1] => [3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,5,4,6,3,2] => [6,5,3,2,4,1] => [3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,5,6,2,3,4] => [4,5,6,2,3,1] => [6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,5,6,2,4,3] => [4,6,5,2,3,1] => [5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,5,6,3,2,4] => [5,4,6,2,3,1] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,5,6,3,4,2] => [6,4,5,2,3,1] => [4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,5,6,4,2,3] => [5,6,4,2,3,1] => [6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,5,6,4,3,2] => [6,5,4,2,3,1] => [5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,6,2,3,4,5] => [3,4,5,6,2,1] => [6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,6,2,3,5,4] => [3,4,6,5,2,1] => [5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,6,2,4,3,5] => [3,5,4,6,2,1] => [5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,6,2,4,5,3] => [3,6,4,5,2,1] => [6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,6,2,5,3,4] => [3,5,6,4,2,1] => [4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,6,2,5,4,3] => [3,6,5,4,2,1] => [4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,6,3,2,4,5] => [4,3,5,6,2,1] => [5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,6,3,2,5,4] => [4,3,6,5,2,1] => [6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,6,3,4,2,5] => [5,3,4,6,2,1] => [6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,6,3,4,5,2] => [6,3,4,5,2,1] => [5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,6,3,5,2,4] => [5,3,6,4,2,1] => [4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,6,3,5,4,2] => [6,3,5,4,2,1] => [4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,6,4,2,3,5] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,6,4,2,5,3] => [4,6,3,5,2,1] => [3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,6,4,3,2,5] => [5,4,3,6,2,1] => [3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,6,4,3,5,2] => [6,4,3,5,2,1] => [3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,6,4,5,2,3] => [5,6,3,4,2,1] => [3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,6,4,5,3,2] => [6,5,3,4,2,1] => [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,6,5,2,3,4] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,6,5,2,4,3] => [4,6,5,3,2,1] => [6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,6,5,3,2,4] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,6,5,3,4,2] => [6,4,5,3,2,1] => [5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,6,5,4,2,3] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,6,5,4,3,2] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => 0
[2,1,3,4,5,6] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,6,5] => [1,3,4,6,5,2] => [1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,1,3,5,4,6] => [1,3,5,4,6,2] => [1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,3,5,6,4] => [1,3,6,4,5,2] => [1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[2,1,3,6,4,5] => [1,3,5,6,4,2] => [1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,6,5,4] => [1,3,6,5,4,2] => [1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[2,1,4,3,5,6] => [1,4,3,5,6,2] => [1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,1,4,3,6,5] => [1,4,3,6,5,2] => [1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[2,1,4,5,3,6] => [1,5,3,4,6,2] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[2,1,4,5,6,3] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[2,1,4,6,3,5] => [1,5,3,6,4,2] => [1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,1,4,6,5,3] => [1,6,3,5,4,2] => [1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[2,1,5,3,4,6] => [1,4,5,3,6,2] => [1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,3,6,4] => [1,4,6,3,5,2] => [1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,1,5,4,3,6] => [1,5,4,3,6,2] => [1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[2,1,5,4,6,3] => [1,6,4,3,5,2] => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,5,6,3,4] => [1,5,6,3,4,2] => [1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,5,6,4,3] => [1,6,5,3,4,2] => [1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[2,1,6,3,4,5] => [1,4,5,6,3,2] => [1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[2,1,6,3,5,4] => [1,4,6,5,3,2] => [1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,3,5] => [1,5,4,6,3,2] => [1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,6,4,5,3] => [1,6,4,5,3,2] => [1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[2,1,6,5,3,4] => [1,5,6,4,3,2] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,6,5,4,3] => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[2,3,1,4,5,6] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,1,4,6,5] => [1,2,4,6,5,3] => [1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[2,3,1,5,4,6] => [1,2,5,4,6,3] => [1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[2,3,1,5,6,4] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => 4
[2,3,1,6,4,5] => [1,2,5,6,4,3] => [1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,1,6,5,4] => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[2,3,4,1,5,6] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,3,4,1,6,5] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => 4
[2,3,4,5,1,6] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => 4
[2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 5
[2,3,4,6,1,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,3,4,6,5,1] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => 3
[2,3,5,1,4,6] => [1,2,5,3,6,4] => [1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,5,1,6,4] => [1,2,6,3,5,4] => [1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 3
[2,3,5,4,1,6] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[2,3,5,4,6,1] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => 3
[2,3,5,6,1,4] => [1,2,6,3,4,5] => [1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,5,6,4,1] => [1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[2,3,6,1,4,5] => [1,2,5,6,3,4] => [1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[2,3,6,1,5,4] => [1,2,6,5,3,4] => [1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,6,4,1,5] => [1,2,4,6,3,5] => [1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,3,6,4,5,1] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[2,3,6,5,1,4] => [1,2,6,4,3,5] => [1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => 3
[2,3,6,5,4,1] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => 3
[2,4,1,3,5,6] => [1,4,2,5,6,3] => [1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,4,1,3,6,5] => [1,4,2,6,5,3] => [1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,4,1,5,3,6] => [1,5,2,4,6,3] => [1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,4,1,5,6,3] => [1,6,2,4,5,3] => [1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => 3
[2,4,1,6,3,5] => [1,5,2,6,4,3] => [1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,4,1,6,5,3] => [1,6,2,5,4,3] => [1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[2,4,3,1,5,6] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,4,3,1,6,5] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[2,4,3,5,1,6] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,4,3,5,6,1] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => 3
[2,4,3,6,1,5] => [1,3,2,6,4,5] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,4,3,6,5,1] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[2,4,5,1,3,6] => [1,5,2,3,6,4] => [1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,4,5,1,6,3] => [1,6,2,3,5,4] => [1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,4,5,3,1,6] => [1,4,2,3,6,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,4,5,3,6,1] => [1,4,2,3,5,6] => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[2,4,5,6,1,3] => [1,6,2,3,4,5] => [1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,4,5,6,3,1] => [1,5,2,3,4,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,4,6,1,3,5] => [1,5,2,6,3,4] => [1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[2,4,6,1,5,3] => [1,6,2,5,3,4] => [1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,4,6,3,1,5] => [1,4,2,6,3,5] => [1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,4,6,3,5,1] => [1,4,2,5,3,6] => [1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,4,6,5,1,3] => [1,6,2,4,3,5] => [1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,4,6,5,3,1] => [1,5,2,4,3,6] => [1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[2,5,1,3,4,6] => [1,4,5,2,6,3] => [1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[2,5,1,3,6,4] => [1,4,6,2,5,3] => [1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,5,1,4,3,6] => [1,5,4,2,6,3] => [1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,5,1,4,6,3] => [1,6,4,2,5,3] => [1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,5,1,6,3,4] => [1,5,6,2,4,3] => [1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[2,5,1,6,4,3] => [1,6,5,2,4,3] => [1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,5,3,1,4,6] => [1,3,5,2,6,4] => [1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,5,3,1,6,4] => [1,3,6,2,5,4] => [1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,5,3,4,1,6] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,5,3,4,6,1] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[2,5,3,6,1,4] => [1,3,6,2,4,5] => [1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,5,3,6,4,1] => [1,3,5,2,4,6] => [1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,5,4,1,3,6] => [1,5,3,2,6,4] => [1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,5,4,1,6,3] => [1,6,3,2,5,4] => [1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => 3
[2,5,4,3,1,6] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => 2
[2,5,4,3,6,1] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,5,4,6,1,3] => [1,6,3,2,4,5] => [1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,5,4,6,3,1] => [1,5,3,2,4,6] => [1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[2,5,6,1,3,4] => [1,5,6,2,3,4] => [1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,5,6,1,4,3] => [1,6,5,2,3,4] => [1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[2,5,6,3,1,4] => [1,4,6,2,3,5] => [1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[2,5,6,3,4,1] => [1,4,5,2,3,6] => [1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[2,5,6,4,1,3] => [1,6,4,2,3,5] => [1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,5,6,4,3,1] => [1,5,4,2,3,6] => [1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,6,1,3,4,5] => [1,4,5,6,2,3] => [1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,6,1,3,5,4] => [1,4,6,5,2,3] => [1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[2,6,1,4,3,5] => [1,5,4,6,2,3] => [1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[2,6,1,4,5,3] => [1,6,4,5,2,3] => [1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,6,1,5,3,4] => [1,5,6,4,2,3] => [1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[2,6,1,5,4,3] => [1,6,5,4,2,3] => [1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,6,3,1,4,5] => [1,3,5,6,2,4] => [1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[2,6,3,1,5,4] => [1,3,6,5,2,4] => [1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,6,3,4,1,5] => [1,3,4,6,2,5] => [1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,6,3,4,5,1] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,6,3,5,1,4] => [1,3,6,4,2,5] => [1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,6,3,5,4,1] => [1,3,5,4,2,6] => [1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[2,6,4,1,3,5] => [1,5,3,6,2,4] => [1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[2,6,4,1,5,3] => [1,6,3,5,2,4] => [1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,6,4,3,1,5] => [1,4,3,6,2,5] => [1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,6,4,3,5,1] => [1,4,3,5,2,6] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[2,6,4,5,1,3] => [1,6,3,4,2,5] => [1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => 3
[2,6,4,5,3,1] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => 3
[2,6,5,1,3,4] => [1,5,6,3,2,4] => [1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[2,6,5,1,4,3] => [1,6,5,3,2,4] => [1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,6,5,3,1,4] => [1,4,6,3,2,5] => [1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,6,5,3,4,1] => [1,4,5,3,2,6] => [1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,6,5,4,1,3] => [1,6,4,3,2,5] => [1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[2,6,5,4,3,1] => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[3,1,2,4,5,6] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,1,2,4,6,5] => [3,1,4,6,5,2] => [5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,1,2,5,4,6] => [3,1,5,4,6,2] => [4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,1,2,5,6,4] => [3,1,6,4,5,2] => [4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[3,1,2,6,4,5] => [3,1,5,6,4,2] => [6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,1,2,6,5,4] => [3,1,6,5,4,2] => [5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[3,1,4,2,5,6] => [4,1,3,5,6,2] => [3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,1,4,2,6,5] => [4,1,3,6,5,2] => [3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[3,1,4,5,2,6] => [5,1,3,4,6,2] => [3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[3,1,4,5,6,2] => [6,1,3,4,5,2] => [3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[3,1,4,6,2,5] => [5,1,3,6,4,2] => [3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,1,4,6,5,2] => [6,1,3,5,4,2] => [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[3,1,5,2,4,6] => [4,1,5,3,6,2] => [6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,1,5,2,6,4] => [4,1,6,3,5,2] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,1,5,4,2,6] => [5,1,4,3,6,2] => [4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[3,1,5,4,6,2] => [6,1,4,3,5,2] => [4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[3,1,5,6,2,4] => [5,1,6,3,4,2] => [6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,1,5,6,4,2] => [6,1,5,3,4,2] => [5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[3,1,6,2,4,5] => [4,1,5,6,3,2] => [5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[3,1,6,2,5,4] => [4,1,6,5,3,2] => [6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,1,6,4,2,5] => [5,1,4,6,3,2] => [6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,1,6,4,5,2] => [6,1,4,5,3,2] => [5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[3,1,6,5,2,4] => [5,1,6,4,3,2] => [4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,1,6,5,4,2] => [6,1,5,4,3,2] => [4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[3,2,1,4,5,6] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[3,2,1,4,6,5] => [2,1,4,6,5,3] => [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[3,2,1,5,4,6] => [2,1,5,4,6,3] => [2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[3,2,1,5,6,4] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[3,2,1,6,4,5] => [2,1,5,6,4,3] => [2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[3,2,1,6,5,4] => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => 0
[3,2,4,1,5,6] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,2,4,1,6,5] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[3,2,4,5,1,6] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[3,2,4,5,6,1] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
[3,2,4,6,1,5] => [2,1,3,6,4,5] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[3,2,4,6,5,1] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[3,2,5,1,4,6] => [2,1,5,3,6,4] => [2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[3,2,5,1,6,4] => [2,1,6,3,5,4] => [2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[3,2,5,4,1,6] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[3,2,5,4,6,1] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[3,2,5,6,1,4] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[3,2,5,6,4,1] => [2,1,5,3,4,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[3,2,6,1,4,5] => [2,1,5,6,3,4] => [2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => 0
[3,2,6,1,5,4] => [2,1,6,5,3,4] => [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[3,2,6,4,1,5] => [2,1,4,6,3,5] => [2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 0
[3,2,6,4,5,1] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => 0
[3,2,6,5,1,4] => [2,1,6,4,3,5] => [2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[3,2,6,5,4,1] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[3,4,1,2,5,6] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,4,1,2,6,5] => [4,1,2,6,5,3] => [5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,4,1,5,2,6] => [5,1,2,4,6,3] => [4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,4,1,5,6,2] => [6,1,2,4,5,3] => [4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[3,4,1,6,2,5] => [5,1,2,6,4,3] => [6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,4,1,6,5,2] => [6,1,2,5,4,3] => [5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[3,4,2,1,5,6] => [3,1,2,5,6,4] => [3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[3,4,2,1,6,5] => [3,1,2,6,5,4] => [3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[3,4,2,5,1,6] => [3,1,2,4,6,5] => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[3,4,2,5,6,1] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[3,4,2,6,1,5] => [3,1,2,6,4,5] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[3,4,2,6,5,1] => [3,1,2,5,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[3,4,5,1,2,6] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,4,5,1,6,2] => [6,1,2,3,5,4] => [5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,4,5,2,1,6] => [4,1,2,3,6,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[3,4,5,2,6,1] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,4,5,6,1,2] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,4,5,6,2,1] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[3,4,6,1,2,5] => [5,1,2,6,3,4] => [5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[3,4,6,1,5,2] => [6,1,2,5,3,4] => [6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,4,6,2,1,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,4,6,2,5,1] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[3,4,6,5,1,2] => [6,1,2,4,3,5] => [4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,4,6,5,2,1] => [5,1,2,4,3,6] => [4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[3,5,1,2,4,6] => [4,1,5,2,6,3] => [4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[3,5,1,2,6,4] => [4,1,6,2,5,3] => [4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[3,5,1,4,2,6] => [5,1,4,2,6,3] => [6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,5,1,4,6,2] => [6,1,4,2,5,3] => [5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,5,1,6,2,4] => [5,1,6,2,4,3] => [5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[3,5,1,6,4,2] => [6,1,5,2,4,3] => [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,5,2,1,4,6] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,5,2,1,6,4] => [3,1,6,2,5,4] => [5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[3,5,2,4,1,6] => [3,1,4,2,6,5] => [4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[3,5,2,4,6,1] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[3,5,2,6,1,4] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,5,2,6,4,1] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[3,5,4,1,2,6] => [5,1,3,2,6,4] => [3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,5,4,1,6,2] => [6,1,3,2,5,4] => [3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[3,5,4,2,1,6] => [4,1,3,2,6,5] => [3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[3,5,4,2,6,1] => [4,1,3,2,5,6] => [3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 2
[3,5,4,6,1,2] => [6,1,3,2,4,5] => [3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,5,4,6,2,1] => [5,1,3,2,4,6] => [3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[3,5,6,1,2,4] => [5,1,6,2,3,4] => [6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,5,6,1,4,2] => [6,1,5,2,3,4] => [5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[3,5,6,2,1,4] => [4,1,6,2,3,5] => [4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[3,5,6,2,4,1] => [4,1,5,2,3,6] => [4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[3,5,6,4,1,2] => [6,1,4,2,3,5] => [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,5,6,4,2,1] => [5,1,4,2,3,6] => [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[3,6,1,2,4,5] => [4,1,5,6,2,3] => [6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,6,1,2,5,4] => [4,1,6,5,2,3] => [5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[3,6,1,4,2,5] => [5,1,4,6,2,3] => [5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[3,6,1,4,5,2] => [6,1,4,5,2,3] => [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,6,1,5,2,4] => [5,1,6,4,2,3] => [4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[3,6,1,5,4,2] => [6,1,5,4,2,3] => [4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,6,2,1,4,5] => [3,1,5,6,2,4] => [5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[3,6,2,1,5,4] => [3,1,6,5,2,4] => [6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,6,2,4,1,5] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,6,2,4,5,1] => [3,1,4,5,2,6] => [5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[3,6,2,5,1,4] => [3,1,6,4,2,5] => [4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[3,6,2,5,4,1] => [3,1,5,4,2,6] => [4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[3,6,4,1,2,5] => [5,1,3,6,2,4] => [3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[3,6,4,1,5,2] => [6,1,3,5,2,4] => [3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,6,4,2,1,5] => [4,1,3,6,2,5] => [3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[3,6,4,2,5,1] => [4,1,3,5,2,6] => [3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[3,6,4,5,1,2] => [6,1,3,4,2,5] => [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[3,6,4,5,2,1] => [5,1,3,4,2,6] => [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[3,6,5,1,2,4] => [5,1,6,3,2,4] => [5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[3,6,5,1,4,2] => [6,1,5,3,2,4] => [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,6,5,2,1,4] => [4,1,6,3,2,5] => [6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[3,6,5,2,4,1] => [4,1,5,3,2,6] => [5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[3,6,5,4,1,2] => [6,1,4,3,2,5] => [4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[3,6,5,4,2,1] => [5,1,4,3,2,6] => [4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[4,1,2,3,5,6] => [3,4,1,5,6,2] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[4,1,2,3,6,5] => [3,4,1,6,5,2] => [3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[4,1,2,5,3,6] => [3,5,1,4,6,2] => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[4,1,2,5,6,3] => [3,6,1,4,5,2] => [3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[4,1,2,6,3,5] => [3,5,1,6,4,2] => [3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[4,1,2,6,5,3] => [3,6,1,5,4,2] => [3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => 0
[4,1,3,2,5,6] => [4,3,1,5,6,2] => [6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,1,3,2,6,5] => [4,3,1,6,5,2] => [5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,1,3,5,2,6] => [5,3,1,4,6,2] => [4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,1,3,5,6,2] => [6,3,1,4,5,2] => [4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[4,1,3,6,2,5] => [5,3,1,6,4,2] => [6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,1,3,6,5,2] => [6,3,1,5,4,2] => [5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[4,1,5,2,3,6] => [4,5,1,3,6,2] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[4,1,5,2,6,3] => [4,6,1,3,5,2] => [4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[4,1,5,3,2,6] => [5,4,1,3,6,2] => [6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,1,5,3,6,2] => [6,4,1,3,5,2] => [5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,1,5,6,2,3] => [5,6,1,3,4,2] => [5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[4,1,5,6,3,2] => [6,5,1,3,4,2] => [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,1,6,2,3,5] => [4,5,1,6,3,2] => [6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,1,6,2,5,3] => [4,6,1,5,3,2] => [5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[4,1,6,3,2,5] => [5,4,1,6,3,2] => [5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[4,1,6,3,5,2] => [6,4,1,5,3,2] => [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,1,6,5,2,3] => [5,6,1,4,3,2] => [4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[4,1,6,5,3,2] => [6,5,1,4,3,2] => [4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,2,1,3,5,6] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,2,1,3,6,5] => [2,4,1,6,5,3] => [5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,2,1,5,3,6] => [2,5,1,4,6,3] => [4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,2,1,5,6,3] => [2,6,1,4,5,3] => [4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 2
[4,2,1,6,3,5] => [2,5,1,6,4,3] => [6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,2,1,6,5,3] => [2,6,1,5,4,3] => [5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[4,2,3,1,5,6] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[4,2,3,1,6,5] => [2,3,1,6,5,4] => [3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[4,2,3,5,1,6] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[4,2,3,5,6,1] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
[4,2,3,6,1,5] => [2,3,1,6,4,5] => [3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 0
[4,2,3,6,5,1] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
[4,2,5,1,3,6] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,2,5,1,6,3] => [2,6,1,3,5,4] => [5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,2,5,3,1,6] => [2,4,1,3,6,5] => [4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[4,2,5,3,6,1] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[4,2,5,6,1,3] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,2,5,6,3,1] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[4,2,6,1,3,5] => [2,5,1,6,3,4] => [5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[4,2,6,1,5,3] => [2,6,1,5,3,4] => [6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,2,6,3,1,5] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,2,6,3,5,1] => [2,4,1,5,3,6] => [5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[4,2,6,5,1,3] => [2,6,1,4,3,5] => [4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,2,6,5,3,1] => [2,5,1,4,3,6] => [4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[4,3,1,2,5,6] => [4,2,1,5,6,3] => [2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,3,1,2,6,5] => [4,2,1,6,5,3] => [2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[4,3,1,5,2,6] => [5,2,1,4,6,3] => [2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[4,3,1,5,6,2] => [6,2,1,4,5,3] => [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => 3
[4,3,1,6,2,5] => [5,2,1,6,4,3] => [2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,3,1,6,5,2] => [6,2,1,5,4,3] => [2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[4,3,2,1,5,6] => [3,2,1,5,6,4] => [2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[4,3,2,1,6,5] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[4,3,2,5,1,6] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[4,3,2,5,6,1] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[4,3,2,6,1,5] => [3,2,1,6,4,5] => [2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[4,3,2,6,5,1] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[4,3,5,1,2,6] => [5,2,1,3,6,4] => [2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,3,5,1,6,2] => [6,2,1,3,5,4] => [2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[4,3,5,2,1,6] => [4,2,1,3,6,5] => [2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[4,3,5,2,6,1] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[4,3,5,6,1,2] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,3,5,6,2,1] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[4,3,6,1,2,5] => [5,2,1,6,3,4] => [2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[4,3,6,1,5,2] => [6,2,1,5,3,4] => [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,3,6,2,1,5] => [4,2,1,6,3,5] => [2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,3,6,2,5,1] => [4,2,1,5,3,6] => [2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[4,3,6,5,1,2] => [6,2,1,4,3,5] => [2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[4,3,6,5,2,1] => [5,2,1,4,3,6] => [2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[4,5,1,2,3,6] => [4,5,1,2,6,3] => [6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,5,1,2,6,3] => [4,6,1,2,5,3] => [5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,5,1,3,2,6] => [5,4,1,2,6,3] => [4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[4,5,1,3,6,2] => [6,4,1,2,5,3] => [4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[4,5,1,6,2,3] => [5,6,1,2,4,3] => [6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,5,1,6,3,2] => [6,5,1,2,4,3] => [5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[4,5,2,1,3,6] => [3,5,1,2,6,4] => [3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[4,5,2,1,6,3] => [3,6,1,2,5,4] => [3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[4,5,2,3,1,6] => [3,4,1,2,6,5] => [3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 0
[4,5,2,3,6,1] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[4,5,2,6,1,3] => [3,6,1,2,4,5] => [3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[4,5,2,6,3,1] => [3,5,1,2,4,6] => [3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[4,5,3,1,2,6] => [5,3,1,2,6,4] => [6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,5,3,1,6,2] => [6,3,1,2,5,4] => [5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,5,3,2,1,6] => [4,3,1,2,6,5] => [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[4,5,3,2,6,1] => [4,3,1,2,5,6] => [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[4,5,3,6,1,2] => [6,3,1,2,4,5] => [6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,5,3,6,2,1] => [5,3,1,2,4,6] => [5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[4,5,6,1,2,3] => [5,6,1,2,3,4] => [5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[4,5,6,1,3,2] => [6,5,1,2,3,4] => [6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,5,6,2,1,3] => [4,6,1,2,3,5] => [6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,5,6,2,3,1] => [4,5,1,2,3,6] => [5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[4,5,6,3,1,2] => [6,4,1,2,3,5] => [4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[4,5,6,3,2,1] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[4,6,1,2,3,5] => [4,5,1,6,2,3] => [5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[4,6,1,2,5,3] => [4,6,1,5,2,3] => [6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,6,1,3,2,5] => [5,4,1,6,2,3] => [6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,6,1,3,5,2] => [6,4,1,5,2,3] => [5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[4,6,1,5,2,3] => [5,6,1,4,2,3] => [4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,6,1,5,3,2] => [6,5,1,4,2,3] => [4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[4,6,2,1,3,5] => [3,5,1,6,2,4] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 0
[4,6,2,1,5,3] => [3,6,1,5,2,4] => [3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[4,6,2,3,1,5] => [3,4,1,6,2,5] => [3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[4,6,2,3,5,1] => [3,4,1,5,2,6] => [3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[4,6,2,5,1,3] => [3,6,1,4,2,5] => [3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[4,6,2,5,3,1] => [3,5,1,4,2,6] => [3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[4,6,3,1,2,5] => [5,3,1,6,2,4] => [5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[4,6,3,1,5,2] => [6,3,1,5,2,4] => [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,6,3,2,1,5] => [4,3,1,6,2,5] => [6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,6,3,2,5,1] => [4,3,1,5,2,6] => [5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[4,6,3,5,1,2] => [6,3,1,4,2,5] => [4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,6,3,5,2,1] => [5,3,1,4,2,6] => [4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[4,6,5,1,2,3] => [5,6,1,3,2,4] => [6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,6,5,1,3,2] => [6,5,1,3,2,4] => [5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[4,6,5,2,1,3] => [4,6,1,3,2,5] => [4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[4,6,5,2,3,1] => [4,5,1,3,2,6] => [4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[4,6,5,3,1,2] => [6,4,1,3,2,5] => [6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[4,6,5,3,2,1] => [5,4,1,3,2,6] => [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[5,1,2,3,4,6] => [3,4,5,1,6,2] => [6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,1,2,3,6,4] => [3,4,6,1,5,2] => [5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[5,1,2,4,3,6] => [3,5,4,1,6,2] => [4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[5,1,2,4,6,3] => [3,6,4,1,5,2] => [4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[5,1,2,6,3,4] => [3,5,6,1,4,2] => [6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,1,2,6,4,3] => [3,6,5,1,4,2] => [5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[5,1,3,2,4,6] => [4,3,5,1,6,2] => [4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[5,1,3,2,6,4] => [4,3,6,1,5,2] => [4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[5,1,3,4,2,6] => [5,3,4,1,6,2] => [6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,1,3,4,6,2] => [6,3,4,1,5,2] => [5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[5,1,3,6,2,4] => [5,3,6,1,4,2] => [5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[5,1,3,6,4,2] => [6,3,5,1,4,2] => [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,1,4,2,3,6] => [4,5,3,1,6,2] => [3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[5,1,4,2,6,3] => [4,6,3,1,5,2] => [3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[5,1,4,3,2,6] => [5,4,3,1,6,2] => [3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,1,4,3,6,2] => [6,4,3,1,5,2] => [3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[5,1,4,6,2,3] => [5,6,3,1,4,2] => [3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[5,1,4,6,3,2] => [6,5,3,1,4,2] => [3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,1,6,2,3,4] => [4,5,6,1,3,2] => [4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[5,1,6,2,4,3] => [4,6,5,1,3,2] => [4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 0
[5,1,6,3,2,4] => [5,4,6,1,3,2] => [6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,1,6,3,4,2] => [6,4,5,1,3,2] => [5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[5,1,6,4,2,3] => [5,6,4,1,3,2] => [5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[5,1,6,4,3,2] => [6,5,4,1,3,2] => [6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,2,1,3,4,6] => [2,4,5,1,6,3] => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[5,2,1,3,6,4] => [2,4,6,1,5,3] => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[5,2,1,4,3,6] => [2,5,4,1,6,3] => [6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,2,1,4,6,3] => [2,6,4,1,5,3] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[5,2,1,6,3,4] => [2,5,6,1,4,3] => [5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[5,2,1,6,4,3] => [2,6,5,1,4,3] => [6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,2,3,1,4,6] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,2,3,1,6,4] => [2,3,6,1,5,4] => [5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[5,2,3,4,1,6] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[5,2,3,4,6,1] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[5,2,3,6,1,4] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,2,3,6,4,1] => [2,3,5,1,4,6] => [5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[5,2,4,1,3,6] => [2,5,3,1,6,4] => [3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,2,4,1,6,3] => [2,6,3,1,5,4] => [3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
[5,2,4,3,1,6] => [2,4,3,1,6,5] => [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[5,2,4,3,6,1] => [2,4,3,1,5,6] => [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => 2
[5,2,4,6,1,3] => [2,6,3,1,4,5] => [3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,2,4,6,3,1] => [2,5,3,1,4,6] => [3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[5,2,6,1,3,4] => [2,5,6,1,3,4] => [6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,2,6,1,4,3] => [2,6,5,1,3,4] => [5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[5,2,6,3,1,4] => [2,4,6,1,3,5] => [4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[5,2,6,3,4,1] => [2,4,5,1,3,6] => [4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[5,2,6,4,1,3] => [2,6,4,1,3,5] => [6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,2,6,4,3,1] => [2,5,4,1,3,6] => [5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[5,3,1,2,4,6] => [4,2,5,1,6,3] => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[5,3,1,2,6,4] => [4,2,6,1,5,3] => [2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[5,3,1,4,2,6] => [5,2,4,1,6,3] => [2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,3,1,4,6,2] => [6,2,4,1,5,3] => [2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[5,3,1,6,2,4] => [5,2,6,1,4,3] => [2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[5,3,1,6,4,2] => [6,2,5,1,4,3] => [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,3,2,1,4,6] => [3,2,5,1,6,4] => [2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,3,2,1,6,4] => [3,2,6,1,5,4] => [2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[5,3,2,4,1,6] => [3,2,4,1,6,5] => [2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => 1
[5,3,2,4,6,1] => [3,2,4,1,5,6] => [2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[5,3,2,6,1,4] => [3,2,6,1,4,5] => [2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,3,2,6,4,1] => [3,2,5,1,4,6] => [2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[5,3,4,1,2,6] => [5,2,3,1,6,4] => [2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[5,3,4,1,6,2] => [6,2,3,1,5,4] => [2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => 3
[5,3,4,2,1,6] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[5,3,4,2,6,1] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[5,3,4,6,1,2] => [6,2,3,1,4,5] => [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[5,3,4,6,2,1] => [5,2,3,1,4,6] => [2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[5,3,6,1,2,4] => [5,2,6,1,3,4] => [2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,3,6,1,4,2] => [6,2,5,1,3,4] => [2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[5,3,6,2,1,4] => [4,2,6,1,3,5] => [2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[5,3,6,2,4,1] => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[5,3,6,4,1,2] => [6,2,4,1,3,5] => [2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,3,6,4,2,1] => [5,2,4,1,3,6] => [2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[5,4,1,2,3,6] => [4,5,2,1,6,3] => [4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[5,4,1,2,6,3] => [4,6,2,1,5,3] => [4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[5,4,1,3,2,6] => [5,4,2,1,6,3] => [6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,4,1,3,6,2] => [6,4,2,1,5,3] => [5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[5,4,1,6,2,3] => [5,6,2,1,4,3] => [5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[5,4,1,6,3,2] => [6,5,2,1,4,3] => [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,4,2,1,3,6] => [3,5,2,1,6,4] => [6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,4,2,1,6,3] => [3,6,2,1,5,4] => [5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[5,4,2,3,1,6] => [3,4,2,1,6,5] => [4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[5,4,2,3,6,1] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[5,4,2,6,1,3] => [3,6,2,1,4,5] => [6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,4,2,6,3,1] => [3,5,2,1,4,6] => [5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[5,4,3,1,2,6] => [5,3,2,1,6,4] => [3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[5,4,3,1,6,2] => [6,3,2,1,5,4] => [3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[5,4,3,2,1,6] => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => 0
[5,4,3,2,6,1] => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[5,4,3,6,1,2] => [6,3,2,1,4,5] => [3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[5,4,3,6,2,1] => [5,3,2,1,4,6] => [3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[5,4,6,1,2,3] => [5,6,2,1,3,4] => [6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,4,6,1,3,2] => [6,5,2,1,3,4] => [5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[5,4,6,2,1,3] => [4,6,2,1,3,5] => [4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[5,4,6,2,3,1] => [4,5,2,1,3,6] => [4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[5,4,6,3,1,2] => [6,4,2,1,3,5] => [6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,4,6,3,2,1] => [5,4,2,1,3,6] => [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[5,6,1,2,3,4] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 0
[5,6,1,2,4,3] => [4,6,5,1,2,3] => [4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[5,6,1,3,2,4] => [5,4,6,1,2,3] => [5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[5,6,1,3,4,2] => [6,4,5,1,2,3] => [6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,6,1,4,2,3] => [5,6,4,1,2,3] => [6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,6,1,4,3,2] => [6,5,4,1,2,3] => [5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[5,6,2,1,3,4] => [3,5,6,1,2,4] => [5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[5,6,2,1,4,3] => [3,6,5,1,2,4] => [6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,6,2,3,1,4] => [3,4,6,1,2,5] => [6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,6,2,3,4,1] => [3,4,5,1,2,6] => [5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[5,6,2,4,1,3] => [3,6,4,1,2,5] => [4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[5,6,2,4,3,1] => [3,5,4,1,2,6] => [4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[5,6,3,1,2,4] => [5,3,6,1,2,4] => [6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,6,3,1,4,2] => [6,3,5,1,2,4] => [5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[5,6,3,2,1,4] => [4,3,6,1,2,5] => [4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[5,6,3,2,4,1] => [4,3,5,1,2,6] => [4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[5,6,3,4,1,2] => [6,3,4,1,2,5] => [6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[5,6,3,4,2,1] => [5,3,4,1,2,6] => [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[5,6,4,1,2,3] => [5,6,3,1,2,4] => [3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,6,4,1,3,2] => [6,5,3,1,2,4] => [3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[5,6,4,2,1,3] => [4,6,3,1,2,5] => [3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[5,6,4,2,3,1] => [4,5,3,1,2,6] => [3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[5,6,4,3,1,2] => [6,4,3,1,2,5] => [3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,6,4,3,2,1] => [5,4,3,1,2,6] => [3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[6,1,2,3,4,5] => [3,4,5,6,1,2] => [5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[6,1,2,3,5,4] => [3,4,6,5,1,2] => [6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,1,2,4,3,5] => [3,5,4,6,1,2] => [6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,1,2,4,5,3] => [3,6,4,5,1,2] => [5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[6,1,2,5,3,4] => [3,5,6,4,1,2] => [4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[6,1,2,5,4,3] => [3,6,5,4,1,2] => [4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[6,1,3,2,4,5] => [4,3,5,6,1,2] => [6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,1,3,2,5,4] => [4,3,6,5,1,2] => [5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[6,1,3,4,2,5] => [5,3,4,6,1,2] => [5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[6,1,3,4,5,2] => [6,3,4,5,1,2] => [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,1,3,5,2,4] => [5,3,6,4,1,2] => [4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[6,1,3,5,4,2] => [6,3,5,4,1,2] => [4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[6,1,4,2,3,5] => [4,5,3,6,1,2] => [3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,1,4,2,5,3] => [4,6,3,5,1,2] => [3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[6,1,4,3,2,5] => [5,4,3,6,1,2] => [3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[6,1,4,3,5,2] => [6,4,3,5,1,2] => [3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,1,4,5,2,3] => [5,6,3,4,1,2] => [3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[6,1,4,5,3,2] => [6,5,3,4,1,2] => [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[6,1,5,2,3,4] => [4,5,6,3,1,2] => [6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,1,5,2,4,3] => [4,6,5,3,1,2] => [5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[6,1,5,3,2,4] => [5,4,6,3,1,2] => [5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[6,1,5,3,4,2] => [6,4,5,3,1,2] => [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,1,5,4,2,3] => [5,6,4,3,1,2] => [4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => 0
[6,1,5,4,3,2] => [6,5,4,3,1,2] => [4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[6,2,1,3,4,5] => [2,4,5,6,1,3] => [6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,2,1,3,5,4] => [2,4,6,5,1,3] => [5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[6,2,1,4,3,5] => [2,5,4,6,1,3] => [5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[6,2,1,4,5,3] => [2,6,4,5,1,3] => [6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,2,1,5,3,4] => [2,5,6,4,1,3] => [4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[6,2,1,5,4,3] => [2,6,5,4,1,3] => [4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[6,2,3,1,4,5] => [2,3,5,6,1,4] => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[6,2,3,1,5,4] => [2,3,6,5,1,4] => [6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,2,3,4,1,5] => [2,3,4,6,1,5] => [6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,2,3,4,5,1] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[6,2,3,5,1,4] => [2,3,6,4,1,5] => [4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[6,2,3,5,4,1] => [2,3,5,4,1,6] => [4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[6,2,4,1,3,5] => [2,5,3,6,1,4] => [3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[6,2,4,1,5,3] => [2,6,3,5,1,4] => [3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,2,4,3,1,5] => [2,4,3,6,1,5] => [3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,2,4,3,5,1] => [2,4,3,5,1,6] => [3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[6,2,4,5,1,3] => [2,6,3,4,1,5] => [3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[6,2,4,5,3,1] => [2,5,3,4,1,6] => [3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[6,2,5,1,3,4] => [2,5,6,3,1,4] => [5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[6,2,5,1,4,3] => [2,6,5,3,1,4] => [6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,2,5,3,1,4] => [2,4,6,3,1,5] => [6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,2,5,3,4,1] => [2,4,5,3,1,6] => [5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[6,2,5,4,1,3] => [2,6,4,3,1,5] => [4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[6,2,5,4,3,1] => [2,5,4,3,1,6] => [4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[6,3,1,2,4,5] => [4,2,5,6,1,3] => [2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[6,3,1,2,5,4] => [4,2,6,5,1,3] => [2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[6,3,1,4,2,5] => [5,2,4,6,1,3] => [2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[6,3,1,4,5,2] => [6,2,4,5,1,3] => [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[6,3,1,5,2,4] => [5,2,6,4,1,3] => [2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[6,3,1,5,4,2] => [6,2,5,4,1,3] => [2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[6,3,2,1,4,5] => [3,2,5,6,1,4] => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[6,3,2,1,5,4] => [3,2,6,5,1,4] => [2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[6,3,2,4,1,5] => [3,2,4,6,1,5] => [2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[6,3,2,4,5,1] => [3,2,4,5,1,6] => [2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[6,3,2,5,1,4] => [3,2,6,4,1,5] => [2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[6,3,2,5,4,1] => [3,2,5,4,1,6] => [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[6,3,4,1,2,5] => [5,2,3,6,1,4] => [2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[6,3,4,1,5,2] => [6,2,3,5,1,4] => [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[6,3,4,2,1,5] => [4,2,3,6,1,5] => [2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[6,3,4,2,5,1] => [4,2,3,5,1,6] => [2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[6,3,4,5,1,2] => [6,2,3,4,1,5] => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => 3
[6,3,4,5,2,1] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[6,3,5,1,2,4] => [5,2,6,3,1,4] => [2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[6,3,5,1,4,2] => [6,2,5,3,1,4] => [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[6,3,5,2,1,4] => [4,2,6,3,1,5] => [2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[6,3,5,2,4,1] => [4,2,5,3,1,6] => [2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[6,3,5,4,1,2] => [6,2,4,3,1,5] => [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[6,3,5,4,2,1] => [5,2,4,3,1,6] => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[6,4,1,2,3,5] => [4,5,2,6,1,3] => [6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,4,1,2,5,3] => [4,6,2,5,1,3] => [5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[6,4,1,3,2,5] => [5,4,2,6,1,3] => [5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[6,4,1,3,5,2] => [6,4,2,5,1,3] => [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,4,1,5,2,3] => [5,6,2,4,1,3] => [4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[6,4,1,5,3,2] => [6,5,2,4,1,3] => [4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[6,4,2,1,3,5] => [3,5,2,6,1,4] => [5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[6,4,2,1,5,3] => [3,6,2,5,1,4] => [6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,4,2,3,1,5] => [3,4,2,6,1,5] => [6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,4,2,3,5,1] => [3,4,2,5,1,6] => [5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[6,4,2,5,1,3] => [3,6,2,4,1,5] => [4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[6,4,2,5,3,1] => [3,5,2,4,1,6] => [4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[6,4,3,1,2,5] => [5,3,2,6,1,4] => [3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => 0
[6,4,3,1,5,2] => [6,3,2,5,1,4] => [3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[6,4,3,2,1,5] => [4,3,2,6,1,5] => [3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[6,4,3,2,5,1] => [4,3,2,5,1,6] => [3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => 0
[6,4,3,5,1,2] => [6,3,2,4,1,5] => [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[6,4,3,5,2,1] => [5,3,2,4,1,6] => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[6,4,5,1,2,3] => [5,6,2,3,1,4] => [5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[6,4,5,1,3,2] => [6,5,2,3,1,4] => [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,4,5,2,1,3] => [4,6,2,3,1,5] => [6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,4,5,2,3,1] => [4,5,2,3,1,6] => [5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[6,4,5,3,1,2] => [6,4,2,3,1,5] => [4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[6,4,5,3,2,1] => [5,4,2,3,1,6] => [4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[6,5,1,2,3,4] => [4,5,6,2,1,3] => [5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[6,5,1,2,4,3] => [4,6,5,2,1,3] => [6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,5,1,3,2,4] => [5,4,6,2,1,3] => [4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => 0
[6,5,1,3,4,2] => [6,4,5,2,1,3] => [4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[6,5,1,4,2,3] => [5,6,4,2,1,3] => [5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[6,5,1,4,3,2] => [6,5,4,2,1,3] => [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,5,2,1,3,4] => [3,5,6,2,1,4] => [6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,5,2,1,4,3] => [3,6,5,2,1,4] => [5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[6,5,2,3,1,4] => [3,4,6,2,1,5] => [4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[6,5,2,3,4,1] => [3,4,5,2,1,6] => [4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[6,5,2,4,1,3] => [3,6,4,2,1,5] => [6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,5,2,4,3,1] => [3,5,4,2,1,6] => [5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[6,5,3,1,2,4] => [5,3,6,2,1,4] => [5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[6,5,3,1,4,2] => [6,3,5,2,1,4] => [6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,5,3,2,1,4] => [4,3,6,2,1,5] => [6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[6,5,3,2,4,1] => [4,3,5,2,1,6] => [5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[6,5,3,4,1,2] => [6,3,4,2,1,5] => [4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[6,5,3,4,2,1] => [5,3,4,2,1,6] => [4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[6,5,4,1,2,3] => [5,6,3,2,1,4] => [3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[6,5,4,1,3,2] => [6,5,3,2,1,4] => [3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,5,4,2,1,3] => [4,6,3,2,1,5] => [3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[6,5,4,2,3,1] => [4,5,3,2,1,6] => [3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[6,5,4,3,1,2] => [6,4,3,2,1,5] => [3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[6,5,4,3,2,1] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
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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 3,2,1 11,9,3,1 53,44,18,4,1 309,265,110,30,5,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 3 + 2\ q + q^{2}$
$F_{4} = 11 + 9\ q + 3\ q^{2} + q^{3}$
$F_{5} = 53 + 44\ q + 18\ q^{2} + 4\ q^{3} + q^{4}$
$F_{6} = 309 + 265\ q + 110\ q^{2} + 30\ q^{3} + 5\ q^{4} + q^{5}$
Description
Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless.
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
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
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