Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
Mp00296: Dyck paths —Knuth-Krattenthaler⟶ Dyck paths
St000120: Dyck paths ⟶ ℤ
Values
[1] => [1,0] => [1,0] => 0
[1,2] => [1,0,1,0] => [1,1,0,0] => 0
[2,1] => [1,1,0,0] => [1,0,1,0] => 1
[1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
[1,3,2] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => 1
[2,1,3] => [1,1,0,0,1,0] => [1,0,1,0,1,0] => 1
[2,3,1] => [1,1,0,1,0,0] => [1,0,1,1,0,0] => 1
[3,1,2] => [1,1,1,0,0,0] => [1,1,0,0,1,0] => 2
[3,2,1] => [1,1,1,0,0,0] => [1,1,0,0,1,0] => 2
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,0] => 1
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0] => 1
[1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0] => 1
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => 2
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0] => 1
[2,4,1,3] => [1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[2,4,3,1] => [1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => 2
[3,1,2,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0] => 2
[3,1,4,2] => [1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => 2
[3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0] => 2
[3,2,4,1] => [1,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0] => 2
[3,4,1,2] => [1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[3,4,2,1] => [1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4,1,2,3] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 3
[4,1,3,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 3
[4,2,1,3] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 3
[4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 3
[4,3,1,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 3
[4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0] => 3
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 2
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 2
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 2
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => 2
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 2
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 3
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 3
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 2
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => 2
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 1
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => 2
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 2
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 2
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 2
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 2
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 3
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 2
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 3
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 2
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
>>> Load all 873 entries. <<<[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 3
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 3
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 3
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 3
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 4
[1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 2
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 2
[1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,4,5,2,6,3] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[1,4,5,3,6,2] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 2
[1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 3
[1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 4
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 2
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 3
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 3
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 3
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 3
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 3
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 3
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 4
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 2
[2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 2
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 2
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 2
[2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 3
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 3
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 2
[2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 3
[2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 2
[2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 2
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 4
[3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
[3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 3
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 3
[3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 3
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 4
[3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 3
[3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 2
[3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 3
[3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 4
[3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 3
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,5,1,2,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,5,1,4,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,5,2,4,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,5,4,2,1,6] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 4
[4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 3
[4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 4
[4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 3
[4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 3
[4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 4
[4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
[4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 4
[4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 3
[4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 3
[4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 4
[5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 4
[5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 4
[5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 4
[5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
[5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,2 1,6,11,6 1,10,35,50,24 1,15,85,225,274,120
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + 2\ q^{2}$
$F_{4} = 1 + 6\ q + 11\ q^{2} + 6\ q^{3}$
$F_{5} = 1 + 10\ q + 35\ q^{2} + 50\ q^{3} + 24\ q^{4}$
$F_{6} = 1 + 15\ q + 85\ q^{2} + 225\ q^{3} + 274\ q^{4} + 120\ q^{5}$
Description
The number of left tunnels of a Dyck path.
A tunnel is a pair (a,b) where a is the position of an open parenthesis and b is the position of the matching close parenthesis. If a+b<n then the tunnel is called left.
A tunnel is a pair (a,b) where a is the position of an open parenthesis and b is the position of the matching close parenthesis. If a+b<n then the tunnel is called left.
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.
Map
Knuth-Krattenthaler
Description
The map that sends the Dyck path to a 321-avoiding permutation, then applies the Robinson-Schensted correspondence and finally interprets the first row of the insertion tableau and the second row of the recording tableau as up steps.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and $321$-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
Interpreting a pair of two-row standard tableaux of the same shape as a Dyck path is explained by Knuth in [1, pp. 60].
Krattenthaler's bijection between Dyck paths and $321$-avoiding permutations used is Mp00119to 321-avoiding permutation (Krattenthaler), see [2].
This is the inverse of the map Mp00127left-to-right-maxima to Dyck path that interprets the left-to-right maxima of the permutation obtained from Mp00024to 321-avoiding permutation as a Dyck path.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!