Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001493: Dyck paths ⟶ ℤ
Values
[1] => [1,0] => [1,0] => 1
[1,2] => [1,0,1,0] => [1,1,0,0] => 1
[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] => 1
[1,3,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,1,3] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[2,3,1] => [1,1,0,1,0,0] => [1,1,0,1,0,0] => 1
[3,1,2] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 1
[3,2,1] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 1
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 1
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 1
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 1
[1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => 1
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 1
[2,4,1,3] => [1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,4,3,1] => [1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0] => 1
[3,1,2,4] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[3,1,4,2] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => 1
[3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[3,2,4,1] => [1,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0] => 1
[3,4,1,2] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[3,4,2,1] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => 1
[4,1,2,3] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[4,1,3,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[4,2,1,3] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[4,3,1,2] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 1
[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] => 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 2
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 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] => 2
[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] => 2
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 1
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 1
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 1
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 1
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,0] => 1
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
>>> Load all 873 entries. <<<[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[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] => 1
[1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,2,3,6,4,5] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 2
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,2,4,6,3,5] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,2,5,3,4,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,2,5,3,6,4] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,2,6,3,4,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,6,3,5,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,6,4,3,5] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,6,4,5,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,6,5,3,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,2,6,5,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,3,6,2,5,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,3,6,4,5,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,3,6,5,2,4] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,3,6,5,4,2] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,4,5,6,2,3] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,5,6,3,2] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,4,6,2,3,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,4,6,3,2,5] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,4,6,3,5,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,4,6,5,2,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,4,6,5,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,5,6,2,3,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,5,6,2,4,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,5,6,3,2,4] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,5,6,3,4,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,5,6,4,2,3] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,5,6,4,3,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => 2
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => 2
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => 2
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 3
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0] => 2
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => 2
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 2
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 2
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 2
[2,1,6,3,4,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,1,6,3,5,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,1,6,4,3,5] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 2
[2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[2,3,5,1,4,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 1
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 1
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 2
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[2,4,5,3,1,6] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[2,4,6,1,3,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[2,4,6,3,1,5] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[2,4,6,3,5,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[2,4,6,5,3,1] => [1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[2,5,1,6,3,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[2,5,1,6,4,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[2,5,3,6,4,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 1
[2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[2,5,4,6,3,1] => [1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[2,5,6,1,3,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[2,5,6,1,4,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[2,5,6,3,1,4] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[2,5,6,3,4,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[2,5,6,4,3,1] => [1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,1,2,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[3,1,2,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[3,1,2,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,1,2,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[3,1,2,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[3,1,4,2,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[3,1,5,2,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[3,1,5,4,2,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[3,1,5,4,6,2] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[3,1,5,6,2,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[3,1,5,6,4,2] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,1,6,2,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,1,6,4,2,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,1,6,4,5,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,1,6,5,4,2] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
[3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
[3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[3,2,1,6,4,5] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 2
[3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[3,2,5,1,4,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[3,2,5,1,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[3,2,5,4,1,6] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[3,2,5,4,6,1] => [1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[3,2,5,6,1,4] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[3,2,5,6,4,1] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,2,6,4,1,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,2,6,4,5,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,2,6,5,1,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,2,6,5,4,1] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[3,4,2,1,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[3,4,5,1,2,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[3,4,6,1,2,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[3,4,6,1,5,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[3,4,6,2,1,5] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[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] => 1
[3,5,1,2,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 1
[3,5,1,4,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[3,5,1,6,2,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,5,1,6,4,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[3,5,2,1,6,4] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 1
[3,5,2,4,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[3,5,2,6,1,4] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,5,2,6,4,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[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] => 1
[3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[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] => 1
[3,5,4,2,6,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[3,5,4,6,1,2] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[3,5,6,1,2,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,5,6,1,4,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,5,6,2,1,4] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,5,6,2,4,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,5,6,4,1,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,5,6,4,2,1] => [1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[3,6,1,2,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,1,2,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,1,4,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,1,4,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,1,5,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,1,5,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,2,1,4,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,2,1,5,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,2,4,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,2,4,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,2,5,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,2,5,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,4,1,2,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,4,2,1,5] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,4,2,5,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,4,5,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,5,1,2,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,5,1,4,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,5,2,4,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,5,4,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,6,5,4,2,1] => [1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,1,2,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,1,2,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,1,2,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,1,3,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,1,3,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[4,1,3,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,1,3,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,1,3,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,1,5,2,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[4,1,5,2,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,1,5,3,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[4,1,5,3,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,1,5,6,2,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[4,1,5,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[4,1,6,2,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,1,6,3,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,1,6,3,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,1,6,5,2,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,1,6,5,3,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,2,1,3,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,2,1,3,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[4,2,1,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,2,1,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,2,1,6,5,3] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[4,2,3,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,2,3,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,2,3,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,2,5,1,3,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[4,2,5,1,6,3] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,2,5,3,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[4,2,5,3,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,2,5,6,1,3] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[4,2,5,6,3,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[4,2,6,1,3,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,2,6,3,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,2,6,3,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,2,6,5,1,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,2,6,5,3,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,3,1,2,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,3,1,2,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,3,1,6,5,2] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[4,3,2,5,6,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[4,3,2,6,1,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,3,2,6,5,1] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[4,3,5,1,2,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[4,3,5,1,6,2] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,3,5,2,1,6] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[4,3,5,2,6,1] => [1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[4,3,5,6,1,2] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[4,3,5,6,2,1] => [1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[4,3,6,1,2,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,3,6,1,5,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,3,6,2,1,5] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,3,6,2,5,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,3,6,5,2,1] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[4,5,1,2,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,5,1,2,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,5,1,3,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,5,1,3,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,5,1,6,2,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,5,1,6,3,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,5,2,1,3,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,5,2,1,6,3] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,5,2,3,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,5,2,3,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,5,2,6,1,3] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,5,2,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,5,3,1,2,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,5,3,1,6,2] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,5,3,2,1,6] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[4,5,3,2,6,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[4,5,3,6,1,2] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,5,3,6,2,1] => [1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,1,3,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,2,1,3] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,2,3,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,3,1,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,5,6,3,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[4,6,1,2,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,1,2,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,1,3,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,1,3,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,1,5,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,1,5,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,2,1,3,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,2,1,5,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,2,3,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,2,3,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,2,5,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,2,5,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,3,1,2,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,3,1,5,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,3,2,5,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,3,5,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,3,5,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,5,1,2,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,5,1,3,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,5,2,1,3] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,5,2,3,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,5,3,1,2] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,6,5,3,2,1] => [1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[5,1,2,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,1,2,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,1,2,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,1,2,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,1,2,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,1,3,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,1,3,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,1,3,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,1,3,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,1,3,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,1,3,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,1,4,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,1,4,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,1,4,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,1,4,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,1,4,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,1,6,2,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,1,6,2,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,1,6,3,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,1,6,3,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,1,6,4,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,1,6,4,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,2,1,3,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,2,1,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,2,1,4,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,2,1,4,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,2,1,6,3,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,2,1,6,4,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,2,3,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,2,3,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,2,3,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,2,3,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,2,3,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,2,4,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,2,4,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,2,4,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,2,4,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,2,4,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,2,6,1,3,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,2,6,1,4,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,2,6,3,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,2,6,3,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,2,6,4,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,2,6,4,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,3,1,2,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,3,1,4,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,3,1,4,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,3,1,6,2,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,1,6,4,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,2,1,4,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,3,2,1,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,3,2,4,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,3,2,6,1,4] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,2,6,4,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,4,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,3,4,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,3,4,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,4,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,3,6,1,2,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,3,6,1,4,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,3,6,2,1,4] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,3,6,2,4,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,3,6,4,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,3,6,4,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,4,1,2,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,4,1,3,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,4,1,3,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,4,1,6,2,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,4,1,6,3,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,4,2,1,3,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,4,2,1,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,4,2,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,4,2,3,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,4,2,6,1,3] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,4,2,6,3,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,4,3,1,2,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,4,3,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[5,4,3,2,6,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[5,4,3,6,1,2] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,4,3,6,2,1] => [1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[5,4,6,1,2,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,4,6,1,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,4,6,2,1,3] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,4,6,2,3,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,4,6,3,1,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,4,6,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,1,3,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,1,3,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,1,4,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,1,4,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,2,1,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,2,3,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,2,3,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,2,4,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,2,4,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,3,1,2,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,3,1,4,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,3,2,1,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,3,2,4,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,3,4,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,4,1,2,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,4,1,3,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,4,2,1,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,4,2,3,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,4,3,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,6,4,3,2,1] => [1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 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:
23,1 111,9 672,47,1
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 6\ q$
$F_{4} = 23\ q + q^{2}$
$F_{5} = 111\ q + 9\ q^{2}$
$F_{6} = 672\ q + 47\ q^{2} + q^{3}$
Description
The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra.
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
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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