Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00310: Permutations —toric promotion⟶ Permutations
St000373: Permutations ⟶ ℤ
Values
[1] => [1,0] => [2,1] => [2,1] => 0
[1,2] => [1,0,1,0] => [3,1,2] => [2,1,3] => 0
[2,1] => [1,1,0,0] => [2,3,1] => [1,3,2] => 0
[1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => [3,4,2,1] => 0
[1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => [1,2,3,4] => 0
[2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => [4,3,2,1] => 1
[2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => [3,2,1,4] => 1
[3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => [4,2,1,3] => 1
[3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => [4,2,1,3] => 1
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [4,5,2,3,1] => 0
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [3,5,4,1,2] => 1
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,2,4,5,3] => 0
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [4,3,5,1,2] => 1
[1,4,2,3] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,2,3,4,5] => 0
[1,4,3,2] => [1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,2,3,4,5] => 0
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5,4,2,3,1] => 1
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,5,3,4,2] => 2
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [4,2,5,3,1] => 1
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,3,5,2,1] => 1
[2,4,1,3] => [1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [1,3,2,4,5] => 0
[2,4,3,1] => [1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [1,3,2,4,5] => 0
[3,1,2,4] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,2,4,3,1] => 2
[3,1,4,2] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [5,4,3,2,1] => 2
[3,2,1,4] => [1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5,2,4,3,1] => 2
[3,2,4,1] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [5,4,3,2,1] => 2
[3,4,1,2] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,2,3,1,5] => 2
[3,4,2,1] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,2,3,1,5] => 2
[4,1,2,3] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,1,4] => 2
[4,1,3,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,1,4] => 2
[4,2,1,3] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,1,4] => 2
[4,2,3,1] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,1,4] => 2
[4,3,1,2] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,1,4] => 2
[4,3,2,1] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,2,3,1,4] => 2
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [5,6,2,3,4,1] => 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [4,6,2,5,1,3] => 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [3,6,5,1,2,4] => 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [5,6,4,1,2,3] => 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [3,6,4,5,1,2] => 2
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [3,6,4,5,1,2] => 2
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,2,5,6,3,4] => 0
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [1,2,4,6,5,3] => 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [5,3,6,1,2,4] => 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [5,4,6,1,2,3] => 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [4,3,6,1,5,2] => 2
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [4,3,6,1,5,2] => 2
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [1,2,3,5,6,4] => 0
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [1,2,5,4,6,3] => 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [1,2,3,5,6,4] => 0
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [1,2,5,4,6,3] => 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [5,3,4,6,1,2] => 2
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [5,3,4,6,1,2] => 2
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,2,3,4,5,6] => 0
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,2,3,4,5,6] => 0
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,2,3,4,5,6] => 0
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,2,3,4,5,6] => 0
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,2,3,4,5,6] => 0
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,2,3,4,5,6] => 0
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [6,5,2,3,4,1] => 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [6,4,2,5,1,3] => 2
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [1,6,3,5,2,4] => 2
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [6,5,4,1,2,3] => 2
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [1,6,3,4,5,2] => 3
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [1,6,3,4,5,2] => 3
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [5,2,6,3,4,1] => 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [4,2,6,5,1,3] => 2
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [5,3,6,2,4,1] => 1
[2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [4,5,6,2,3,1] => 0
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,3,6,5,1,2] => 2
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,3,6,5,1,2] => 2
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [1,3,2,5,6,4] => 0
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [1,5,2,4,6,3] => 1
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [1,3,2,5,6,4] => 0
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [1,5,2,4,6,3] => 1
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [1,5,3,4,6,2] => 2
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [1,5,3,4,6,2] => 2
[2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,3,2,4,5,6] => 0
[2,5,1,4,3] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,3,2,4,5,6] => 0
[2,5,3,1,4] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,3,2,4,5,6] => 0
[2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,3,2,4,5,6] => 0
[2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,3,2,4,5,6] => 0
[2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,3,2,4,5,6] => 0
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,2,5,3,4,1] => 2
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,2,1,4,5,3] => 3
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [6,5,3,2,4,1] => 2
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [6,5,4,2,3,1] => 2
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,6,4,3,5,2] => 2
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,6,4,3,5,2] => 2
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [6,2,5,3,4,1] => 2
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [6,2,1,4,5,3] => 3
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [6,5,3,2,4,1] => 2
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [6,5,4,2,3,1] => 2
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,6,4,3,5,2] => 2
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,6,4,3,5,2] => 2
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,3,6,4,1] => 2
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,2,4,6,3,1] => 2
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,3,6,4,1] => 2
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,2,4,6,3,1] => 2
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [5,4,3,6,2,1] => 2
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [5,4,3,6,2,1] => 2
[3,5,1,2,4] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,2,1,3,5,6] => 1
[3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,2,1,3,5,6] => 1
>>> Load all 1245 entries. <<<[3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,2,1,3,5,6] => 1
[3,5,2,4,1] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,2,1,3,5,6] => 1
[3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,2,1,3,5,6] => 1
[3,5,4,2,1] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,2,1,3,5,6] => 1
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,2,3,5,4,1] => 3
[4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,2,5,4,3,1] => 3
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,2,3,5,4,1] => 3
[4,1,3,5,2] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,2,5,4,3,1] => 3
[4,1,5,2,3] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,5,3,4,2,1] => 3
[4,1,5,3,2] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,5,3,4,2,1] => 3
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,2,3,5,4,1] => 3
[4,2,1,5,3] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,2,5,4,3,1] => 3
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,2,3,5,4,1] => 3
[4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,2,5,4,3,1] => 3
[4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,5,3,4,2,1] => 3
[4,2,5,3,1] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,5,3,4,2,1] => 3
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,2,3,5,4,1] => 3
[4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,2,5,4,3,1] => 3
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [6,2,3,5,4,1] => 3
[4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [6,2,5,4,3,1] => 3
[4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,5,3,4,2,1] => 3
[4,3,5,2,1] => [1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [6,5,3,4,2,1] => 3
[4,5,1,2,3] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,2,3,4,1,6] => 3
[4,5,1,3,2] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,2,3,4,1,6] => 3
[4,5,2,1,3] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,2,3,4,1,6] => 3
[4,5,2,3,1] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,2,3,4,1,6] => 3
[4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,2,3,4,1,6] => 3
[4,5,3,2,1] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,2,3,4,1,6] => 3
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,2,3,4,1,5] => 3
[1,2,5,6,3,4] => [1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [6,7,4,5,1,2,3] => 2
[1,2,5,6,4,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [6,7,4,5,1,2,3] => 2
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [1,2,6,7,3,4,5] => 0
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [1,2,5,7,3,6,4] => 1
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [1,2,4,7,6,3,5] => 1
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [1,2,6,7,5,3,4] => 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [1,2,4,7,5,6,3] => 2
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [1,2,4,7,5,6,3] => 2
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [1,5,6,7,2,3,4] => 0
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [1,2,3,6,7,4,5] => 0
[1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [1,2,3,5,7,6,4] => 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [1,2,6,4,7,3,5] => 1
[1,4,2,5,6,3] => [1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [1,2,6,5,7,3,4] => 1
[1,4,2,6,3,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [1,2,5,4,7,6,3] => 2
[1,4,2,6,5,3] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [1,2,5,4,7,6,3] => 2
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [1,2,3,6,7,4,5] => 0
[1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [1,2,3,5,7,6,4] => 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [1,2,6,4,7,3,5] => 1
[1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [1,2,6,5,7,3,4] => 1
[1,4,3,6,2,5] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [1,2,5,4,7,6,3] => 2
[1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [1,2,5,4,7,6,3] => 2
[1,4,5,2,3,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [6,3,4,7,1,2,5] => 2
[1,4,5,3,2,6] => [1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [6,3,4,7,1,2,5] => 2
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,2,3,4,6,7,5] => 0
[1,5,2,3,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,2,3,6,5,7,4] => 1
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,2,3,4,6,7,5] => 0
[1,5,2,4,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,2,3,6,5,7,4] => 1
[1,5,2,6,3,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,2,6,4,5,7,3] => 2
[1,5,2,6,4,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,2,6,4,5,7,3] => 2
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,2,3,4,6,7,5] => 0
[1,5,3,2,6,4] => [1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,2,3,6,5,7,4] => 1
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,2,3,4,6,7,5] => 0
[1,5,3,4,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,2,3,6,5,7,4] => 1
[1,5,3,6,2,4] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,2,6,4,5,7,3] => 2
[1,5,3,6,4,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,2,6,4,5,7,3] => 2
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,2,3,4,6,7,5] => 0
[1,5,4,2,6,3] => [1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,2,3,6,5,7,4] => 1
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,2,3,4,6,7,5] => 0
[1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,2,3,6,5,7,4] => 1
[1,5,4,6,2,3] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,2,6,4,5,7,3] => 2
[1,5,4,6,3,2] => [1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,2,6,4,5,7,3] => 2
[1,6,2,3,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,2,3,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,2,4,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,2,4,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,2,5,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,2,5,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,3,2,4,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,3,2,5,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,3,4,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,3,4,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,3,5,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,3,5,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,4,2,3,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,4,2,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,4,3,2,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,4,3,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,4,5,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,4,5,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,5,2,3,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,5,2,4,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,5,3,2,4] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,5,3,4,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,5,4,2,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[1,6,5,4,3,2] => [1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,2,3,4,5,6,7] => 0
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [7,6,5,1,2,3,4] => 2
[2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [7,6,4,5,1,2,3] => 3
[2,1,5,6,4,3] => [1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [7,6,4,5,1,2,3] => 3
[2,4,1,3,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [1,3,2,6,7,4,5] => 0
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [1,3,2,5,7,6,4] => 1
[2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [1,3,2,6,7,4,5] => 0
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [1,3,2,5,7,6,4] => 1
[2,5,1,3,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,3,2,4,6,7,5] => 0
[2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,3,2,6,5,7,4] => 1
[2,5,1,4,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,3,2,4,6,7,5] => 0
[2,5,1,4,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,3,2,6,5,7,4] => 1
[2,5,3,1,4,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,3,2,4,6,7,5] => 0
[2,5,3,1,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,3,2,6,5,7,4] => 1
[2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,3,2,4,6,7,5] => 0
[2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,3,2,6,5,7,4] => 1
[2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,3,2,4,6,7,5] => 0
[2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,3,2,6,5,7,4] => 1
[2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,3,2,4,6,7,5] => 0
[2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,3,2,6,5,7,4] => 1
[2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,1,3,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,1,4,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,1,4,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,1,5,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,3,1,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,3,1,5,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,3,4,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,3,5,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,4,1,5,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,4,3,1,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,5,1,4,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,5,3,1,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,5,3,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,5,4,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,3,2,4,5,6,7] => 0
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,5,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,5,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,5,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,5,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,1,5,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,1,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,1,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,1,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,1,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,1,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,1,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,3,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,3,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,3,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,3,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,4,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,4,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,4,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,4,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,5,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,5,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,5,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,5,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,5,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,1,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,1,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,1,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,1,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,2,1,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,2,1,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,2,4,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,2,5,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,4,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,4,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,5,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,5,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,5,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,5,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,1,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,1,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,1,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,1,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,2,1,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,2,1,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,2,3,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,2,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,2,5,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,2,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,3,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,3,1,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,3,2,1,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,3,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,5,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,5,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,5,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,5,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,4,5,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,1,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,1,2,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,1,3,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,1,3,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,1,4,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,1,4,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,2,1,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,2,1,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,2,3,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,2,3,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,2,4,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,2,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,3,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,3,1,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,3,2,1,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,3,2,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,3,4,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,4,1,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,4,2,1,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,4,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,4,3,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,2,3,4,5,1,6] => 4
[1,2,6,7,3,4,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [7,8,4,5,6,1,2,3] => 3
[1,2,6,7,3,5,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [7,8,4,5,6,1,2,3] => 3
[1,2,6,7,4,3,5] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [7,8,4,5,6,1,2,3] => 3
[1,2,6,7,4,5,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [7,8,4,5,6,1,2,3] => 3
[1,2,6,7,5,3,4] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [7,8,4,5,6,1,2,3] => 3
[1,2,6,7,5,4,3] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [8,1,2,5,6,7,3,4] => [7,8,4,5,6,1,2,3] => 3
[1,4,2,5,6,3,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [1,2,7,5,8,3,4,6] => 1
[1,4,3,5,6,2,7] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,8,6,2,4,5,7] => [1,2,7,5,8,3,4,6] => 1
[1,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,4,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,4,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,4,6,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,5,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,5,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,5,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,5,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,6,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,6,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,2,4,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,2,4,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,2,5,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,2,5,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,2,6,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,2,6,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,4,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,4,2,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,4,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,4,6,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,4,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,5,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,5,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,5,4,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,5,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,5,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,5,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,6,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,6,2,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,6,4,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,6,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,6,5,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,3,6,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,2,3,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,2,3,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,2,5,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,2,5,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,2,6,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,2,6,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,3,2,5,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,3,2,6,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,3,5,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,3,6,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,3,6,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,5,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,5,2,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,5,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,5,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,6,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,6,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,6,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,6,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,6,5,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,2,3,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,2,3,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,2,4,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,2,4,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,2,6,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,2,6,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,3,2,4,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,3,2,6,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,3,4,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,3,4,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,3,6,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,3,6,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,4,2,3,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,4,2,6,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,4,6,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,6,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,6,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,6,3,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,6,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,2,3,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,2,4,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,2,4,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,2,5,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,3,2,4,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,3,4,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,3,4,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,3,5,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,3,5,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,4,2,3,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,4,2,5,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,4,3,5,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,4,5,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,5,3,4,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[1,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,2,3,4,5,6,7,8] => 0
[2,5,6,7,1,3,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [6,7,4,5,8,1,2,3] => 2
[2,5,6,7,1,4,3] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [6,7,4,5,8,1,2,3] => 2
[2,5,6,7,3,1,4] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [6,7,4,5,8,1,2,3] => 2
[2,5,6,7,3,4,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [6,7,4,5,8,1,2,3] => 2
[2,5,6,7,4,1,3] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [6,7,4,5,8,1,2,3] => 2
[2,5,6,7,4,3,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [6,7,4,5,8,1,2,3] => 2
[2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,3,4,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,3,5,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,3,5,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,3,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,3,6,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,4,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,4,3,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,4,5,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,4,5,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,4,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,4,6,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,5,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,5,3,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,5,4,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,5,4,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,5,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,5,6,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,6,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,6,3,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,6,4,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,6,4,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,6,5,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,1,6,5,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,1,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,1,4,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,1,5,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,1,5,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,1,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,1,6,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,4,1,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,4,1,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,4,5,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,4,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,4,6,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,4,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,5,1,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,5,1,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,5,4,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,5,4,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,5,6,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,5,6,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,6,1,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,6,1,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,6,4,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,6,4,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,6,5,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,3,6,5,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,1,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,1,3,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,1,5,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,1,5,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,1,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,1,6,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,3,1,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,3,1,6,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,3,5,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,3,5,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,3,6,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,3,6,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,5,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,5,1,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,5,3,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,5,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,5,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,5,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,6,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,6,1,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,6,3,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,6,3,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,6,5,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,4,6,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,1,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,1,3,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,1,4,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,1,4,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,1,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,1,6,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,3,1,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,3,1,6,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,3,4,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,3,4,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,3,6,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,3,6,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,4,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,4,1,6,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,4,3,1,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,4,3,6,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,4,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,4,6,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,6,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,6,1,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,6,3,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,6,3,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,6,4,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,5,6,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,1,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,1,3,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,1,4,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,1,4,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,1,5,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,1,5,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,3,1,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,3,1,5,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,3,4,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,3,4,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,3,5,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,3,5,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,4,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,4,1,5,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,4,3,1,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,4,3,5,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,4,5,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,4,5,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,5,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,5,1,4,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,5,3,1,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,5,3,4,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,5,4,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[2,7,6,5,4,3,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,3,2,4,5,6,7,8] => 0
[4,1,6,2,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,1,6,2,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,1,6,3,2,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,1,6,3,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,1,6,5,2,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,1,6,5,3,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,2,6,1,3,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,2,6,1,5,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,2,6,3,1,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,2,6,3,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,2,6,5,1,7,3] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,2,6,5,3,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,3,6,1,2,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,3,6,1,5,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,3,6,2,1,7,5] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,3,6,2,5,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,3,6,5,1,7,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[4,3,6,5,2,7,1] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,8,4,5,1,7,3,6] => [8,7,3,1,4,6,2,5] => 3
[5,1,6,7,2,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,1,6,7,2,4,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,1,6,7,3,2,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,1,6,7,3,4,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,1,6,7,4,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,1,6,7,4,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,2,6,7,1,3,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,2,6,7,1,4,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,2,6,7,3,1,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,2,6,7,3,4,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,2,6,7,4,1,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,2,6,7,4,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,3,6,7,1,2,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,3,6,7,1,4,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,3,6,7,2,1,4] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,3,6,7,2,4,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,3,6,7,4,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,3,6,7,4,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,4,6,7,1,2,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,4,6,7,1,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,4,6,7,2,1,3] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,4,6,7,2,3,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,4,6,7,3,1,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[5,4,6,7,3,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,8,7,5,6,1,3,4] => [8,7,6,4,5,2,3,1] => 4
[1,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,5,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,6,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,7,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,4,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,4,7,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,6,4,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,6,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,7,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,5,4,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,5,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,6,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,5,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,5,7,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,6,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,6,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,3,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,6,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,5,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,5,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,6,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,3,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,3,7,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,6,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,6,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,7,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,5,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,5,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,5,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,4,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,4,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[] => [] => [1] => [1] => 0
[1,8,6,7,4,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,7,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,3,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,3,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,3,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,2,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,2,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,3,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,7,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,3,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,3,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,4,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,5,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,2,3,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,3,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,3,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,3,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,6,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,7,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,7,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,2,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,6,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,7,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,2,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,6,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,5,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,6,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,7,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,3,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,5,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,4,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,5,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,3,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,4,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,2,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,7,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,7,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,2,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,2,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,6,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,2,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,2,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,6,5,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,7,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,4,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,4,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,2,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,3,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,3,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,3,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,3,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,4,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,4,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,3,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,3,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,3,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,7,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,7,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,6,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,2,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,7,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,7,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,7,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,6,5,4,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,7,5,6,4,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,6,5,7,4,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,5,7,6,4,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,4,2,5,3,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,7,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,7,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,4,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,2,5,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,2,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,5,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,4,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,2,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,5,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,5,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,4,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,2,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,2,3,4,5,6,7,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,5,2,7,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,4,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,7,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,3,7,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,5,7,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,7,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,3,2,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,6,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,5,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,3,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,2,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,4,3,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,2,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,7,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,5,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,2,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,5,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,7,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,6,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,3,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,6,3,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,2,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,7,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,6,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,5,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,5,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,2,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,6,5,4,3,2,8,7] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,2,4,3,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,3,7,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,7,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,2,5,4,3,8,7,6] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,5,2,3,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,2,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,2,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,7,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,5,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,5,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,4,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,7,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,6,5,4,2,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,3,4,2,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,5,2,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,6,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,5,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,7,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,2,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,2,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,2,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,3,2,4,5,6,7,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,2,5,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,6,2,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,3,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,2,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,3,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,3,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,6,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,3,2,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,7,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,6,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,6,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,3,2,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,5,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,4,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,7,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,3,6,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,3,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,7,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,5,3,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,2,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,2,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,4,5,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,5,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,6,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,6,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,6,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,5,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,4,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,4,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,4,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,2,7,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,2,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,6,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,4,6,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,3,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,6,4,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,3,7,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,4,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,5,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,3,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,3,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,3,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,3,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,2,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,2,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,6,2,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,2,6,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,2,3,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,3,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,5,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,6,7,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,6,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,6,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,7,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,2,5,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,2,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,2,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,6,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,3,6,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,4,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,6,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,4,6,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,7,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,4,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,4,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,3,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,5,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,7,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,2,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,3,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,3,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,3,5,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,2,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,2,4,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,2,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,4,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,5,4,6,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,7,3,6,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,4,6,5,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,6,3,2,5,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,5,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,6,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,4,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,5,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,4,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,2,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,3,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,7,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,3,6,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,3,5,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,2,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,3,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,6,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,6,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,6,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,7,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,7,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,4,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,3,4,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,4,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,4,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,4,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,5,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,7,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,3,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,3,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,6,5,3,2,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,6,5,2,4,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,6,2,4,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,4,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,7,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,3,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,7,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,7,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,2,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,6,7,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,7,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,7,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,6,2,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,4,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,3,7,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,7,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,3,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,2,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,5,7,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,2,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,7,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,2,3,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,2,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,6,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,7,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,6,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,5,2,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,6,4,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,3,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,7,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,4,7,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,4,5,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,7,4,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,6,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,3,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,2,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,2,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,6,5,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,6,2,5,4,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,2,7,6,5,4,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,2,8,7,6,5,4,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,7,4,2,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,6,3,2,5,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,7,4,2,6,5,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,6,2,8,7,5,4,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,7,4,3,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,2,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,6,5,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,7,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,6,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,5,3,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,7,6,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,4,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,4,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,5,3,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,6,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,6,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,6,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,4,6,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,4,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,6,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,7,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,7,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,5,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,4,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,5,7,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,5,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,3,4,5,6,7,8,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,4,5,6,7,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,6,7,2,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,3,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,4,7,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,3,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,3,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,2,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,4,6,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,4,3,5,6,7,8,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,5,4,2,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,6,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,2,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,2,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,3,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,2,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,2,5,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,3,6,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,6,7,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,2,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,2,3,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,6,7,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,5,6,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,2,4,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,4,2,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,3,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,2,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,4,6,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,7,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,7,2,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,4,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,4,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,6,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,3,7,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,6,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,3,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,7,3,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,3,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,4,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,7,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,4,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,3,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,7,5,3,2,8,6,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,7,6,4,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,6,4,2,7,5,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,3,6,7,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,4,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,2,3,4,5,6,8,7] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,2,3,4,5,7,6,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,3,5,7,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,5,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,5,2,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,2,5,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,2,7,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,2,5,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,2,5,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,5,6,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,3,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,5,2,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,4,7,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,6,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,7,3,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,5,2,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,2,5,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,6,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,5,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,2,6,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,7,4,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,4,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,2,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,2,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,2,4,5,6,7,8,3] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,2,6,5,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,6,2,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,7,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,3,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,7,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,6,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,4,5,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,4,5,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,6,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,2,4,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,5,2,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,5,2,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,4,5,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,5,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,5,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,3,6,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,3,2,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,4,5,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,4,6,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,4,7,6,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,2,5,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,6,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,3,2,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,6,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,6,3,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,6,5,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,7,5,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,3,7,6,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,5,7,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,5,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,4,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,5,3,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,2,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,4,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,3,4,7,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,6,2,3,4,5,8,7] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,2,6,7,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,4,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,5,4,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,2,4,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,2,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,5,7,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,2,3,5,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,7,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,7,5,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,4,7,5,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,5,4,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,5,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,3,7,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,7,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,5,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,7,6,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,6,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,4,6,2,7,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,2,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,3,5,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,4,6,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,5,7,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,2,7,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,4,3,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,2,4,6,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,3,4,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,4,3,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,4,2,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,4,7,5,6,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,5,6,4,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,3,7,6,4,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,2,3,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,7,6,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,2,4,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,6,4,2,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,2,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,5,2,3,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,4,5,6,7,8,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,6,7,5,3,2,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,5,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,7,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,6,3,5,4,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,6,4,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,6,7,5,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,3,2,7,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,2,3,5,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,5,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,6,7,2,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,7,6,4,3,2,5] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,7,5,4,3,2,6] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,6,5,4,3,2,7] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,7,6,5,4,3,2,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,7,6,5,2,3,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,7,6,3,4,2,5] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,7,4,5,3,2,6] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,5,6,4,3,2,7] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,4,5,6,3,2,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,6,7,5,4,3,2,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,2,4,6,5,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,5,2,7,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,7,4,3,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,7,6,3,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,5,2,6,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,5,6,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,2,5,7,3,4,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,2,6,3,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,4,5,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,3,6,4,2,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,6,4,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,4,7,6,2,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,2,3,4,6,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,7,6,2,5,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,5,2,3,8,4,6,7] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,5,6,2,3,7,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,4,6,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,2,4,7,5,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,4,5,7,2,6] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,7,4,6,3,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,9,8,5,6,7,4,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,8,5,4,6,7,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,9,5,4,6,7,8,3,2] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => 0
[1,8,5,4,2,6,3,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,3,6,2,4,7,5] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,7,5,6,4,2,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,6,3,7,4,5,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
[1,8,5,2,7,6,4,3] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,4 6,5,13 19,19,30,52
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 2 + 4\ q$
$F_{4} = 6 + 5\ q + 13\ q^{2}$
$F_{5} = 19 + 19\ q + 30\ q^{2} + 52\ q^{3}$
Description
The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$.
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j \geq j$ and there exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also St000213The number of weak exceedances (also weak excedences) of a permutation. and St000119The number of occurrences of the pattern 321 in a permutation..
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j \geq j$ and there exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also St000213The number of weak exceedances (also weak excedences) of a permutation. and St000119The number of occurrences of the pattern 321 in a permutation..
Map
toric promotion
Description
Toric promotion of a permutation.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
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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