Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000931: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => [1,1] => [1,1] => [1,0,1,0] => 0
[1,1,0,0] => [2] => [2] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,1,1] => [1,1,1] => [1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => [1,2] => [2,1] => [1,1,0,0,1,0] => 0
[1,1,0,0,1,0] => [2,1] => [1,2] => [1,0,1,1,0,0] => 0
[1,1,0,1,0,0] => [2,1] => [1,2] => [1,0,1,1,0,0] => 0
[1,1,1,0,0,0] => [3] => [3] => [1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,1,1,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0] => [1,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0] => [1,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0] => [1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0] => [2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => [2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0] => [2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0] => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,0] => [3,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0] => [3,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0] => [3,1] => [1,3] => [1,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => [4] => [4] => [1,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,2,1,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,2,1,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,1,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,1,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,1,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,2,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,3,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,3,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,3,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,3,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,3,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
>>> Load all 1922 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => [1,4,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,4,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,4,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,1,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,2,1,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,2,1,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,2,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,2,1,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,2,1,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,2,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,2,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,2,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,3,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,3,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,4,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,4,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,4,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,5,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,5,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,5,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,5,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,3,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,2,2,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,3,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,2] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,4,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,5] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,2,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,1,3] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,3,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,1,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,2,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,3] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,2,1,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,2,1,1] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,3,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,3,1] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,2,1,1,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,2,1,2] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,2,1,1,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,2,1,1,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,2,1,2] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,2,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,2,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,2,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,3,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,3,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,3,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,3,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,3,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,3,1,1] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,3,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,4,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,4,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,4,1] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,3,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,3,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,2,1,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,2,1,1,1,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,2,1,1,2] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,2,1,1,1,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,2,1,1,1,1] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,2,1,1,2] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,2,1,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,2,1,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,2,1,2,1] => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,2,1,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,2,2,2] => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,2,3,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,2,3,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,2,3,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,2,3,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,3,1,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,3,1,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,3,1,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,3,1,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,3,1,1,1] => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,3,1,2] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,3,2,1] => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,4,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,4,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,4,1,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,4,2] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,5,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,5,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,5,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,5,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,2,1,2,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,1,1,1,1,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,2] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,2,1,1,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,2,1,2,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,2,1,2,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,2,1,2,1,1] => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [1,2,1,2,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,2,1,3,1] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,2,2,1,1,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,2,2,1,2] => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,2,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,2,3,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,2,3,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [1,2,3,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,1,1] => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,2,4,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,3,1,1,1,1] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,3,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,3,1,2,1] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,3,2,1,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,3,2,2] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,3,3,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,4,1,1,1] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,4,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,4,2,1] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,5,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [1,5,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,5,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,5,1,1] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,5,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,6,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,6,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,6,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,6,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,6,1] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,2,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,1,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,1,1,2,2] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,3,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,1,2,1,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,1,2,1,2] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,1,2,2,1] => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,1,3,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,1,3,2] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,4,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,2,1,1,2] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,2,1,2,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,2,2,1,1] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,2,3,1] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,1,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,1,2] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,2,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,4,1,1] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,5,1] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,1,1,1,2] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,1,1,2,1] => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,1,2,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [3,1,2,2] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,1,3,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,2,1,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,3,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,1,1,2] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,1,2,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,2,1,1] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,2,2] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,3,1] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,1,2] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,2,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,2] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,2] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,2] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [6,2] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,2] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,2] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 9,4,1 21,15,5,1 51,50,24,6,1 127,161,98,35,7,1
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 9 + 4\ q + q^{2}$
$F_{5} = 21 + 15\ q + 5\ q^{2} + q^{3}$
$F_{6} = 51 + 50\ q + 24\ q^{2} + 6\ q^{3} + q^{4}$
$F_{7} = 127 + 161\ q + 98\ q^{2} + 35\ q^{3} + 7\ q^{4} + q^{5}$
Description
The number of occurrences of the pattern UUU in a Dyck path.
The number of Dyck paths with statistic value 0 are counted by the Motzkin numbers [1].
The number of Dyck paths with statistic value 0 are counted by the Motzkin numbers [1].
Map
reverse
Description
Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!