Identifier
-
Mp00102:
Dyck paths
—rise composition⟶
Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St000660: Dyck paths ⟶ ℤ
Values
[1,0] => [1] => [1] => [1,0] => 0
[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] => 1
[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] => 1
[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] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [5] => [5] => [1,1,1,1,1,0,0,0,0,0] => 1
[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] => 1
[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
>>> Load all 2193 entries. <<<[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,4,3] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [1,4,3] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,4,3] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,7] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[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
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 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
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,6] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[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
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,1,1,1,3] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,1,1,1,3] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 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
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,4] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 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
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,4] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,6] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[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] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,8] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,7,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,9] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,7,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,6,2] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,10] => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,7,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [1,7,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [1,6,2] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,7,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [1,7,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [1,7,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [1,8,1,1] => [1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,2] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,7,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [1,6,2] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [1,7,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,7] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,6,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,8] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,6,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,7] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,2] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [7,2] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [7,2] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [7,2] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,2] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,1,1] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,2] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,3,1] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,3,1] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,6,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,3,1] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,8] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,2,1,1,1,1,2] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,6,1] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,7,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,6,2] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,2,1,1,1,1,2] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,2] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,2,1] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0] => [6,2,1] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,7,1,1] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,8,1] => [1,8,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [2,2,1,1,1,1,1] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0] => [10,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,7,1] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [8,2] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0] => [8,1,1] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 9,5 21,21 51,78,3 127,274,28
$F_{1} = 1$
$F_{2} = 2$
$F_{3} = 4 + q$
$F_{4} = 9 + 5\ q$
$F_{5} = 21 + 21\ q$
$F_{6} = 51 + 78\ q + 3\ q^{2}$
$F_{7} = 127 + 274\ q + 28\ q^{2}$
Description
The number of rises of length at least 3 of a Dyck path.
The number of Dyck paths without such rises are counted by the Motzkin numbers [1].
The number of Dyck paths without such rises 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.
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