Identifier
-
Mp00043:
Integer partitions
—to Dyck path⟶
Dyck paths
Mp00142: Dyck paths —promotion⟶ Dyck paths
St000011: Dyck paths ⟶ ℤ
Values
[1] => [1,0,1,0] => [1,1,0,0] => 1
[2] => [1,1,0,0,1,0] => [1,1,1,0,0,0] => 1
[1,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 2
[3] => [1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0] => 1
[2,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => 2
[4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[3,1] => [1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => 3
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 2
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0] => 1
[3,2] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => 1
[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0] => 1
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => 1
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => 3
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 1
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => 1
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => 3
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 4
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 1
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 1
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => 1
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 2
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 1
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 1
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 1
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 1
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 2
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 2
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 3
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 2
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 2
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 2
[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 2
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 1
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 1
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => 1
[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => 1
>>> Load all 803 entries. <<<[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => 1
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => 1
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 1
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 1
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 2
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => 2
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 1
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 4
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 4
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 2
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 4
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 2
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 2
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 2
[10,1] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => 1
[9,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => 1
[9,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => 1
[8,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => 1
[8,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => 1
[8,1,1,1] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => 1
[7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => 1
[7,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => 1
[7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 1
[7,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => 1
[7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 1
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 1
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 1
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 1
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 3
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 2
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 2
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => 2
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 3
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 4
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 5
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 3
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 2
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 2
[10,1,1] => [1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => 1
[9,3] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => 1
[9,1,1,1] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[8,2,1,1] => [1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => 1
[8,1,1,1,1] => [1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => 1
[7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => 1
[7,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => 1
[7,3,1,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => 1
[7,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[7,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => 1
[7,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 1
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 1
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 1
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 2
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 2
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 1
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 2
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 2
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 2
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 3
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 3
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 4
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 2
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 2
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 2
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 2
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 2
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[9,4] => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => 1
[9,2,1,1] => [1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => 1
[9,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[8,2,2,1] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => 1
[8,2,1,1,1] => [1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[8,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => 1
[7,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => 1
[7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => 1
[7,4,1,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => 1
[7,3,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => 1
[7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => 1
[7,3,1,1,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => 1
[7,2,2,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => 1
[7,2,2,1,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 1
[7,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 2
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 1
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 2
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 1
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 1
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 2
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 2
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 2
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 2
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 3
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 2
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 3
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 3
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 2
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 2
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 2
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[2,2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 2
[9,2,2,1] => [1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 1
[9,1,1,1,1,1] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => 1
[8,2,2,1,1] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[8,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 2
[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => 1
[7,5,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => 1
[7,5,1,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => 1
[7,4,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => 1
[7,4,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => 1
[7,4,1,1,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => 1
[7,3,3,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => 1
[7,3,2,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => 1
[7,3,2,1,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => 1
[7,3,1,1,1,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[7,2,2,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => 1
[7,2,2,1,1,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[7,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 3
[6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 2
[6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 2
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 1
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 1
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 1
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 1
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 2
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 2
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 2
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 1
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 4
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 2
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 2
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 3
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 2
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 4
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[4,3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 2
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 2
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 2
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[9,1,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => 1
[8,3,3,1] => [1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => 1
[8,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1
[7,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 2
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => 1
[7,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => 1
[7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => 1
[7,5,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => 1
[7,5,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => 1
[7,4,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => 1
[7,4,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => 1
[7,4,2,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => 1
[7,4,2,1,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => 1
[7,4,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[7,3,3,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => 1
[7,3,3,1,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => 1
[7,3,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => 1
[7,3,2,1,1,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[7,2,2,2,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => 1
[7,2,2,2,1,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 2
[6,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 2
[6,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 2
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 1
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 1
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 1
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 1
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 1
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 1
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 1
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 1
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 2
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 2
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 2
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 3
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 5
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 3
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 5
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 2
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 3
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 3
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => 2
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 3
[3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 3
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => 2
[3,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 2
[2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[9,7] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => 1
[9,1,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 2
[8,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => 1
[8,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 1
[7,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 2
[7,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 2
[7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => 1
[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => 1
[7,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => 1
[7,5,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => 1
[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 1
[7,5,2,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => 1
[7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 1
[7,5,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[7,4,4,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => 1
[7,4,3,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => 1
[7,4,3,1,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => 1
[7,4,2,2,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => 1
[7,4,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[7,3,3,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 1
[7,3,3,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => 1
[7,3,3,1,1,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[7,3,2,2,2] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => 1
[7,3,2,2,1,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[7,2,2,2,2,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[6,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => 2
[6,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => 2
[6,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[6,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 3
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 1
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 1
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 1
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 1
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 1
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 1
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 1
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 1
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 1
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 3
[5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => 2
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 2
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 2
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 2
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 2
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 2
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 2
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 4
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 5
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 4
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 2
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 2
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 4
[4,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => 2
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 2
[2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 2
[9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => 1
[9,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 1
[8,8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 2
[8,7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => 1
[8,7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => 1
[8,3,3,2,1] => [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => 1
[8,3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 1
[8,2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1
[7,7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => 1
[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 1
[7,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => 1
[7,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 1
[7,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[7,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => 1
[7,5,4,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => 1
[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => 1
[7,5,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => 1
[7,5,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => 1
[7,5,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[7,4,4,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => 1
[7,4,4,1,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => 1
[7,4,3,3] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => 1
[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[7,4,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[7,4,2,2,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => 1
[7,4,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[7,3,3,3,1] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 1
[7,3,3,2,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => 1
[7,3,3,2,1,1] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[7,3,2,2,2,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[6,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => 2
[6,6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => 2
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => 2
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 1
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 1
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 1
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 1
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 1
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 1
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 1
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[5,5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => 2
[5,5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => 2
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 2
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 2
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 2
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[5,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => 2
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 4
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => 2
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 2
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 2
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => 2
[4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => 2
[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => 3
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 3
[3,3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
[] => [] => [] => 0
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 3
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 2
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 1
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 2
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 1
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 1
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 2
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 1
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 1
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 2
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 1
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 2
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 1
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 1
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => 1
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => 2
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 2
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => 4
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 5
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => 4
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => 1
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 5
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => 1
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => 1
[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[7,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 1
[6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => 2
[6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => 3
[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => 1
[4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => 2
[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => 1
[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => 1
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => 1
[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => 1
[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => 1
[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => 1
[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => 1
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => 1
[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => 3
[7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => 1
[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => 1
[3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 2
[4,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => 2
[4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[4,4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 2
[5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 2
[6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 2
[6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 2
[7,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 3
[10,10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => 2
[7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 2
[8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[8,7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[7,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[8,7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[7,6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[8,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => 5
[7,6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 5
[8,7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 6
[7,6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[8,7,6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[7,6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[8,7,6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[8,7,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 9
[8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[8,7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => 1
[8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[9,9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 2
[8,5,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => 1
[7,7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 2
[5,4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 2
[6,5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 2
[8,6,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => 1
[7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[6,6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => 2
[6,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => 2
[5,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => 2
[8,7,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[9,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => 1
[4,4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => 2
[5,5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => 2
[6,6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => 2
[7,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[7,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => 2
[6,6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => 2
[6,6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 7
[7,6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
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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:
1,1 2,1 2,2,1 4,3 5,4,2 7,6,1,1 10,9,3 15,12,3 18,16,5,3
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + q^{2}$
$F_{4} = 2\ q + 2\ q^{2} + q^{3}$
$F_{5} = 4\ q + 3\ q^{2}$
$F_{6} = 5\ q + 4\ q^{2} + 2\ q^{3}$
$F_{7} = 7\ q + 6\ q^{2} + q^{3} + q^{4}$
$F_{8} = 10\ q + 9\ q^{2} + 3\ q^{3}$
$F_{9} = 15\ q + 12\ q^{2} + 3\ q^{3}$
$F_{10} = 18\ q + 16\ q^{2} + 5\ q^{3} + 3\ q^{4}$
Description
The number of touch points (or returns) of a Dyck path.
This is the number of points, excluding the origin, where the Dyck path has height 0.
This is the number of points, excluding the origin, where the Dyck path has height 0.
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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