Identifier
-
Mp00133:
Integer compositions
—delta morphism⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00229: Dyck paths —Delest-Viennot⟶ Dyck paths
St001035: Dyck paths ⟶ ℤ
Values
[1,1] => [2] => [1,1,0,0] => [1,0,1,0] => 0
[1,1,1] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[1,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,1,2] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,2,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,3] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1,1] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,2] => [2] => [1,1,0,0] => [1,0,1,0] => 0
[3,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,3] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,2,2] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,3,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,4] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[2,1,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,2,1] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[2,3] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[3,1,1] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[3,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[4,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,4] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,2,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,3,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,4,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,5] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[2,2,2] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[2,3,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,4] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[3,1,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,2,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,3] => [2] => [1,1,0,0] => [1,0,1,0] => 0
[4,1,1] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[4,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[5,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,5] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,3] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,4,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,5,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,6] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[2,2,3] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
>>> Load all 2052 entries. <<<[2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,3,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,4,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,5] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[3,2,2] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[3,3,1] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[3,4] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[4,1,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,2,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,3] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[5,1,1] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[5,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[6,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1,1,1,1,1] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,2,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,2,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,2,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,6] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,3,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,5,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,6,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,7] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,2,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[2,2,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,2,2,2] => [4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[2,2,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,4] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,3,3] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,4,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,5,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,6] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[3,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[3,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[3,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[3,2,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[3,3,2] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[3,4,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,5] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[4,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[4,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,1,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[4,2,2] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[4,3,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,4] => [2] => [1,1,0,0] => [1,0,1,0] => 0
[5,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[5,1,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,2,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,3] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[6,1,1] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[6,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[7,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1,1,1,1,2] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,2,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,3] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,2,1,1] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,2,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,3,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1,1,1] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,2,1,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,2,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,2,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,3,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,3,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1,1,1] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,2,1,1,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,2,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,2,1,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,2,2,2] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,2,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,3,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,3,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,4,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,6] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1,1,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,1,1,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,2,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,2,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,2,2,1,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,2,2,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,2,2,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,2,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,3,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,3,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,3,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,3,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,3,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,4,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,4,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,5,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,7] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,2,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,2,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,2,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,2,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,2,2,1,1,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,2,1,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,6] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[1,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,4] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,5,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,6,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,7,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,8] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1,1,1,1,1,1,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,1,1,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[2,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[2,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[2,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[2,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,6] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,2,1,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[2,2,1,1,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,2,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,2,1,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,2,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[2,2,1,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[2,2,1,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,2,1,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
[2,2,2,1,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[2,2,2,2,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[2,2,2,3] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[2,2,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[2,2,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,5] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[2,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,3,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,4,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,5,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,6,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,7] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[3,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[3,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[3,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[3,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[3,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[3,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,3,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[3,3,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[3,3,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[3,3,3] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[3,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[3,4,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,5,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,6] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[4,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[4,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[4,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[4,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[4,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[4,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[4,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,1,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[4,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[4,2,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[4,3,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,4,1] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[4,5] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[5,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[5,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,1,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[5,2,2] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[5,3,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,4] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[6,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[6,1,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[6,2,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[6,3] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[7,1,1] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[7,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[8,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1,1,1,1,3] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,1,2,2] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,1,3,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,4] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,1,2,1,2] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,2,2,1] => [5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,1,2,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,3,1,1] => [5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,1,3,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,4,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,1,2,1,1,2] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,2,1,2,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,1,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,2,1,1] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,2,2,2] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,2,3,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,3,1,1,1] => [4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,1,3,1,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,4,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,4,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,5,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,6] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,2,1,1,1,2] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,2,1,1,2,1] => [3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,2,1,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,2,1,2,1,1] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,2,1,2,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,2,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,2,1,1,1] => [3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,2,2,1,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,2,2,2,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,2,2,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,2,3,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,2,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,4,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,5] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,3,1,1,1,1] => [3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,3,1,1,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,3,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,3,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,3,2,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,3,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,3,3,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,3,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,4,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,4,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,4,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,5,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,5,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,6,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,7] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,2,1,1,1,1,2] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,2,1,1,1,2,1] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,2,1,1,1,3] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,2,1,1,2,1,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,2,1,1,2,2] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,2,1,1,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,1,2,1,1,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,2,1,2,1,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,4,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,2,1,1,1,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,2,2,1,1,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,2,2,1,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,2,2,1,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,2,2,1,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,2,2,2,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,2,2,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,2,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,2,3,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,2,3,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,2,4,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,4,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,2,6] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,3,1,1,1,1,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,3,1,1,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,3,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,3,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,3,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,3,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,3,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,3,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,3,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,3,3,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[1,1,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,4,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,4,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,4,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,4,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,4,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[1,1,5,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,5,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,5,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,6,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,7,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,1,8] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[1,2,1,1,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,1,2,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,1,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,2,1,1,1,2,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,2,1,1,1,2,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,2,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,1,2,1,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,1,1,2,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,2,1,1,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,1,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,1,5] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,1,1,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,2,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,2,1,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,1,2,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,1,3,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,1,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,2,1,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,6] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,2,1,1,1,1,1] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,2,2,1,1,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,2,2,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,2,2,1,1,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,2,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,2,2,1,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,2,2,1,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,2,1,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,2,2,2,1,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,2,2,2,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,2,2,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,2,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,2,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,7] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,3,1,1,1,1,1,1] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,3,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,3,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,3,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,3,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,3,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,3,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,3,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,3,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,3,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,3,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,3,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,3,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,3,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,3,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,3,3,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,3,3,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[1,3,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,3,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,6] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,4,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,4,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,4,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,4,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,4,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,4,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,4,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,4,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,5,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,5,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,5,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,5,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,6,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,6,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,6,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,6,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,7,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,7,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,8,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,9] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,1,1,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,1,2,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,1,1,3] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,2,1,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[2,1,1,1,1,2,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[2,1,1,1,1,3,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,2,1,1,1] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,1,1,1,2,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,1,2,2,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[2,1,1,1,2,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[2,1,1,1,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,1,1,2,1,1,1,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[2,1,1,2,1,1,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[2,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[2,1,1,2,1,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,2,2,1,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,1,1,2,2,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,1,1,2,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,2,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,1,1,3,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,3,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,1,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,5,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,6] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,1,2,1,1,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[2,1,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,1,2,1,1,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[2,1,2,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,1,2,1,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,1,2,1,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,1,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,1,2,2,1,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[2,1,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,1,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,1,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[2,1,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[2,1,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,1,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,1,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,1,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,1,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,1,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,7] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,2,1,1,1,1,1,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[2,2,1,1,1,1,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,2,1,1,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[2,2,1,1,1,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,2,1,1,2,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[2,2,1,1,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[2,2,1,1,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[2,2,1,1,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,2,1,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[2,2,1,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[2,2,1,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,2,1,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[2,2,1,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,1,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,2,1,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[2,2,2,1,1,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[2,2,2,1,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[2,2,2,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[2,2,2,2,1,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[2,2,2,2,2] => [5] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
[2,2,2,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[2,2,2,4] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[2,2,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[2,2,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[2,2,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[2,2,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,6] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[2,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[2,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,3,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[2,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,4,4] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,5,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,6,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,7,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,8] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[3,1,1,1,1,1,1,1] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[3,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[3,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[3,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[3,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[3,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[3,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[3,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[3,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[3,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[3,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[3,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[3,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[3,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[3,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[3,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,6] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[3,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[3,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[3,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[3,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[3,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[3,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,3,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[3,3,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[3,3,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,3,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[3,3,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[3,3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[3,3,3,1] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[3,3,4] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[3,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[3,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,4,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[3,5,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,6,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,7] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[4,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[4,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[4,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[4,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[4,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[4,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[4,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[4,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[4,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[4,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[4,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,1,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[4,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[4,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[4,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[4,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[4,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,2,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[4,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,3,3] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[4,4,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[4,4,2] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[4,5,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,6] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[5,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[5,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[5,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[5,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[5,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[5,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[5,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,1,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[5,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[5,2,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[5,3,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,4,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,5] => [2] => [1,1,0,0] => [1,0,1,0] => 0
[6,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[6,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[6,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[6,1,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[6,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[6,2,2] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[6,3,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[6,4] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[7,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[7,1,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[7,2,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[7,3] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[8,1,1] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[8,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[9,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,10] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,8,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,7,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,6,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,2,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,1,8,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[10,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,1,1,1,1,3,3] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,2,2,2,2] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,1,2,1,2,3] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,3,1,1] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,1,3,2,1,2] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,1,1,3] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,4,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,2,2,1,1,2,2] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,1,2,2,2,2,1,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[1,1,2,2,2,1,1,2] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[1,1,2,2,3,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,2,1,1,2,2,2] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,2,1,1,1,2,3] => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,2,1,2,3,1,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,2,2,1,2] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,2,1,1,3] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,1,3,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,3,1,1,1,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,1,3,3,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,3,2,1,2,1,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,3,2,1,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,3,2,2,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,3,1,1,3,1,1] => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,3,1,1,2,1,2] => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,3,1,1,1,1,3] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,3,1,2,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,4,4,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,4,3,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,4,2,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,4,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,5,5] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[2,2,1,1,1,1,2,2] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 4
[2,2,1,1,2,2,1,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 6
[2,2,1,1,2,1,1,2] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 5
[2,2,1,1,3,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[2,2,2,2,1,1,1,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[2,2,2,2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[2,2,2,1,1,2,1,1] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[2,2,2,1,1,1,1,2] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[2,2,2,1,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[2,2,3,3,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[2,2,3,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[2,2,3,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,2,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[2,1,1,2,1,1,2,2] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 5
[2,1,1,2,2,2,1,1] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5
[2,1,1,2,2,1,1,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[2,1,1,2,3,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,1,1,1,2,2,2] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[2,1,1,1,1,1,2,3] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,2,3,1,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[2,1,1,1,2,2,1,2] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[2,1,1,1,2,1,1,3] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[2,1,1,1,3,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,2,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,1,2,2,2,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[2,1,2,1,2,4] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[2,1,3,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,1,3,3,1,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,1,3,2,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[2,1,3,1,1,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[2,1,4,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,3,1,1,1,1,1,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
[3,3,1,1,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[3,3,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => 4
[3,3,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[3,3,3,3] => [4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[3,2,1,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,2,1,1,1,2,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[3,2,1,1,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[3,2,1,1,2,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[3,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[3,2,2,2,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[3,2,2,1,1,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[3,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,1,1,3,1,1,1,1] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[3,1,1,3,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[3,1,1,2,1,2,1,1] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[3,1,1,2,1,1,1,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[3,1,1,2,2,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[3,1,1,1,1,3,1,1] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[3,1,1,1,1,2,1,2] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[3,1,1,1,1,1,1,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[3,1,1,1,2,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[3,1,2,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[3,1,2,3,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[3,1,2,2,1,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[3,1,2,1,1,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[3,1,3,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,4,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
[4,4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[4,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[4,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[4,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[4,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[4,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[4,1,1,3,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[4,1,1,2,1,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[4,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[4,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,5,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => 2
[5,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[6,6] => [2] => [1,1,0,0] => [1,0,1,0] => 0
[1,2,2,2,2,2,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,2,2,2,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,2,3,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,2,3,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,2,2,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,2,3,3,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,3,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,2,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,3,3,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,2,4,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,2,4,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,4,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,5,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,3,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,3,3,3,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,3,4,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,4,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,3,5,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,2,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,2,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,3,2,2,2,2] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,3,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,3,3,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,3,3,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,3,4,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,4,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,4,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,4,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,4,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,4,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,4,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,4,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,5,5,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[1,5,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,5,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,5,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,6,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,3,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[2,3,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,3,3,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[2,3,3,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,3,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,4,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,4,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,4,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[2,4,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,5,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,5,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,6,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,2,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,2,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 3
[2,2,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[2,2,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,2,2,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[2,2,2,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[2,2,2,2,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[2,2,2,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[2,2,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,2,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[2,3,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,3,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,3,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,3,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,3,3,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[2,4,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,4,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,5,5] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[3,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[3,6,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,3,3,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[3,3,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[3,3,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,3,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 2
[3,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[3,4,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,5,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,2,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[3,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[3,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[3,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[3,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[3,3,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[3,3,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[3,4,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,6,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,4,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[4,5,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[4,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[4,4,4] => [3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[4,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[4,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[4,3,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,6,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,5,2] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[5,4,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,3,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[5,2,5] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,8,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,7,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,6,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,5,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,4,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,3,1,1,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,11] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,9,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,7,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,8,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[1,7,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,5,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,6,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,4,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,5,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,3,2,1,1,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,4,1,1,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,2,2,1,1,1,1,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,2,2,2,2,2] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,2,2,2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,2,1,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,2,1,2,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,2,1,1,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,1,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,2,1,3,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,2,3,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,2,2,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,1,4] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,1,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,1,3,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,2,1,1,2,4] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,3,2,2,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,3,2,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,3,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,3,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,2,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,2,2,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,2,2,1,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,4,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,3,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,2,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,1,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,4,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,4,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,3,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,3,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,3,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,4,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,3,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,2,2,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,2,1,5] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,5,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,4,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,3,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,2,5] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,6] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,2,2,2,2,2,2] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,2,2,2,2,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,2,2,2,1,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,2,2,2,1,2,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,2,2,2,1,1,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[1,2,2,1,3,2,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,2,2,1,3,1,3] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,2,2,1,2,3,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,2,2,1,2,2,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,2,2,1,2,1,4] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,2,2,1,1,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,2,2,1,1,3,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[1,2,2,1,1,2,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,2,2,1,1,1,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,2,1,3,2,2,2] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,1,3,2,1,3] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,3,1,3,2] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,3,1,2,3] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,3,1,1,4] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,2,3,2,2] => [1,1,1,1,1,2] => [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] => 1
[1,2,1,2,3,1,3] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,2,2,3,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,2,2,2,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,2,1,2,2,1,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,2,1,4,2] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,2,1,3,3] => [1,1,1,1,1,2] => [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] => 1
[1,2,1,2,1,2,4] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,2,1,1,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,1,4,2,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,2,1,1,4,1,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,3,3,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,1,1,3,2,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,3,1,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,2,4,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,2,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,2,1,1,2,2,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,2,1,1,2,1,5] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,1,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,3,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,2,5] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,1,1,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,3,2,2,2,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,3,2,2,1,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,3,2,1,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,2,1,2,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,2,1,1,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,3,1,3,2,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,3,1,3,1,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,2,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,2,2,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,3,1,2,1,4] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,3,1,1,4,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,3,1,1,3,3] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,3,1,1,2,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,3,1,1,1,5] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,2,3,2,2,2] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,2,3,2,1,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,3,1,3,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,3,1,2,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,3,1,1,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,2,3,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,2,2,3,1,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,2,2,2,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,2,2,2,2,3] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,2,2,2,1,4] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,2,2,1,4,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,2,2,1,3,3] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,2,2,1,2,4] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,2,2,1,1,5] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,2,1,4,2,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,4,1,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,3,3,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,1,3,2,3] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,3,1,4] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,2,4,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,2,3,3] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,2,2,4] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,2,1,2,1,5] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,2,1,1,5,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,1,4,3] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,1,3,4] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,1,2,5] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[1,1,2,1,1,1,6] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,4,2,2,2] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,4,2,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,4,1,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,4,1,2,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,4,1,1,4] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,3,3,2,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,3,3,1,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,3,2,3,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,3,2,2,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,3,2,1,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,3,1,4,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,3,1,3,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,3,1,2,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,3,1,1,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,2,4,2,2] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,2,4,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,3,3,2] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,2,3,2,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,3,1,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,2,4,2] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,2,2,3,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,2,2,2,4] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,2,2,1,5] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,1,1,2,1,5,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,4,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,3,4] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,2,5] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,1,6] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,1,5,2,2] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,1,5,1,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,4,3,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,4,2,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,4,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,4,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,3,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,1,1,3,2,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,3,1,5] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,5,2] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,4,3] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,3,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,2,2,5] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,1,1,2,1,6] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,6,2] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,5,3] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,4,4] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,1,3,5] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,2,6] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,1,1,1,7] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,2,9] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,2,7] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,4,7] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,1,2,1,7] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,2,2,2,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,1,2,3,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,1,2,1,5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,1,5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,4,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,1,5] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[7,2,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,1,2,1,2,2,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,8,3] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,1,2,5,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,1,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,4,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,2,1,3,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[5,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,2,1,2,1,3] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[3,3,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,5,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,2,2,2,1,3] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[3,1,4,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,4,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,6,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,3,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[3,1,1,2,1,1,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,3,1,2,1,1,3] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,3,2,1,1,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,4,1,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[9,2,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,2,6,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,2,1,4,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[5,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => 2
[1,6,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[1,1,2,3,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,1,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,3,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,4,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[7,4,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,1,2,1,2,4,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,2,2,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[3,8,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,10,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,1,2,7,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[3,1,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,4,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,5,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[5,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,2,1,2,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,5,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,2,2,2,3,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[3,1,4,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,1,6,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,2,3,3,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[3,1,1,2,1,3,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,3,1,2,1,3,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,1,3,2,1,3,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,4,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[7,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,4,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[3,2,2,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,4,2,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[5,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,2,3,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[3,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,7,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,2,4,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[3,1,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,3,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,4,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[5,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,2,2,1,4,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[3,3,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,5,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,2,2,4,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[3,1,6,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,3,6,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,1,8,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => 2
[1,1,1,2,5,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[3,1,1,2,3,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,3,1,2,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[1,1,3,2,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,4,3,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[5,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[3,3,1,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,5,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,1,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,3,3,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,5,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[3,1,1,4,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,3,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,3,4,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,6,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[2,2,2,2,1,2,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[2,2,2,1,2,1,2] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[2,2,2,1,2,2,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[2,2,2,1,1,2,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 4
[2,2,1,2,1,2,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[2,2,1,2,1,1,2,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 3
[2,2,1,2,2,1,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[2,2,1,2,2,2,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[2,2,1,1,2,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[2,2,1,1,2,1,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[2,2,1,1,1,2,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 5
[2,1,2,1,2,2,2] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,1,2,2,1,2,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,2,2,2,1,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,2,2,2,2,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,2,2,2,2] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[2,1,1,2,2,1,2,1] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[2,1,1,2,1,2,1,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[2,1,1,2,1,2,2,1] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[2,1,1,1,2,2,2,1] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[2,1,1,1,2,1,2,2] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,2,1,2,2,2,2] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,2,1,1,1,2,2,2] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,2,2,1,2,2,2] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,2,2,1,2,1,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,2,2,1,1,2,1,2] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 4
[1,2,2,1,1,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 6
[1,2,2,1,1,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 5
[1,2,2,2,1,2,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,2,2,2,1,1,2,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,2,2,2,2,1,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[1,1,2,2,2,2,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,2,2,2,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,1,2,2,1,2,1,2] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,2,2,1,2,2,1] => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 5
[1,1,2,1,2,1,2,2] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,2,2,2,1] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,2,2,1,2,2] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,1,2,2,2,1,2] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,2,2,2,2,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,1,2,1,2,2,2] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[3,3,3,2] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[3,4,4] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[2,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[4,4,3] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[3,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[4,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[4,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[4,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[4,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[5,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[5,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[5,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[5,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => 2
[6,5,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[6,4,2] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[6,3,3] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[6,2,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[7,5] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,8,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,1,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,1,1,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,1,1,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,1,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,1,1,3,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[11,1] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[2,9,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[3,7,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[2,1,8,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[2,2,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[2,1,1,7,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,1,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,1,1,1,6,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,2,4,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,1,1,5,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,2,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,1,1,1,4,1] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,1,1,1,1,2,2,1] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 4
[2,2,2,2,2,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[3,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[2,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[3,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[4,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[2,2,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[3,1,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[2,3,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[3,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[4,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[2,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[3,3,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[4,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[5,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,2,2,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 2
[3,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,3,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[3,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[4,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,2,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[3,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[2,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 3
[4,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[2,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[3,3,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[4,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[5,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,2,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[3,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[3,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,3,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 2
[4,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => 3
[5,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[4,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[5,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[6,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,2,2,2,2,2,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[3,1,2,2,2,2,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 2
[2,3,1,2,2,2,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[3,2,1,2,2,2,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[4,1,1,2,2,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[2,2,3,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 3
[3,1,3,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[2,3,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[3,2,2,1,2,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[4,1,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[2,4,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[3,3,1,1,2,2,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
[4,2,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[5,1,1,1,2,2,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[2,2,2,3,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[3,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[2,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[3,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[4,1,1,3,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[2,2,3,2,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[3,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[2,3,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[3,2,2,2,1,2,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[4,1,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[2,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[3,3,1,2,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[4,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[5,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[2,2,4,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[3,1,4,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,3,3,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[3,2,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[4,1,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,4,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[3,3,2,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[4,2,2,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[5,1,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,5,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[3,4,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[4,3,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[5,2,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[6,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,2,2,2,3,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 2
[3,1,2,2,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,3,1,2,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[3,2,1,2,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[4,1,1,2,3,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[2,2,3,1,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[3,1,3,1,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,3,2,1,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[3,2,2,1,3,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[4,1,2,1,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,4,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[3,3,1,1,3,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[4,2,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[5,1,1,1,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[2,2,2,3,2,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[3,1,2,3,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,3,1,3,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[3,2,1,3,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[4,1,1,3,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[2,2,3,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[3,1,3,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[2,3,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[3,2,2,2,2,1,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[4,1,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[2,4,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,3,1,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[4,2,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[5,1,1,2,2,1,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[2,2,4,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[3,1,4,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,3,3,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[3,2,3,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[4,1,3,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,4,2,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[3,3,2,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[4,2,2,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[5,1,2,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,5,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[3,4,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[4,3,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[5,2,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[6,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[2,2,2,4,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[3,1,2,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,3,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,2,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,1,1,4,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,2,3,3,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[3,1,3,3,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,3,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,2,2,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[4,1,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,4,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,3,1,3,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[4,2,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[5,1,1,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,2,4,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[3,1,4,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,3,3,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[3,2,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,1,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,4,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[3,3,2,2,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 4
[4,2,2,2,1,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[5,1,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,5,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,4,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,3,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[5,2,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[6,1,1,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[2,2,5,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[3,1,5,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,3,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,2,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[4,1,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,4,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,3,3,1,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[4,2,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[5,1,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,5,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,4,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[4,3,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[5,2,2,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[6,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,6,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[3,5,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[4,4,1,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[5,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[6,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[7,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,2,1,2,1,2,1,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,2,2,2,1,2,1,1] => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,2,2,1,2,1,1,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 4
[1,2,2,1,2,2,1,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 5
[2,1,1,1,1,1,1,3] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[2,1,1,1,1,1,2,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 3
[2,1,1,1,1,2,1,2] => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[2,1,1,1,2,1,1,2] => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 4
[2,1,1,2,1,1,1,2] => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 4
[2,2,1,1,1,1,1,2] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[3,1,1,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,2,2,4,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,4,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,5,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,3,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,5,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,5,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,5,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[2,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => 1
[2,2,5,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[6,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 1
[2,2,2,2,2,1,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[2,2,2,1,2,1,1,1] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[2,2,1,2,2,1,1,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 4
[2,1,2,2,2,1,1,1] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,2,2,2,2,1,1,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 3
[9,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,9,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[10,2] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,2,2,2,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,2,2,3,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,2,2,4,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,2,3,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,3,1,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[1,2,3,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,4,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,3,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,2,3,3,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,2,4,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,5,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,3,1,2,2,2,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,3,1,3,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[1,3,2,1,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[1,4,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,4,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,3,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,3,3,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[1,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,4,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,5,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,3,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,3,3,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,3,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,4,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,4,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,5,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,4,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,4,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,5,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,6,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[2,1,2,2,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,1,2,3,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[2,1,2,3,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,1,2,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,1,3,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[2,1,3,1,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,1,3,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[2,1,4,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,1,3,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[2,1,3,3,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,1,4,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,1,4,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,1,5,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,2,1,2,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[2,2,1,3,1,2,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[2,2,1,3,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[2,2,1,4,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[3,1,1,2,2,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 4
[3,1,1,3,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[3,1,1,3,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 3
[2,2,2,1,3,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[2,3,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[2,3,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[3,1,2,1,3,1,1] => [1,1,1,1,1,2] => [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] => 1
[3,2,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 4
[3,2,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[4,1,1,1,2,2,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 4
[4,1,1,1,3,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[2,2,3,1,1,2,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 3
[2,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[2,3,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[2,4,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[3,1,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[3,1,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[3,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[4,1,1,2,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[3,2,2,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 4
[3,3,1,1,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[4,1,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[4,2,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[5,1,1,1,1,2,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 2
[2,2,2,3,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[2,2,3,1,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[2,2,3,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[2,2,4,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[2,3,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[2,3,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,3,2,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[2,4,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[2,3,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[2,3,3,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[2,4,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[2,4,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[2,5,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[3,1,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[3,1,3,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[3,1,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,2,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 3
[3,2,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,1,1,2,2,1,1] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 5
[4,1,1,3,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[3,3,1,1,2,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[4,1,2,1,2,1,1] => [1,1,1,1,1,2] => [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] => 1
[4,2,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 3
[5,1,1,1,2,1,1] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[3,2,2,2,1,1,1] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[3,2,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[3,3,2,1,1,1,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 2
[3,4,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[4,1,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[4,1,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[4,2,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[4,2,2,1,1,1,1] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[4,3,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[5,1,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[5,2,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[6,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[2,9] => [1,1] => [1,0,1,0] => [1,1,0,0] => 0
[1,1,2,2,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,3,1,3,1,3,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,3,1,2,3,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,3,1,2,1,4,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,3,1,1,1,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,3,2,1,3,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,3,1,3,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,3,1,1,4,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,2,3,2,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,2,2,1,4,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,2,2,1,2,4,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,2,1,4,1,3,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,3,3,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,1,3,1,4,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,2,1,5,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,1,5,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,3,4,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,1,1,1,6,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,1,5,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,4,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,4,1,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,3,1,5,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,5,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,3,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,6,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,1,7,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,2,3,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[2,2,2,2,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,2,2,2,2,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,2,2,3,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[2,2,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,2,3,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[2,3,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 0
[1,3,2,2,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => 2
[5,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,1,1,1,5,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,3,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,5,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,7,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,4,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,1,4,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,1,2,3,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,3,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,3,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,3,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,5,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,5,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,7,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,6,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,4,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,2,1,3,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,1,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,3,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,1,1,1,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,2,1,1,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,3,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,2,1,2,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 4
[1,1,1,7,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,9,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,1,1,6,1,2,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,3,1,5,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,3,1,7,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,3,1,4,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,5,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,5,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,5,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,5,1,2,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,7,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,7,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,9,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,11,1] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,8,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,6,1,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,6,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,6,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,6,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,1,2,1,3,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,4,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,4,1,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,1,3,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,4,1,1,1,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,4,1,1,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,4,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,4,3,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,3,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,4,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,4,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,2,1,6,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,1,8,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,1,5,1,2,1] => [1,1,1,1,1,1,1] => [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] => 0
[1,2,3,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,3,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,3,3,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,2,5,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,2,5,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,5,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 2
[1,2,7,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,4,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,9] => [2,1] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => 1
[2,2,2,2,1,1,2] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,2,2,1,2,3] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,2,2,2,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[2,2,2,6] => [3,1] => [1,1,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0] => 1
[2,2,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0] => 1
[1,6,4] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,5,5] => [1,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
[1,4,6] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,3,7] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,2,8] => [1,1,1] => [1,0,1,0,1,0] => [1,1,0,1,0,0] => 0
[1,2,5,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,2,2,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => 2
[2,2,2,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 1
[1,2,3,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,2,2,5,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => 2
[1,1,2,2,2,2,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,2,2,2,1,1,1] => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 4
[1,1,2,2,3,1,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 4
[1,1,2,2,1,2,1,1] => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,1,2,3,2,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,2,1,2,2,1,1] => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,3,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 4
[1,1,1,2,2,2,1,1] => [3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,2,2,2,2,1,1] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,2,2,2,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,2,5,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,5,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,4,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => 3
[2,2,1,1,1,2,1,2] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 3
[1,2,2,2,1,1,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 4
[2,2,1,2,1,1,1,2] => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 3
[2,2,2,1,1,1,2,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
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Description
The convexity degree of the parallelogram polyomino associated with the Dyck path.
A parallelogram polyomino is $k$-convex if $k$ is the maximal number of turns an axis-parallel path must take to connect two cells of the polyomino.
For example, any rotation of a Ferrers shape has convexity degree at most one.
The (bivariate) generating function is given in Theorem 2 of [1].
A parallelogram polyomino is $k$-convex if $k$ is the maximal number of turns an axis-parallel path must take to connect two cells of the polyomino.
For example, any rotation of a Ferrers shape has convexity degree at most one.
The (bivariate) generating function is given in Theorem 2 of [1].
Map
Delest-Viennot
Description
Return the Dyck path corresponding to the parallelogram polyomino obtained by applying Delest-Viennot's bijection.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\gamma^{(-1)}\circ\beta)(D)$.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
bounce path
Description
The bounce path determined by an integer composition.
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