Identifier
-
Mp00133:
Integer compositions
—delta morphism⟶
Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
St000700: Ordered trees ⟶ ℤ
Values
[1] => [1] => [1,0] => [[]] => 1
[1,1] => [2] => [1,1,0,0] => [[[]]] => 2
[2] => [1] => [1,0] => [[]] => 1
[1,1,1] => [3] => [1,1,1,0,0,0] => [[[[]]]] => 3
[1,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[3] => [1] => [1,0] => [[]] => 1
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[1,1,2] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[1,2,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,3] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,1,1] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[2,2] => [2] => [1,1,0,0] => [[[]]] => 2
[3,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[4] => [1] => [1,0] => [[]] => 1
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,3] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,2,2] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[1,3,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,4] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[2,1,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,2,1] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[2,3] => [1,1] => [1,0,1,0] => [[],[]] => 1
[3,1,1] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[3,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[4,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[5] => [1] => [1,0] => [[]] => 1
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 6
[1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 1
[1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,4] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,2,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,3,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,4,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,5] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 1
[2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[2,2,2] => [3] => [1,1,1,0,0,0] => [[[[]]]] => 3
[2,3,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,4] => [1,1] => [1,0,1,0] => [[],[]] => 1
[3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[3,1,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,2,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,3] => [2] => [1,1,0,0] => [[[]]] => 2
[4,1,1] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[4,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[5,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[6] => [1] => [1,0] => [[]] => 1
[1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 7
[1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 1
[1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 1
[1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 2
[1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,5] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,3] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,4,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,5,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,6] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => 1
[2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
>>> Load all 2066 entries. <<<[2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 2
[2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[2,2,3] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,3,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,4,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,5] => [1,1] => [1,0,1,0] => [[],[]] => 1
[3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 1
[3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[3,2,2] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[3,3,1] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[3,4] => [1,1] => [1,0,1,0] => [[],[]] => 1
[4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[4,1,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,2,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,3] => [1,1] => [1,0,1,0] => [[],[]] => 1
[5,1,1] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[5,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[6,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[7] => [1] => [1,0] => [[]] => 1
[1,1,1,1,1,1,2] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[[]]]]]],[]] => 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
[1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 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
[1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[[]]]],[[]]] => 2
[1,1,1,1,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 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
[1,1,1,2,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => 1
[1,1,1,2,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 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
[1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[1,1,2,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[1,1,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 2
[1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,6] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 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
[1,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[1,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => 1
[1,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[1,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,3,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,5,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,6,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,7] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => 1
[2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[2,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[2,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[2,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[2,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,2,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => 2
[2,2,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 2
[2,2,2,2] => [4] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[2,2,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,4] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[2,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,3,3] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[2,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,4,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,5,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,6] => [1,1] => [1,0,1,0] => [[],[]] => 1
[3,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => 1
[3,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[3,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[3,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[3,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[3,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[3,2,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[3,3,2] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[3,4,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,5] => [1,1] => [1,0,1,0] => [[],[]] => 1
[4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 1
[4,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[4,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,1,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[4,2,2] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[4,3,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,4] => [2] => [1,1,0,0] => [[[]]] => 2
[5,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[5,1,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,2,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,3] => [1,1] => [1,0,1,0] => [[],[]] => 1
[6,1,1] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[6,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[7,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[8] => [1] => [1,0] => [[]] => 1
[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
[1,1,1,1,1,1,3] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[[]]]]]],[]] => 1
[1,1,1,1,1,2,2] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[[]]]]],[[]]] => 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
[1,1,1,1,1,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 1
[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
[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
[1,1,1,1,2,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 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
[1,1,1,1,3,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 1
[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
[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
[1,1,1,2,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 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] => [[[[]]],[[]],[[]]] => 2
[1,1,1,2,2,2] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[[]]],[[[]]]] => 3
[1,1,1,2,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,2,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 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
[1,1,1,3,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 2
[1,1,1,4,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[1,1,1,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,6] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 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
[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
[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
[1,1,2,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[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
[1,1,2,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,2,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,2,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 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] => [[[]],[[]],[[[]]]] => 2
[1,1,2,2,1,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[1,1,2,2,2,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => 1
[1,1,2,2,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[1,1,2,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,2,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,2,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,2,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 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
[1,1,3,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[1,1,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,3,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,3,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[1,1,3,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[1,1,4,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,4,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,5,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,7] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 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
[1,2,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1
[1,2,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[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
[1,2,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[1,2,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[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
[1,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 1
[1,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[1,2,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[1,2,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[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
[1,2,2,1,1,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[1,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[1,2,2,1,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => 1
[1,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 1
[1,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[1,2,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,6] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[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
[1,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[1,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[1,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[1,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[1,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[1,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,4] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[1,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,5,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,6,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,7,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,8] => [1,1] => [1,0,1,0] => [[],[]] => 1
[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
[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
[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
[2,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[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
[2,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => 1
[2,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[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
[2,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[2,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[2,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[2,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[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
[2,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[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
[2,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[2,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[2,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[2,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,6] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,2,1,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[[[[[]]]]]] => 2
[2,2,1,1,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => 1
[2,2,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[2,2,1,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[2,2,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[2,2,1,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[2,2,1,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,1,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,2,1,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[[]]],[[[]]]] => 3
[2,2,2,1,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[2,2,2,2,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 1
[2,2,2,3] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[2,2,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[2,2,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,5] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[2,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[2,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,3,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[2,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,4,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,5,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,6,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,7] => [1,1] => [1,0,1,0] => [[],[]] => 1
[3,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => 1
[3,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[3,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[3,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[3,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[3,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[3,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[3,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[3,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[3,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[3,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[3,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[3,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[3,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,3,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 2
[3,3,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[3,3,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[3,3,3] => [3] => [1,1,1,0,0,0] => [[[[]]]] => 3
[3,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[3,4,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,5,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,6] => [1,1] => [1,0,1,0] => [[],[]] => 1
[4,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => 1
[4,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[4,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[4,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[4,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[4,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[4,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,1,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[4,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[4,2,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[4,3,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,4,1] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[4,5] => [1,1] => [1,0,1,0] => [[],[]] => 1
[5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 1
[5,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[5,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,1,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[5,2,2] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[5,3,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,4] => [1,1] => [1,0,1,0] => [[],[]] => 1
[6,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[6,1,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[6,2,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[6,3] => [1,1] => [1,0,1,0] => [[],[]] => 1
[7,1,1] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[7,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[8,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[9] => [1] => [1,0] => [[]] => 1
[1,1,1,1,1,1,1,1,2] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 1
[1,1,1,1,1,1,1,3] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 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
[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
[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
[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
[1,1,1,1,1,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 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
[1,1,1,1,2,2,2] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[[]]]],[[[]]]] => 3
[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
[1,1,1,1,2,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[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
[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
[1,1,1,1,3,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[[]]]],[[]]] => 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
[1,1,1,1,4,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,5,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,6] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 1
[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
[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
[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
[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
[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
[1,1,1,2,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[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
[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
[1,1,1,2,2,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => 1
[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
[1,1,1,2,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,2,4,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,2,5] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[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
[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
[1,1,1,3,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 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
[1,1,1,3,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[1,1,1,3,3,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => 1
[1,1,1,3,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 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
[1,1,1,4,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,4,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,5,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[1,1,1,5,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,6,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,1,1,7] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 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
[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
[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
[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
[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
[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
[1,1,2,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[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
[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
[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
[1,1,2,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 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
[1,1,2,1,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 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
[1,1,2,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 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] => [[[]],[[]],[[[[]]]]] => 2
[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
[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
[1,1,2,2,1,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[1,1,2,2,2,1,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[[]],[[[]]],[[]]] => 2
[1,1,2,2,2,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => 2
[1,1,2,2,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[1,1,2,2,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[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
[1,1,2,3,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 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
[1,1,2,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,2,4,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,2,4,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,2,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,2,6] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 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
[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
[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
[1,1,3,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[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
[1,1,3,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,3,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,3,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 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
[1,1,3,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[1,1,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,3,3,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[1,1,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[1,1,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 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
[1,1,4,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[1,1,4,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,4,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,4,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[1,1,5,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[1,1,5,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,5,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,1,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,6,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,1,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,7,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,1,8] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 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
[1,2,1,1,1,1,2,1] => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[],[[[[]]]],[],[]] => 1
[1,2,1,1,1,1,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1
[1,2,1,1,1,2,1,1] => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[],[[[]]],[],[[]]] => 1
[1,2,1,1,1,2,2] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1
[1,2,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,1,1,1,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[1,2,1,1,2,1,1,1] => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[],[[]],[],[[[]]]] => 1
[1,2,1,1,2,1,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1
[1,2,1,1,2,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[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
[1,2,1,1,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,2,1,1,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,2,1,1,5] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,2,1,2,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[],[[[[]]]]] => 1
[1,2,1,2,1,1,2] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1
[1,2,1,2,1,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,2,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 1
[1,2,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[[]],[[]]] => 1
[1,2,1,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 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
[1,2,1,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,1,3,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 1
[1,2,1,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 1
[1,2,1,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 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
[1,2,1,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,1,6] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[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
[1,2,2,1,1,1,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1
[1,2,2,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1
[1,2,2,1,1,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[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
[1,2,2,1,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[1,2,2,1,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[1,2,2,1,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[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
[1,2,2,2,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[1,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[1,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[1,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[1,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,2,2,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[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
[1,2,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[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
[1,2,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[1,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[1,2,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,7] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[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
[1,3,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1
[1,3,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,3,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[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
[1,3,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[1,3,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,3,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[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
[1,3,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 1
[1,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[1,3,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[1,3,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[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
[1,3,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[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
[1,3,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[1,3,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,3,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => 1
[1,3,3,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,3,3,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[1,3,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,3,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,6] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[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
[1,4,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[1,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,4,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[1,4,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,4,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,4,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[1,4,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,4,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,4,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[1,5,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,5,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,5,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,5,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,6,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,6,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,6,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,6,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,7,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,7,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,8,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,9] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,1,1,1,1,1,1,1,1] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[]]]]]]]]] => 1
[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
[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
[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
[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
[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
[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
[2,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[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
[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
[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
[2,1,1,1,2,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[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
[2,1,1,1,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,1,1,1,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,1,1,1,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[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
[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
[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
[2,1,1,2,1,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[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
[2,1,1,2,2,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => 1
[2,1,1,2,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[2,1,1,2,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[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
[2,1,1,3,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[2,1,1,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[2,1,1,3,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[2,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[2,1,1,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,5,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,6] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,1,2,1,1,1,1,1] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[],[[[[[]]]]]] => 1
[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
[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
[2,1,2,1,1,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[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
[2,1,2,1,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 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
[2,1,2,1,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[2,1,2,2,1,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[2,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[2,1,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[2,1,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[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
[2,1,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[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
[2,1,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[2,1,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,1,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,1,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[2,1,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,1,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,7] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[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] => [[[]],[[[[[[]]]]]]] => 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
[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
[2,2,1,1,1,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => 1
[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
[2,2,1,1,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[2,2,1,1,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[2,2,1,1,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[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
[2,2,1,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[2,2,1,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[2,2,1,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,1,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[2,2,1,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,1,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,1,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,2,1,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[]]],[[[[]]]]] => 3
[2,2,2,1,1,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => 1
[2,2,2,1,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[2,2,2,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[2,2,2,2,1,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[[]]]],[[]]] => 2
[2,2,2,2,2] => [5] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 5
[2,2,2,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[2,2,2,4] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[2,2,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[2,2,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[2,2,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[2,2,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,6] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 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
[2,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[2,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[2,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[2,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[2,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[2,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,3,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[2,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[2,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,4,4] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[2,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[2,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,5,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,6,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,7,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,8] => [1,1] => [1,0,1,0] => [[],[]] => 1
[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
[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
[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
[3,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[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
[3,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => 1
[3,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[3,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[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
[3,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[3,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[3,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[3,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[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
[3,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[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
[3,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[3,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[3,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[3,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[3,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[3,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,1,6] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[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
[3,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[3,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[3,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[3,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[3,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[3,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => 1
[3,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[3,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[3,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[3,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,3,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => 2
[3,3,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[3,3,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[3,3,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[3,3,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[3,3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[3,3,3,1] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[3,3,4] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[3,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[3,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,4,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[3,5,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,6,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,7] => [1,1] => [1,0,1,0] => [[],[]] => 1
[4,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => 1
[4,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[4,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[4,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[4,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[4,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[4,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[4,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[4,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[4,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[4,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[4,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[4,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,1,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[4,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[4,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[4,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[4,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[4,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,2,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[4,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,3,3] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[4,4,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[4,4,2] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[4,5,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,6] => [1,1] => [1,0,1,0] => [[],[]] => 1
[5,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => 1
[5,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[5,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[5,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[5,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[5,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[5,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,1,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[5,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[5,2,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[5,3,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,4,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,5] => [2] => [1,1,0,0] => [[[]]] => 2
[6,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 1
[6,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[6,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[6,1,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[6,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[6,2,2] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[6,3,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[6,4] => [1,1] => [1,0,1,0] => [[],[]] => 1
[7,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[7,1,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[7,2,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[7,3] => [1,1] => [1,0,1,0] => [[],[]] => 1
[8,1,1] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[8,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[9,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[10] => [1] => [1,0] => [[]] => 1
[1,10] => [1,1] => [1,0,1,0] => [[],[]] => 1
[1,8,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,7,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,6,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,2,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,1,8,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[10,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[1,1,1,1,4,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[[]]]],[[]]] => 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] => [[[]],[[]],[[]],[[]]] => 2
[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] => [[[]],[[[[]]]],[[]]] => 2
[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
[1,1,2,2,3,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[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
[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
[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
[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
[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
[1,1,2,1,3,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 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] => [[[]],[[]],[[[[]]]]] => 2
[1,1,3,3,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[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
[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
[1,1,3,2,2,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[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
[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
[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
[1,1,3,1,2,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,4,4,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[1,1,4,3,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 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
[1,1,4,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[1,1,5,5] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 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] => [[[]],[[[[]]]],[[]]] => 2
[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] => [[[]],[[]],[[]],[[]]] => 2
[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
[2,2,1,1,3,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[2,2,2,2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 6
[2,2,2,1,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[2,2,3,3,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[2,2,3,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[2,2,3,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[2,2,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 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
[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
[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
[2,1,1,2,3,3] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[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
[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
[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
[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
[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
[2,1,1,1,3,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,1,2,3,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[],[[[[]]]]] => 1
[2,1,2,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[2,1,2,2,1,2,1,1] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[],[[]],[],[],[[]]] => 1
[2,1,2,2,1,1,1,2] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[],[[]],[[[]]],[]] => 1
[2,1,2,2,2,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[2,1,2,1,1,3,1,1] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[],[[]],[],[[]]] => 1
[2,1,2,1,1,2,1,2] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[],[[]],[],[],[]] => 1
[2,1,2,1,1,1,1,3] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[],[[[[]]]],[]] => 1
[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
[2,1,3,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 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
[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
[2,1,3,1,1,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[2,1,4,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[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] => [[[]],[[[[[[]]]]]]] => 2
[3,3,1,1,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[3,3,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 2
[3,3,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[3,3,3,3] => [4] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 4
[3,2,1,2,1,1,1,1] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[],[[[[]]]]] => 1
[3,2,1,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 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
[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
[3,2,1,1,2,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[3,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[3,2,2,2,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[3,2,2,1,1,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[3,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[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
[3,1,1,3,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[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
[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
[3,1,1,2,2,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[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
[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
[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
[3,1,1,1,2,4] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[3,1,2,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 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
[3,1,2,2,1,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[3,1,2,1,1,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[3,1,3,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,4,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => 2
[4,4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 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
[4,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[4,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 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
[4,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[4,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[4,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[4,1,1,3,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[4,1,1,2,1,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[4,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[4,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,5,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[5,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[6,6] => [2] => [1,1,0,0] => [[[]]] => 2
[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
[1,2,2,2,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[1,2,2,3,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[1,2,2,3,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[1,2,2,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,2,3,3,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,2,3,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,3,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[1,2,3,3,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,2,4,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,2,4,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,4,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,5,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,3,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[1,3,3,3,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[1,3,4,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,4,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,3,5,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[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
[1,3,2,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,2,2,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,3,2,2,2,2] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[1,3,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,3,3,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,3,3,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,3,4,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,4,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[1,4,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,4,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,4,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,4,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,4,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,4,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,4,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,4,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,5,5,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[1,5,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,5,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,5,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,6,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,3,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[2,3,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,3,3,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[2,3,3,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 1
[2,3,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,4,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,4,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,4,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[2,4,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,5,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,5,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,6,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,2,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[2,2,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 1
[2,2,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[2,2,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,2,2,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[2,2,2,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[2,2,2,2,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[2,2,2,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 2
[2,2,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,2,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[2,3,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,3,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,3,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,3,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,3,3,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[2,4,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,4,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,5,5] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[3,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[3,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[3,6,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,3,3,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[3,3,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[3,3,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[3,3,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 2
[3,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[3,4,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,5,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,2,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[3,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[3,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[3,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[3,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[3,3,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[3,3,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[3,4,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,6,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,4,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[4,5,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[4,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[4,4,4] => [3] => [1,1,1,0,0,0] => [[[[]]]] => 3
[4,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[4,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[4,3,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,6,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,5,2] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[5,4,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,3,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[5,2,5] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,8,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,7,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,6,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,5,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[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
[1,3,1,1,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]] => 1
[1,1,1,1,1,1,1,1,1,2] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 1
[1,11] => [1,1] => [1,0,1,0] => [[],[]] => 1
[1,9,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,7,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,8,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[1,7,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[1,5,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,6,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[1,4,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[1,5,1,1,1,1,2] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1
[1,3,2,1,1,1,2] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => 1
[1,4,1,1,1,1,1,2] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]] => 1
[1,2,2,1,1,1,1,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 1
[1,1,1,1,1,1,1,1,1,1,2] => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => 1
[1,2,2,2,2,2] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => 1
[1,2,2,2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[1,2,2,1,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[1,2,2,1,2,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[1,2,2,1,1,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[1,2,1,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[1,2,1,3,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 1
[1,2,1,2,3,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 1
[1,2,1,2,2,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[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
[1,2,1,1,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,2,1,1,3,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[1,2,1,1,2,4] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[1,2,1,1,1,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[1,1,3,2,2,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[1,1,3,2,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 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
[1,1,3,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,3,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[1,1,2,3,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,2,3,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,2,2,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[1,1,2,2,2,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => 1
[1,1,2,2,1,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[1,1,2,1,4,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,2,1,3,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,2,1,2,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[1,1,2,1,1,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 1
[1,1,1,4,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[1,1,1,4,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,3,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => 1
[1,1,1,3,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,3,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,2,4,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,2,3,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[1,1,1,2,2,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => 1
[1,1,1,2,1,5] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 1
[1,1,1,1,5,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,4,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,3,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,2,5] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 1
[1,1,1,1,1,6] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 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
[1,2,2,2,2,1,3] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => 1
[1,2,2,2,1,3,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1
[1,2,2,2,1,2,3] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 1
[1,2,2,2,1,1,4] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 1
[1,2,2,1,3,2,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[[]]] => 1
[1,2,2,1,3,1,3] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1
[1,2,2,1,2,3,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1
[1,2,2,1,2,2,3] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1
[1,2,2,1,2,1,4] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1
[1,2,2,1,1,4,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1
[1,2,2,1,1,3,3] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]],[[]]] => 1
[1,2,2,1,1,2,4] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1
[1,2,2,1,1,1,5] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 1
[1,2,1,3,2,2,2] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,2,1,3,2,1,3] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,3,1,3,2] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,3,1,2,3] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,3,1,1,4] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1
[1,2,1,2,3,2,2] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1
[1,2,1,2,3,1,3] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,2,2,3,2] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1
[1,2,1,2,2,2,3] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => 1
[1,2,1,2,2,1,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1
[1,2,1,2,1,4,2] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,2,1,3,3] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1
[1,2,1,2,1,2,4] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,2,1,1,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1
[1,2,1,1,4,2,2] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1
[1,2,1,1,4,1,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,3,3,2] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1
[1,2,1,1,3,2,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,3,1,4] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,2,4,2] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,2,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1
[1,2,1,1,2,2,4] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1
[1,2,1,1,2,1,5] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,1,5,2] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,1,1,1,4,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,1,1,1,3,4] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,1,1,1,2,5] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,1,1,1,1,6] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 1
[1,1,3,2,2,2,2] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[[]],[],[[[[]]]]] => 1
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[1,1,1,3,3,2,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[1,1,1,2,2,3,3] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[1,1,1,1,3,3,3] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[[]]]],[[[]]]] => 3
[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
[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
[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
[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
[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
[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
[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
[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
[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
[1,1,1,1,1,4,4] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[[]]]]],[[]]] => 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
[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
[1,1,1,1,1,1,7] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[[]]]]]],[]] => 1
[12] => [1] => [1,0] => [[]] => 1
[1,2,9] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,2,7] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,4,7] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,1,2,1,7] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,2,2,2,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[1,1,2,3,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[3,1,2,1,5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,2,1,5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,1,4,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 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
[7,2,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[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
[1,8,3] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,1,2,5,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[3,1,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,1,4,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[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
[5,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[3,3,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[1,5,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[3,1,4,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,4,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,1,6,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 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
[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
[1,3,1,2,1,1,3] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1
[1,1,3,2,1,1,3] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1
[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
[9,2,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,2,6,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[5,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 1
[1,6,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[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
[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
[1,3,2,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1
[1,1,4,1,2,2,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 1
[7,4,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[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
[1,2,2,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[3,8,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,10,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,1,2,7,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[3,1,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,3,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,1,4,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 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
[5,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,5,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[3,1,4,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,1,6,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 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
[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
[1,3,1,2,1,3,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,1,3,2,1,3,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => 1
[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
[7,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 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
[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
[1,4,2,1,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1
[5,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 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
[3,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,7,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 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
[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
[1,3,2,2,2,1,1] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[[[]]],[[]]] => 1
[1,1,4,2,2,1,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[[]],[],[[]],[[]]] => 1
[5,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 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
[3,3,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[1,5,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 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
[3,1,6,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,3,6,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,1,8,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 1
[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
[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
[1,3,1,2,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1
[1,1,3,2,3,1,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[],[[]]] => 1
[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
[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
[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
[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
[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
[1,3,3,2,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => 1
[1,1,5,2,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => 1
[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
[1,3,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,1,3,4,1,1,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[[]],[],[],[[[]]]] => 1
[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
[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
[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
[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
[2,2,2,1,1,2,2] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[[]]],[[]],[[]]] => 2
[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
[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
[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
[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
[2,2,1,1,2,2,2] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2
[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
[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
[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
[2,1,2,1,2,1,2,1] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[]] => 1
[2,1,2,1,1,2,2,1] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]] => 1
[2,1,2,1,1,1,2,2] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[],[[[]]],[[]]] => 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
[2,1,2,2,1,1,2,1] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1
[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
[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
[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
[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
[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
[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
[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
[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
[1,2,1,2,2,2,2] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[[[[]]]]] => 1
[1,2,1,2,2,1,2,1] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[],[[]],[],[],[]] => 1
[1,2,1,2,1,2,1,2] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[]] => 1
[1,2,1,2,1,2,2,1] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[],[[]],[]] => 1
[1,2,1,2,1,1,2,2] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[[]],[[]]] => 1
[1,2,1,1,2,1,2,2] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[],[[]],[],[],[[]]] => 1
[1,2,1,1,2,2,1,2] => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 1
[1,2,1,1,2,2,2,1] => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[],[[]],[[[]]],[]] => 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
[1,2,2,1,2,2,2] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => 1
[1,2,2,1,2,1,2,1] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[],[]] => 1
[1,2,2,1,1,2,1,2] => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[[]],[],[],[]] => 1
[1,2,2,1,1,2,2,1] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 1
[1,2,2,1,1,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[],[[]],[[[]]],[[]]] => 1
[1,2,2,2,1,2,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[],[[[]]],[],[[]]] => 1
[1,2,2,2,1,1,2,1] => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[],[[[]]],[[]],[],[]] => 1
[1,2,2,2,2,1,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => 1
[1,1,2,2,2,2,2] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[[[[[]]]]]] => 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
[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
[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
[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
[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
[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
[3,3,3,2] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[3,4,4] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[2,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[4,4,3] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[2,1,1,1,1,1,1,1,1,1] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[]]]]]]]]]] => 1
[3,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[4,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[4,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[4,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[4,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 1
[5,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[5,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[5,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[5,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 1
[6,5,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[6,4,2] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[6,3,3] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[6,2,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[7,5] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,8,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,1,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,1,1,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,1,1,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[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
[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
[11,1] => [1,1] => [1,0,1,0] => [[],[]] => 1
[2,9,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[3,7,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[2,1,8,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[2,2,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[2,1,1,7,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,1,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,1,1,1,6,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,1,1,2,4,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[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
[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
[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
[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
[2,1,1,1,1,1,1,1,1,1,1] => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[[]]]]]]]]]]] => 1
[2,2,2,2,2,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 1
[3,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[2,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[3,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[4,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 1
[2,2,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 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
[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
[3,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[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
[2,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[3,3,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[4,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 1
[5,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,2,2,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[[]]],[],[[]]] => 1
[3,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 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
[3,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[4,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[2,2,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[3,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[2,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[3,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => 1
[4,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[2,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[3,3,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[4,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[[]]] => 1
[5,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 1
[2,2,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[3,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[2,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => 1
[3,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[4,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[2,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[3,3,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[[]],[],[[[]]]] => 1
[4,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[],[[]],[[[]]]] => 1
[5,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 1
[2,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[3,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[4,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[5,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 1
[6,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => 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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[2,2,3,3,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[3,3,2,2,1,1,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[[]],[[]],[[[]]]] => 2
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[3,3,3,1,1,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[]]],[[[[]]]]] => 3
[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
[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
[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
[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
[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
[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
[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
[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
[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
[4,4,1,1,1,1,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[[[[[]]]]]] => 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
[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
[7,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => 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
[2,1,2,1,2,1,1,2] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[],[[]],[]] => 1
[2,1,2,1,2,2,1,1] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[],[[]],[[]]] => 1
[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
[1,2,2,1,2,1,1,2] => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]] => 1
[1,2,2,1,2,2,1,1] => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[],[[]],[],[[]],[[]]] => 1
[1,2,1,2,2,1,1,2] => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[],[[]],[[]],[]] => 1
[1,2,1,2,2,2,1,1] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[],[],[],[[[]]],[[]]] => 1
[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
[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
[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
[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
[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
[2,1,2,1,1,1,1,2] => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[],[[[[]]]],[]] => 1
[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
[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
[1,2,2,4,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 1
[1,2,4,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 1
[1,2,5,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 1
[1,3,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,4,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 1
[1,5,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,5,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,5,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[2,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 1
[2,2,5,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 1
[6,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 1
[2,2,2,2,2,1,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[[]]]]],[[]]] => 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
[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
[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
[1,2,2,2,2,1,1,1] => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[],[[[[]]]],[[[]]]] => 1
[9,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[1,9,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[10,2] => [1,1] => [1,0,1,0] => [[],[]] => 1
[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
[1,2,2,3,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1
[1,2,2,4,1,1,1] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[],[[]],[],[[[]]]] => 1
[1,2,3,1,2,2,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 1
[1,2,3,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1
[1,2,3,2,1,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,4,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1
[1,2,3,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[[]],[[]]] => 1
[1,2,3,3,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[[]],[[[]]]] => 1
[1,2,4,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,2,5,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[[[[]]]]] => 1
[1,3,1,2,2,2,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => 1
[1,3,1,3,1,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,3,1,3,2,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1
[1,3,2,1,3,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[],[],[],[],[],[[]]] => 1
[1,4,1,1,2,2,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 1
[1,4,1,1,3,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1
[1,3,2,2,1,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,3,3,1,1,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 1
[1,4,1,2,1,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,4,2,1,1,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1
[1,5,1,1,1,2,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,3,2,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,3,3,1,2,1,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[],[[]],[],[],[[]]] => 1
[1,3,4,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[[[[]]]]] => 1
[1,4,1,2,2,1,1] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[],[[]],[[]]] => 1
[1,4,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,5,1,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[],[],[[]],[],[[]]] => 1
[1,4,2,2,1,1,1] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[],[],[[]],[[[]]]] => 1
[1,4,3,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[[[[]]]]] => 1
[1,5,2,1,1,1,1] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[],[[[[]]]]] => 1
[1,6,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[[[[[]]]]]] => 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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[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
[6,1,1,1,1,1,1] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => 1
[11] => [1] => [1,0] => [[]] => 1
[2,9] => [1,1] => [1,0,1,0] => [[],[]] => 1
[1,1,2,2,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 1
[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
[1,3,1,2,3,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,3,1,2,1,4,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,3,1,1,1,5,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,3,2,1,3,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,3,1,3,2,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,3,1,1,4,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1
[1,2,2,3,2,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 1
[1,2,2,1,4,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1
[1,2,2,1,2,4,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 1
[1,2,1,4,1,3,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,3,3,2,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 1
[1,2,1,3,1,4,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,2,1,5,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 1
[1,2,1,1,5,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,3,4,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,1,1,1,6,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,1,1,5,1,3,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => 1
[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
[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
[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
[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
[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
[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
[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
[1,1,2,3,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 1
[2,2,2,2,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 1
[1,2,2,2,2,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[1,2,2,3,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[2,2,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,2,3,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[2,3,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 1
[1,3,2,2,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 1
[5,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 1
[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
[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
[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
[1,1,1,7,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 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
[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
[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
[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
[1,3,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,3,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,5,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[[[[[]]]]]] => 1
[1,5,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,7,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,6,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,4,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,2,1,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,1,1,1,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,2,1,1,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,2,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,2,3,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,1,1,7,1,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[[]]],[],[[[]]]] => 1
[1,1,1,9,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 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
[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
[1,3,1,7,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,5,1,1,1,3,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,5,1,3,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,5,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,7,1,1,1,1,1] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[[[[[]]]]]] => 1
[1,7,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,9,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 1
[1,11,1] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,8,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,6,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,6,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,4,1,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,4,1,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,4,1,1,1,4,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 1
[1,4,1,1,3,2,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 1
[1,4,3,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,4,3,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,4,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,1,6,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,2,1,8,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,3,4,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,2,3,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,5,2,1,1,1] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[],[[[]]]] => 1
[1,2,5,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,2,7,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[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
[1,1,9] => [2,1] => [1,1,0,0,1,0] => [[[]],[]] => 1
[1,1,1,1,1,1,1,1,3] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 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
[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
[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
[2,2,2,6] => [3,1] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 1
[2,2,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 1
[1,6,4] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,5,5] => [1,2] => [1,0,1,1,0,0] => [[],[[]]] => 1
[1,4,6] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,3,7] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,2,8] => [1,1,1] => [1,0,1,0,1,0] => [[],[],[]] => 1
[1,2,5,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,2,2,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 1
[2,2,2,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 1
[1,2,3,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 1
[1,2,2,5,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 1
[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
[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] => [[[]],[[[]]],[[[]]]] => 2
[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
[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
[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
[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
[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
[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
[1,1,2,2,2,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => 1
[1,1,2,5,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,1,5,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[[]],[],[],[[]]] => 1
[1,4,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[],[],[[]],[[]]] => 1
[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
[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
[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
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 3,0,1 6,1,0,1 15,0,0,0,1 27,3,1,0,0,1 61,2,0,0,0,0,1
F1=q
F2=q+q2
F3=3 q+q3
F4=6 q+q2+q4
F5=15 q+q5
F6=27 q+3 q2+q3+q6
F7=61 q+2 q2+q7
Description
The protection number of an ordered tree.
This is the minimal distance from the root to a leaf.
This is the minimal distance from the root to a leaf.
Map
bounce path
Description
The bounce path determined by an integer composition.
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
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path D of semilength n may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths D1,…,Dk of respective semilengths n1,…,nk (so one has n=n1+…nk) each of which has no returns.
Denote by ˜Di the path of semilength ni−1 obtained from Di by removing the initial up- and the final down-step.
This map then sends D to the tree T having a root note with ordered children T1,…,Tk which are again ordered trees computed from D1,…,Dk respectively.
The unique path of semilength 1 is sent to the tree consisting of a single node.
This map is recursively defined as follows: A Dyck path D of semilength n may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths D1,…,Dk of respective semilengths n1,…,nk (so one has n=n1+…nk) each of which has no returns.
Denote by ˜Di the path of semilength ni−1 obtained from Di by removing the initial up- and the final down-step.
This map then sends D to the tree T having a root note with ordered children T1,…,Tk which are again ordered trees computed from D1,…,Dk respectively.
The unique path of semilength 1 is sent to the tree consisting of a single node.
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