Identifier
-
Mp00040:
Integer compositions
—to partition⟶
Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
St000167: Ordered trees ⟶ ℤ
Values
[1] => [1] => [1,0,1,0] => [[],[]] => 2
[1,1] => [1,1] => [1,0,1,1,0,0] => [[],[[]]] => 2
[2] => [2] => [1,1,0,0,1,0] => [[[]],[]] => 2
[1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => [[],[[[]]]] => 2
[1,2] => [2,1] => [1,0,1,0,1,0] => [[],[],[]] => 3
[2,1] => [2,1] => [1,0,1,0,1,0] => [[],[],[]] => 3
[3] => [3] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 2
[1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [[],[[[[]]]]] => 2
[1,1,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 3
[1,2,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 3
[1,3] => [3,1] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => 3
[2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 3
[2,2] => [2,2] => [1,1,0,0,1,1,0,0] => [[[]],[[]]] => 2
[3,1] => [3,1] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => 3
[4] => [4] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 2
[1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[],[[[[[]]]]]] => 2
[1,1,1,2] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[1,1,2,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[1,1,3] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 3
[1,2,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[1,2,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 3
[1,3,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 3
[1,4] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 3
[2,1,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 3
[2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => [[],[],[[]]] => 3
[2,3] => [3,2] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 3
[3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 3
[3,2] => [3,2] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 3
[4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 3
[5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 2
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[],[[[[[[]]]]]]] => 2
[1,1,1,1,2] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => 3
[1,1,1,2,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => 3
[1,1,1,3] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[1,1,2,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => 3
[1,1,2,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[1,1,3,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[1,1,4] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[1,2,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => 3
[1,2,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[1,2,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[1,2,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 4
[1,3,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[1,3,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 4
[1,4,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[1,5] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[[],[]]]],[]] => 3
[2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => 3
[2,1,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[2,1,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[2,1,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 4
[2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [[],[[],[[]]]] => 3
[2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [[[]],[[[]]]] => 2
[2,3,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 4
[2,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 3
[3,1,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 4
[3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 4
[3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => [[[[]]],[[]]] => 2
[4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 3
[4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 3
[5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[[],[]]]],[]] => 3
[6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[[]]]]]],[]] => 2
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[],[[[[[[[]]]]]]]] => 2
[1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => 3
[1,1,1,1,2,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => 3
[1,1,1,1,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => 3
[1,1,1,2,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => 3
[1,1,1,2,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[1,1,1,3,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => 3
[1,1,1,4] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[1,1,2,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => 3
[1,1,2,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[1,1,2,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[1,1,2,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[1,1,3,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => 3
[1,1,3,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[1,1,4,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[1,1,5] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[[],[[]]]],[]] => 3
[1,2,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => 3
[1,2,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[1,2,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[1,2,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[1,2,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[1,2,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[1,2,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[1,2,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 4
[1,3,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => 3
[1,3,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[1,3,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[1,3,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 3
[1,4,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[1,4,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 4
[1,5,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[[],[[]]]],[]] => 3
[1,6] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[]]]]],[]] => 3
[2,1,1,1,1,1] => [2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => 3
[2,1,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[2,1,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[2,1,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[2,1,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[2,1,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
>>> Load all 1199 entries. <<<[2,1,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[2,1,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 4
[2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[],[[[],[[]]]]] => 3
[2,2,1,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [[],[],[[[]]]] => 3
[2,2,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 3
[2,3,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[2,3,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 3
[2,4,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 4
[2,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[[]],[]]],[]] => 3
[3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => 3
[3,1,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[3,1,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[3,1,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 3
[3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 4
[3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 3
[3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [[[],[]],[[]]] => 3
[3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 3
[4,1,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 4
[4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 4
[4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 3
[5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[[],[[]]]],[]] => 3
[5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[[]],[]]],[]] => 3
[6,1] => [6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[]]]]],[]] => 3
[7] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 2
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[]]]]]]]]] => 2
[1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 3
[1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 3
[1,1,1,1,1,3] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => 3
[1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 3
[1,1,1,1,2,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,1,1,1,3,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => 3
[1,1,1,1,4] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => 3
[1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 3
[1,1,1,2,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,1,1,2,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,1,1,2,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,1,1,3,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => 3
[1,1,1,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,1,1,4,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => 3
[1,1,1,5] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => 3
[1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 3
[1,1,2,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,1,2,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,1,2,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,1,2,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,1,2,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[1,1,2,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,1,2,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[1,1,3,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => 3
[1,1,3,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,1,3,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,1,3,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 3
[1,1,4,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => 3
[1,1,4,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[1,1,5,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => 3
[1,1,6] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[[],[[]]]]],[]] => 3
[1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 3
[1,2,1,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,2,1,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,2,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,2,1,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,2,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[1,2,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,2,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[1,2,2,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[1,2,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[1,2,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[1,2,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[1,2,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,2,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[1,2,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[1,2,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => 4
[1,3,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => 3
[1,3,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,3,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,3,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 3
[1,3,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[1,3,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[1,3,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 3
[1,3,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 4
[1,4,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => 3
[1,4,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[1,4,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[1,4,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 4
[1,5,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => 3
[1,5,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => 4
[1,6,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[[],[[]]]]],[]] => 3
[1,7] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[[],[]]]]]],[]] => 3
[2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 3
[2,1,1,1,1,2] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[2,1,1,1,2,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[2,1,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[2,1,1,2,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[2,1,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[2,1,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[2,1,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[2,1,2,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[2,1,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[2,1,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[2,1,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[2,1,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[2,1,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[2,1,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[2,1,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => 4
[2,2,1,1,1,1] => [2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[],[[[[],[[]]]]]] => 3
[2,2,1,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[2,2,1,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[2,2,1,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [[],[[],[[[]]]]] => 3
[2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[[]],[[[[]]]]] => 2
[2,2,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 3
[2,3,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[2,3,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[2,3,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[2,3,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 3
[2,4,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 3
[2,5,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => 4
[2,6] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[[]],[]]]],[]] => 3
[3,1,1,1,1,1] => [3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => 3
[3,1,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[3,1,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[3,1,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 3
[3,1,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[3,1,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[3,1,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 3
[3,1,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 4
[3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 4
[3,2,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 4
[3,2,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 3
[3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [[],[[]],[[]]] => 3
[3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [[[]],[],[[]]] => 3
[3,4,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 4
[3,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[[]]],[]],[]] => 3
[4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => 3
[4,1,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[4,1,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[4,1,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 4
[4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 4
[4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 3
[4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 4
[4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[[]]]],[[]]] => 2
[5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => 3
[5,1,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => 4
[5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => 4
[5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[[]]],[]],[]] => 3
[6,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[[],[[]]]]],[]] => 3
[6,2] => [6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[[]],[]]]],[]] => 3
[7,1] => [7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[[],[]]]]]],[]] => 3
[8] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 2
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[]]]]]]]]]] => 2
[1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 3
[1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 3
[1,1,1,1,1,4] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => 3
[1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,1,1,2,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 3
[1,1,1,1,3,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,1,1,4,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => 3
[1,1,1,1,5] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 3
[1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,1,2,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,1,2,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,1,1,2,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,1,2,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 3
[1,1,1,3,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,1,3,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,1,3,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[1,1,1,4,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => 3
[1,1,1,4,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,1,1,5,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 3
[1,1,1,6] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[[[]]]]],[]] => 3
[1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,2,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,2,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,1,2,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,2,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,1,2,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,1,2,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,1,2,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,1,2,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,2,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,1,2,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,1,2,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 3
[1,1,3,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,3,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,3,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[1,1,3,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,1,3,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,1,3,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[1,1,3,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[1,1,4,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => 3
[1,1,4,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,1,4,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,1,4,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[1,1,5,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 3
[1,1,5,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[1,1,6,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[[[]]]]],[]] => 3
[1,1,7] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[[],[[]]]]]],[]] => 3
[1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,2,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,2,1,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,2,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,2,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,2,1,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,2,1,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,2,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,2,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,2,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,2,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,2,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[1,2,2,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,2,2,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,2,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,2,2,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[1,2,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 3
[1,2,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,2,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[1,2,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,2,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,2,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,2,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[1,2,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,2,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[1,2,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[1,2,6] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => 4
[1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 3
[1,3,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,3,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,3,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[1,3,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,3,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,3,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[1,3,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[1,3,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[1,3,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,3,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[1,3,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[1,3,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[1,3,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[1,3,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[1,3,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => 4
[1,4,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => 3
[1,4,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,4,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,4,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[1,4,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[1,4,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[1,4,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[1,4,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[[[],[]]],[[]]] => 3
[1,5,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 3
[1,5,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[1,5,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[1,5,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => 4
[1,6,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[[[]]]]],[]] => 3
[1,6,2] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => 4
[1,7,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[[],[[]]]]]],[]] => 3
[1,8] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[],[]]]]]]],[]] => 3
[2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 3
[2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[2,1,1,1,1,3] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[2,1,1,1,2,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,1,1,1,3,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[2,1,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[2,1,1,2,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,1,1,2,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,1,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,1,1,3,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[2,1,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,1,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[2,1,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[2,1,2,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,1,2,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,1,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,1,2,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,1,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 3
[2,1,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,1,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[2,1,3,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[2,1,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,1,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,1,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[2,1,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[2,1,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[2,1,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[2,1,6] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => 4
[2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[],[[[[[],[[]]]]]]] => 3
[2,2,1,1,1,2] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,2,1,1,2,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,2,1,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,2,1,2,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,2,1,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 3
[2,2,1,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,2,1,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[2,2,2,1,1,1] => [2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[],[[[],[[[]]]]]] => 3
[2,2,2,1,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 3
[2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[],[],[[[[]]]]] => 3
[2,2,2,3] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => 3
[2,2,3,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,2,3,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => 3
[2,2,4,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]]],[]] => 3
[2,3,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[2,3,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,3,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,3,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[2,3,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[2,3,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => 3
[2,3,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[2,3,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 4
[2,4,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[2,4,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[2,4,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[2,4,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 4
[2,5,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]]],[]] => 3
[2,6,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => 4
[2,7] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[[]],[]]]]],[]] => 3
[3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 3
[3,1,1,1,1,2] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[3,1,1,1,2,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[3,1,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[3,1,1,2,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[3,1,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[3,1,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[3,1,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[3,1,2,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[3,1,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[3,1,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[3,1,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[3,1,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[3,1,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[3,1,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[3,1,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => 4
[3,2,1,1,1,1] => [3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 4
[3,2,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[3,2,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[3,2,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 4
[3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => 3
[3,2,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[3,2,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 4
[3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [[],[[[]],[[]]]] => 3
[3,3,1,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [[],[],[],[[]]] => 4
[3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[[]]],[[[]]]] => 2
[3,4,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[3,4,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 4
[3,5,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => 4
[3,6] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[[]]],[]]],[]] => 3
[4,1,1,1,1,1] => [4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => 3
[4,1,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[4,1,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[4,1,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[4,1,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[4,1,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[4,1,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[4,1,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[[[],[]]],[[]]] => 3
[4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 4
[4,2,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 4
[4,2,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 4
[4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 4
[4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 4
[4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [[[[],[]]],[[]]] => 3
[4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 3
[5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 3
[5,1,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[5,1,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[5,1,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => 4
[5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 4
[5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]]],[]] => 3
[5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => 4
[5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 3
[6,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[[[]]]]],[]] => 3
[6,1,2] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => 4
[6,2,1] => [6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => 4
[6,3] => [6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[[]]],[]]],[]] => 3
[7,1,1] => [7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[[],[[]]]]]],[]] => 3
[7,2] => [7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[[]],[]]]]],[]] => 3
[8,1] => [8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[],[]]]]]]],[]] => 3
[9] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 2
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[],[[[[[[[[[[]]]]]]]]]]] => 2
[1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 3
[1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 3
[1,1,1,1,1,5] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => 3
[1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,1,2,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,1,3,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 3
[1,1,1,1,4,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,1,1,5,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => 3
[1,1,1,1,6] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => 3
[1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,2,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,1,2,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,2,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,1,2,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,1,2,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,3,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,1,3,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,1,3,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,1,1,3,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 3
[1,1,1,4,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,1,4,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,1,4,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,1,1,5,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => 3
[1,1,1,5,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,1,1,6,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => 3
[1,1,1,7] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[[],[[[]]]]]],[]] => 3
[1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,2,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,2,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,2,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,2,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,2,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,2,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,1,2,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[1,1,2,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,2,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,2,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,2,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,2,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,1,2,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,2,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,1,2,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,1,2,6] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,3,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,3,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,3,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,1,3,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,1,3,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,3,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,1,3,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,1,3,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,1,3,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,1,3,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,1,3,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 3
[1,1,4,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,4,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,4,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,1,4,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,1,4,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,1,4,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,1,4,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => 3
[1,1,5,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => 3
[1,1,5,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,1,5,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,1,5,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[1,1,6,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => 3
[1,1,6,2] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[1,1,7,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[[],[[[]]]]]],[]] => 3
[1,1,8] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[],[[]]]]]]],[]] => 3
[1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,2,1,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,2,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,1,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,2,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,1,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[1,2,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,2,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,2,1,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,2,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,2,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,2,1,6] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,2,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[1,2,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,2,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[1,2,2,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[1,2,2,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[1,2,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[1,2,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[1,2,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,2,2,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,2,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,3,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,2,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,2,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[1,2,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,2,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[1,2,4,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,2,4,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,2,4,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,2,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[1,2,5,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,2,5,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[1,2,6,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[1,2,7] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => 4
[1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,3,1,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,3,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,3,1,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,3,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,3,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,3,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,3,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,3,1,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,3,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,3,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,3,1,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[1,3,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,3,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,3,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,3,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[1,3,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[1,3,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,3,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[1,3,3,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[1,3,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,3,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[1,3,3,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[[],[]],[[[]]]] => 3
[1,3,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,3,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[1,3,5,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[1,3,6] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => 4
[1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 3
[1,4,1,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,4,1,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,4,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,4,1,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,4,1,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,4,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,4,1,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => 3
[1,4,2,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[1,4,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,4,2,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[1,4,2,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[1,4,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[1,4,3,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[1,4,4,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => 3
[1,4,5] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => 4
[1,5,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => 3
[1,5,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,5,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,5,1,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[1,5,2,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[1,5,2,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[1,5,3,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[1,5,4] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => 4
[1,6,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => 3
[1,6,1,2] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[1,6,2,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[1,6,3] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => 4
[1,7,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[[],[[[]]]]]],[]] => 3
[1,7,2] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => 4
[1,8,1] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[],[[]]]]]]],[]] => 3
[1,9] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[],[]]]]]]]],[]] => 3
[2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 3
[2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[2,1,1,1,1,4] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,1,1,2,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[2,1,1,1,3,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,1,1,4,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[2,1,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,1,2,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,1,2,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,1,1,2,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[2,1,1,3,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,1,3,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[2,1,1,4,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[2,1,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,1,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[2,1,1,6] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,2,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,2,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,1,2,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,2,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,1,2,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,1,2,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,1,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,1,2,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,1,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,1,2,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[2,1,3,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,3,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,3,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[2,1,3,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,1,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,1,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[2,1,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[2,1,4,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[2,1,4,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,1,4,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,1,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[2,1,5,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[2,1,5,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[2,1,6,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[2,1,7] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => 4
[2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[],[[[[[[],[[]]]]]]]] => 3
[2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,2,1,1,1,3] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,2,1,1,2,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,2,1,1,3,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,2,1,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,2,1,2,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,2,1,2,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,2,1,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,2,1,3,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,2,1,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,2,1,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,2,1,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[],[[[[],[[[]]]]]]] => 3
[2,2,2,1,1,2] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,2,2,1,2,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,2,2,1,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,2,2,2,1,1] => [2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[],[[],[[[[]]]]]] => 3
[2,2,2,2,2] => [2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[[]],[[[[[]]]]]] => 2
[2,2,2,3,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => 3
[2,2,3,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,2,3,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,2,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,2,3,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => 3
[2,2,4,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,2,4,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => 3
[2,2,5,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[2,2,6] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[[]],[[]]]],[]] => 3
[2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[2,3,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,3,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,3,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[2,3,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,3,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,3,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[2,3,1,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[2,3,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[2,3,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,3,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[2,3,2,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => 3
[2,3,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[2,3,3,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => 3
[2,3,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[2,3,5] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => 4
[2,4,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[2,4,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,4,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,4,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[2,4,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[2,4,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => 3
[2,4,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[2,4,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[[]],[]],[[]]] => 3
[2,5,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[2,5,1,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[2,5,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[2,5,3] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => 4
[2,6,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[2,6,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[[]],[[]]]],[]] => 3
[2,7,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => 4
[2,8] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[[]],[]]]]]],[]] => 3
[3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 3
[3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[3,1,1,1,1,3] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[3,1,1,1,2,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,1,1,1,3,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[3,1,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[3,1,1,2,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,1,1,2,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,1,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,1,1,3,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[3,1,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,1,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[3,1,1,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[3,1,2,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,1,2,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,1,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,1,2,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,1,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[3,1,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,1,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[3,1,3,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[3,1,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,1,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,1,3,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[[],[]],[[[]]]] => 3
[3,1,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[3,1,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[3,1,5,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[3,1,6] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => 4
[3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 4
[3,2,1,1,1,2] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,2,1,1,2,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,2,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,2,1,2,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,2,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[3,2,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,2,1,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[3,2,2,1,1,1] => [3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 4
[3,2,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 4
[3,2,2,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => 3
[3,2,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,2,3,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => 3
[3,2,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[3,2,5] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => 4
[3,3,1,1,1,1] => [3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[],[[[[]],[[]]]]] => 3
[3,3,1,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,3,1,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,3,1,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[[],[]],[[[]]]] => 3
[3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[],[[],[],[[]]]] => 4
[3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[[]],[[],[[]]]] => 3
[3,3,3,1] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[[],[]],[[[]]]] => 3
[3,3,4] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[[]]],[[],[]]] => 3
[3,4,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[3,4,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[3,4,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[3,4,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[[]]],[[],[]]] => 3
[3,5,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[3,5,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => 4
[3,6,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => 4
[3,7] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[[]]],[]]]],[]] => 3
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 3
[4,1,1,1,1,2] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[4,1,1,1,2,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[4,1,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[4,1,1,2,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[4,1,1,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[4,1,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[4,1,1,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => 3
[4,1,2,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[4,1,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[4,1,2,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[4,1,2,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[4,1,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[4,1,3,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[4,1,4,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => 3
[4,1,5] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => 4
[4,2,1,1,1,1] => [4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 4
[4,2,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[4,2,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[4,2,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[4,2,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 4
[4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => 3
[4,2,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[4,2,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[[]],[]],[[]]] => 3
[4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 4
[4,3,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 5
[4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[[]]],[[],[]]] => 3
[4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[[],[[]]],[[]]] => 3
[4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[[[]],[]],[[]]] => 3
[4,5,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => 4
[4,6] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[[]]]],[]],[]] => 3
[5,1,1,1,1,1] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => 3
[5,1,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[5,1,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[5,1,1,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[5,1,2,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[5,1,2,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[5,1,3,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[5,1,4] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => 4
[5,2,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 4
[5,2,1,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 4
[5,2,3] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => 4
[5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 4
[5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => 4
[5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => 4
[5,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[[]]]]],[[]]] => 2
[6,1,1,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => 3
[6,1,1,2] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[6,1,2,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[6,1,3] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => 4
[6,2,1,1] => [6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 4
[6,2,2] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[[]],[[]]]],[]] => 3
[6,3,1] => [6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => 4
[6,4] => [6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[[]]]],[]],[]] => 3
[7,1,1,1] => [7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[[],[[[]]]]]],[]] => 3
[7,1,2] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => 4
[7,2,1] => [7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => 4
[7,3] => [7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[[]]],[]]]],[]] => 3
[8,1,1] => [8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[],[[]]]]]]],[]] => 3
[8,2] => [8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[[]],[]]]]]],[]] => 3
[9,1] => [9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[],[]]]]]]]],[]] => 3
[10] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => 2
[1,5,4,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[],[[]]],[],[]] => 4
[1,4,5,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[],[[]]],[],[]] => 4
[2,2,2,1,2,3] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,2,3,2,1,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,2,4,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 3
[2,1,2,3,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,1,2,2,2,3] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,1,4,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[3,3,3,3] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[[]]],[[[[]]]]] => 2
[3,2,1,2,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[3,2,2,2,1,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[3,2,3,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[3,1,3,5] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 4
[4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 3
[4,3,2,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[4,2,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 3
[4,1,2,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[5,4,1,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[5,3,1,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 4
[5,2,1,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[1,2,2,2,3,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[1,2,2,3,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[1,2,2,4,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,2,3,4,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,2,3,2,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[1,2,3,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[1,2,4,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[],[[],[]],[[]]] => 4
[1,2,4,3,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,2,4,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,2,5,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[1,3,3,3,2] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[1,3,4,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[1,3,4,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,3,5,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 4
[1,3,2,4,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,3,2,2,2,2] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[1,3,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[1,3,3,4,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[1,3,3,2,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[1,3,4,4] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => 4
[1,4,4,2,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[],[[],[]],[[]]] => 4
[1,4,5,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[1,4,3,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[1,4,3,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,4,4,3] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => 4
[1,4,2,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[],[[],[]],[[]]] => 4
[1,4,2,3,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,4,2,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[1,4,3,4] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => 4
[1,5,4,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[1,5,3,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 4
[1,5,2,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[2,3,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,3,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[2,3,4,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[2,4,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[2,4,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 3
[2,4,2,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[2,4,3,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[2,5,4,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[2,5,3,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[2,5,2,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[2,2,3,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,2,4,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[2,2,5,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[2,2,2,3,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,2,2,2,3,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[2,2,3,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[2,3,4,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[2,3,5,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[2,3,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[2,3,3,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[2,4,5,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[2,4,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 3
[3,4,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[3,4,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[3,5,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 4
[3,5,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[3,3,4,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[3,3,2,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[3,4,4,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => 4
[3,4,2,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[3,5,4] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 4
[3,2,4,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[3,2,5,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[3,2,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[3,2,4,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[3,2,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[3,3,5,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 4
[3,3,2,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[3,4,5] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 4
[4,5,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[4,4,3,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => 4
[4,5,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 4
[4,3,4,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[[],[]],[],[[]]] => 4
[4,3,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[4,4,4] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[[]]]],[[[]]]] => 2
[4,2,5,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[4,2,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[[]],[[]],[[]]] => 3
[4,2,3,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 4
[4,3,5] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 4
[5,4,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 4
[5,3,4] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 4
[1,5,1,1,1,2] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,5,2,1,2] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[],[[],[[]]],[]] => 4
[1,2,2,2,2,2] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[[[[[]]]]]] => 3
[1,2,1,1,1,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,1,2,1,1,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,1,1,2,1,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,1,1,1,5,2] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,1,1,1,2,5] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,1,1,1,1,6] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[[[[[]]]]],[]] => 3
[1,2,2,2,5] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 4
[1,1,2,3,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[3,1,2,1,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[1,3,2,1,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[1,1,4,1,5] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 4
[1,1,2,5,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[3,1,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[1,1,4,3,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[5,1,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[3,3,2,1,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[],[],[],[[[]]]] => 4
[1,5,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[3,1,4,1,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[1,3,4,1,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[5,2,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 4
[3,1,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[1,3,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[1,1,4,5,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 4
[5,1,2,3,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[1,5,2,3,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[3,1,4,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[5,3,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[3,5,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[5,1,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 4
[3,3,4,1,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 4
[1,5,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 4
[3,2,2,2,2,1] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[4,2,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[4,2,2,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 5
[5,4,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[5,3,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 4
[5,3,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[5,2,4,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 5
[5,2,3,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[5,2,2,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 4
[2,1,1,1,5,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[2,1,2,5,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[],[[],[[]]],[]] => 4
[2,2,2,2,2,1] => [2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[],[],[[[[[]]]]]] => 3
[5,1,1,1,2,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[5,1,1,2,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[5,1,2,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[2,5,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[5,2,1,1,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[6,1,1,1,1,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[[[[[]]]]],[]] => 3
[1,2,5,2,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 4
[1,3,5,2,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[1,5,2,2,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 4
[1,5,3,2,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 5
[2,5,2,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 4
[2,2,5,2,1] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 4
[1,2,2,2,2,3] => [3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 4
[5,1,1,1,1,2] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,3,1,5,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[],[[[]],[]],[]] => 4
[1,5,1,3,1] => [5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[],[[[]],[]],[]] => 4
[1,4,1,4,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[],[[[]]],[[]]] => 3
[1,4,3,2,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[]]] => 5
[1,2,3,4,1] => [4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[]]] => 5
[1,2,5,2,1] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[],[[],[[]]],[]] => 4
[1,4,3,4,1] => [4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[],[[]],[],[[]]] => 4
[1,4,5,2,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[],[[],[]],[],[]] => 5
[1,2,5,4,1] => [5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[],[[],[]],[],[]] => 5
[1,1,2,5,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
[1,1,5,2,1,1] => [5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 4
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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:
2,2 3,5 2,14 4,22,6 2,44,18 4,68,56 3,107,146 4,172,312,24
$F_{1} = q^{2}$
$F_{2} = 2\ q^{2}$
$F_{3} = 2\ q^{2} + 2\ q^{3}$
$F_{4} = 3\ q^{2} + 5\ q^{3}$
$F_{5} = 2\ q^{2} + 14\ q^{3}$
$F_{6} = 4\ q^{2} + 22\ q^{3} + 6\ q^{4}$
$F_{7} = 2\ q^{2} + 44\ q^{3} + 18\ q^{4}$
$F_{8} = 4\ q^{2} + 68\ q^{3} + 56\ q^{4}$
$F_{9} = 3\ q^{2} + 107\ q^{3} + 146\ q^{4}$
$F_{10} = 4\ q^{2} + 172\ q^{3} + 312\ q^{4} + 24\ q^{5}$
Description
The number of leaves of an ordered tree.
This is the number of nodes which do not have any children.
This is the number of nodes which do not have any children.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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 $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ 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 $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ 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 $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ 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 $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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