- FindStat

Identifier

Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
St000974: Ordered trees ⟶ ℤ

Values

[1] => [1,0,1,0] => [1,0,1,0] => [[],[]] => 0

[2] => [1,1,0,0,1,0] => [1,1,0,0,1,0] => [[[]],[]] => 0

[1,1] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => [[[],[]]] => 1

[3] => [1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => [[[[]]],[]] => 0

[2,1] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => [[],[],[]] => 0

[1,1,1] => [1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0] => [[[[],[]]]] => 2

[4] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => [[[[[]]]],[]] => 0

[3,1] => [1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [[],[[]],[]] => 0

[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 1

[2,1,1] => [1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0] => [[],[[],[]]] => 0

[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [[[[[],[]]]]] => 3

[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[[]]]]],[]] => 0

[4,1] => [1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[]] => 0

[3,2] => [1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => [[[]],[],[]] => 0

[3,1,1] => [1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0] => [[[],[]],[]] => 0

[2,2,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 1

[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [[],[[[],[]]]] => 0

[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 4

[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[[]]]]]],[]] => 0

[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0] => [[],[[[[]]]],[]] => 0

[4,2] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[]] => 0

[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => [[[],[[]]],[]] => 0

[3,3] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 1

[3,2,1] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [[],[],[],[]] => 0

[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => [[],[[[]],[]]] => 0

[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => [[[[[]],[]]]] => 2

[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => [[[],[[],[]]]] => 1

[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[],[[[[],[]]]]] => 0

[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[[],[]]]]]]] => 5

[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[]]]]]]],[]] => 0

[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[[[[[]]]]],[]] => 0

[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[[]]],[]] => 0

[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0] => [[[[],[[]]]],[]] => 0

[4,3] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => [[[[]]],[],[]] => 0

[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[]] => 0

[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => [[[[],[]]],[]] => 0

[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 1

[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => [[[]],[[],[]]] => 0

[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => [[],[],[[],[]]] => 0

[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,0,0] => [[],[[[[]],[]]]] => 0

[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => [[[[],[],[]]]] => 2

[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [[[],[[[],[]]]]] => 1

[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[[[[[],[]]]]]] => 0

[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[]]]]]]]],[]] => 0

[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[],[[[[[[]]]]]],[]] => 0

[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[[[[]]]],[]] => 0

[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[[],[[]]]]],[]] => 0

[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[[]]],[[]],[]] => 0

[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[[[]]],[]] => 0

[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0] => [[[],[[[]]]],[]] => 0

[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 1

[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [[],[[]],[],[]] => 0

[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => [[[[]],[]],[]] => 0

[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => [[],[[],[]],[]] => 0

[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[],[[[[]]],[]]] => 0

[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 1

[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => [[[[],[]],[]]] => 1

[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => [[],[[],[],[]]] => 0

[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[[[],[]]]] => 0

[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[[[[[]],[]]]]] => 0

[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[[]],[]]]]] => 3

[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[[[],[[],[]]]]] => 2

[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[[],[[[[],[]]]]]] => 1

[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[],[[[[[[],[]]]]]]] => 0

[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[]]]]]]]]],[]] => 0

[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[]],[[[[[]]]]],[]] => 0

[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[[],[[]]]]]],[]] => 0

[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[]]],[[[]]],[]] => 0

[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[[[[]]]],[]] => 0

[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[[],[[[]]]]],[]] => 0

[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[[]]]],[],[]] => 0

[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[]] => 0

[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => [[[[]],[[]]],[]] => 0

[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[],[[],[[]]],[]] => 0

[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0] => [[[[[],[]]]],[]] => 0

[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[],[[[]]],[]]] => 1

[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [[[]],[],[],[]] => 0

[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0] => [[[],[]],[],[]] => 0

[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0] => [[[],[],[]],[]] => 0

[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[[[]],[]]] => 0

[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[[[[[]]],[]]]] => 0

[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[[]]],[]]]] => 2

[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 1

[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [[[],[[[]],[]]]] => 1

[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[[],[]]]] => 0

[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => [[],[[],[[],[]]]] => 0

[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[[[[],[]]]]] => 0

[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[],[[[[[[]],[]]]]]] => 0

[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[],[],[]]]]] => 3

[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[[],[[[],[]]]]]] => 2

[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[],[[[[[[[],[]]]]]]]] => 0

[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[[]]]]]]]]]],[]] => 0

[8,1,1] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[],[[]]]]]]],[]] => 0

[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[],[],[[[[[]]]]],[]] => 0

[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[[],[[[]]]]]],[]] => 0

[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[[]]]],[[]],[]] => 0

[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[[]],[[[]]],[]] => 0

[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[[]],[[]]]],[]] => 0

[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[],[[],[[[]]]],[]] => 0

[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[[],[[[[]]]]],[]] => 0

[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 1

>>> Load all 632 entries. <<<

[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[],[[[]]],[],[]] => 0

[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[[]],[],[[]],[]] => 0

[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[[],[]],[[]],[]] => 0

[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[[]]],[]] => 0

[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => [[],[[[],[]]],[]] => 0

[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[[[[[]]]],[]]] => 0

[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[[[]],[[]],[]]] => 1

[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[[[],[[]]],[]]] => 1

[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[[[]]],[[],[]]] => 0

[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[]] => 0

[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[],[[]],[[],[]]] => 0

[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[[]],[[[]],[]]] => 0

[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[],[[],[[]],[]]] => 0

[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[],[],[[[[]],[]]]] => 0

[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[],[[[[[[]]],[]]]]] => 0

[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [[[[],[[]],[]]]] => 2

[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [[[[]],[[],[]]]] => 1

[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[[],[]]]] => 1

[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[[],[[[[]],[]]]]] => 1

[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[],[[[],[],[]]]] => 0

[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[[],[]]]]] => 0

[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[],[],[[[[[],[]]]]]] => 0

[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[],[[[[[[[]],[]]]]]]] => 0

[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[[[[]],[]]]]]] => 4

[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[[],[[],[]]]]]] => 3

[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[],[[[[[[[[],[]]]]]]]]] => 0

[7,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[],[[]],[[[[]]]],[]] => 0

[7,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[],[[],[[[[]]]]],[]] => 0

[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[[]]]]],[],[]] => 0

[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[[[]]],[[]],[]] => 0

[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[[[]]],[]] => 0

[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[[],[]],[[[]]],[]] => 0

[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[[],[],[[]]]],[]] => 0

[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[],[[[],[[]]]],[]] => 0

[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[]]]]],[]] => 0

[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => 1

[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[[]],[[]],[],[]] => 0

[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[[],[[]]],[],[]] => 0

[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => [[[[[]]],[]],[]] => 0

[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[[]],[]] => 0

[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[],[[[]],[]],[]] => 0

[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => [[[[[]],[]]],[]] => 0

[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => [[[],[[],[]]],[]] => 0

[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[],[],[[[[]]],[]]] => 0

[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[],[[[[[[]]]],[]]]] => 0

[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => 1

[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[[]],[]]] => 1

[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[[[[],[]]],[]]] => 1

[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[[],[]],[[],[]]] => 0

[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[],[[],[]]] => 0

[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[[],[]]] => 0

[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[],[[]],[[[],[]]]] => 0

[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[],[[[],[]],[]]] => 0

[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[],[[[],[[]],[]]]] => 0

[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[],[],[[[[[]],[]]]]] => 0

[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [[[[[]],[],[]]]] => 2

[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [[[[[],[]],[]]]] => 2

[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [[[],[[],[],[]]]] => 1

[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[[],[],[[[],[]]]]] => 1

[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[[]],[[[[],[]]]]] => 0

[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[],[[],[[[],[]]]]] => 0

[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[],[[[[],[[],[]]]]]] => 0

[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[[[],[],[]]]]]] => 4

[7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[],[[[]]],[[[]]],[]] => 0

[7,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[]],[],[[[[]]]],[]] => 0

[7,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[],[[[],[[[]]]]],[]] => 0

[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[[[[]]]],[],[]] => 0

[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[[]],[[]],[]] => 0

[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[],[[]]],[[]],[]] => 0

[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[[]]],[[]]],[]] => 0

[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[[[]]],[]] => 0

[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[],[[[]],[[]]],[]] => 0

[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[[]],[[[]]]],[]] => 0

[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[],[[],[[]]]],[]] => 0

[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[],[[[[],[]]]],[]] => 0

[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[],[[[[[[]]]]],[]]] => 0

[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[]],[[[]]],[]]] => 1

[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[[],[[]]]],[]]] => 1

[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[[]]],[],[],[]] => 0

[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[],[]] => 0

[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => [[[[],[]]],[],[]] => 0

[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[[],[[]],[]],[]] => 0

[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[[]],[[],[]],[]] => 0

[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[],[],[[],[]],[]] => 0

[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[],[[]],[[[]],[]]] => 0

[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[]]],[]] => 0

[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[],[[[],[[]]],[]]] => 0

[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[],[],[[[[[]]],[]]]] => 0

[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[[[[[]]]],[]]]] => 2

[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[[],[[]],[],[]]] => 1

[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [[[[[]],[]],[]]] => 1

[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [[[],[[],[]],[]]] => 1

[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[[],[[[[]]],[]]]] => 1

[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[[]],[[],[],[]]] => 0

[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[],[[[]],[],[]]] => 0

[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[[],[],[]]] => 0

[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[],[[[],[]]]] => 0

[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[],[[]],[[[[],[]]]]] => 0

[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[[]],[[[[]],[]]]] => 0

[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[],[[],[[[]],[]]]] => 0

[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[],[[[[],[[]],[]]]]] => 0

[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[[[[]]],[]]]]] => 3

[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[]]]] => 2

[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[[],[[[]],[]]]]] => 2

[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[[]],[[[],[]]]]] => 1

[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[],[[],[[],[]]]]] => 1

[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[[[[],[],[]]]]] => 0

[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[],[[[],[[[],[]]]]]] => 0

[7,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[],[[[[]]]],[[]],[]] => 0

[7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[[]],[[]],[[[]]],[]] => 0

[7,3,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[],[],[],[[[[]]]],[]] => 0

[7,3,1,1,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[],[[[]],[[[]]]],[]] => 0

[7,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[],[[[[],[[]]]]],[]] => 0

[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[[],[]]]]]],[]] => 0

[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[[]],[[[]]],[],[]] => 0

[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[[],[[]]]],[],[]] => 0

[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[[]],[]] => 0

[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[],[],[[]],[[]],[]] => 0

[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[[],[]]],[[]],[]] => 0

[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[[],[]],[[]]],[]] => 0

[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[[]],[[],[[]]],[]] => 0

[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[],[],[[],[[]]],[]] => 0

[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[],[[[[]],[]]],[]] => 0

[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[[],[],[[[]]]],[]] => 0

[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[],[[[],[]]]],[]] => 0

[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[],[],[[[[[]]]],[]]] => 0

[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[[]]],[[]],[]]] => 1

[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[[],[],[[[]]],[]]] => 1

[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[[],[[[]]]],[]]] => 1

[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[[]]]],[[],[]]] => 0

[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[],[[]],[],[],[]] => 0

[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[[[]],[]],[],[]] => 0

[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[],[[],[]],[],[]] => 0

[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[],[[[]]],[[],[]]] => 0

[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[[[]],[],[]],[]] => 0

[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => [[[[],[]],[]],[]] => 0

[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[],[[],[],[]],[]] => 0

[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[],[[[]],[]]] => 0

[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[],[[]],[[[[]],[]]]] => 0

[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[[]],[[[[]]],[]]] => 0

[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[],[[],[[[]]],[]]] => 0

[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[],[[[[],[[]]],[]]]] => 0

[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[[],[[[]]],[]]]] => 2

[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[],[],[]]] => 1

[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[[[],[]],[],[]]] => 1

[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[]],[]]] => 1

[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[[],[],[[[]],[]]]] => 1

[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[[]]],[[[],[]]]] => 0

[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[]]] => 0

[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[],[[[]],[[],[]]]] => 0

[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[[]],[],[[[],[]]]] => 0

[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[],[],[[],[[],[]]]] => 0

[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[],[],[],[[[[],[]]]]] => 0

[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[[[[],[]],[]]]] => 0

[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[],[[[],[[[]],[]]]]] => 0

[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[[],[[]],[]]]]] => 3

[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[[]],[[],[]]]]] => 2

[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[[],[],[[],[]]]]] => 2

[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[[],[[],[],[]]]]] => 2

[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[]],[[[[[],[]]]]]] => 0

[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[],[[],[[[[],[]]]]]] => 0

[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[],[[[[[]]]]],[],[]] => 0

[7,5,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[[]],[[[]]],[[]],[]] => 0

[7,4,2,1] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[],[],[[]],[[[]]],[]] => 0

[7,3,2,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[[]],[[],[[[]]]],[]] => 0

[7,3,2,1,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[],[],[[[],[[]]]],[]] => 0

[7,3,1,1,1,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[],[[[[]],[[]]]],[]] => 0

[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[],[[[[[],[]]]]],[]] => 0

[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[[]]],[[]],[],[]] => 0

[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[[[]]],[],[]] => 0

[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[],[[[]]]],[],[]] => 0

[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[[]]]],[]],[]] => 0

[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[[]],[]] => 0

[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[]],[]],[[]],[]] => 0

[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[],[[],[]],[[]],[]] => 0

[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[],[[[[]]],[]],[]] => 0

[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[[]],[],[[]]],[]] => 0

[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[[],[[]],[[]]],[]] => 0

[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[],[[],[],[[]]],[]] => 0

[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[],[],[[[],[]]],[]] => 0

[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[],[[]],[[[[]]],[]]] => 0

[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[[]],[]]]],[]] => 0

[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[[],[[],[]]]],[]] => 0

[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[],[[[[],[[]]]],[]]] => 0

[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[[]]]],[],[]]] => 1

[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[[],[]],[[]],[]]] => 1

[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[[]],[[]]],[]]] => 1

[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[[],[[],[[]]],[]]] => 1

[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[[[],[]]]],[]]] => 1

[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[],[]]],[[],[]]] => 0

[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[]] => 0

[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[[],[]],[],[],[]] => 0

[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[]],[],[]] => 0

[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[],[],[[]],[[],[]]] => 0

[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[],[[[]]],[[[],[]]]] => 0

[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[[]]],[[[]],[]]] => 0

[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[]],[]] => 0

[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[],[[[]],[[]],[]]] => 0

[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[[]],[],[[[]],[]]] => 0

[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[],[],[[],[[]],[]]] => 0

[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[],[],[],[[[[]],[]]]] => 0

[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[],[[[[],[]]],[]]] => 0

[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[],[[[],[[[]]],[]]]] => 0

[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[[]],[[]],[]]]] => 2

[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[[],[[]]],[]]]] => 2

[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[[]]],[[],[]]]] => 1

[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[]]] => 1

[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[[],[[]],[[],[]]]] => 1

[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[[]],[[[]],[]]]] => 1

[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[[],[[],[[]],[]]]] => 1

[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[[],[]],[[[],[]]]] => 0

[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[]],[[],[[],[]]]] => 0

[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[],[[],[],[[],[]]]] => 0

[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[],[[[[]],[[],[]]]]] => 0

[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[],[],[[[],[],[]]]] => 0

[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[],[],[[],[[[],[]]]]] => 0

[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[]],[[[[[]],[]]]]] => 0

[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[],[[],[[[[]],[]]]]] => 0

[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[[]],[],[]]]]] => 3

[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[[[],[]],[]]]]] => 3

[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[[],[[[],[],[]]]]] => 1

[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[],[[[[[],[],[]]]]]] => 0

[8,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[],[]]]]]]],[]] => 0

[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[[]],[[[[]]]],[],[]] => 0

[7,5,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[],[],[[[]]],[[]],[]] => 0

[7,4,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[],[[]],[],[[[]]],[]] => 0

[7,4,2,1,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[],[],[[[]],[[]]],[]] => 0

[7,4,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[],[[[[]]],[[]]],[]] => 0

[7,3,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[],[[],[],[[[]]]],[]] => 0

[7,3,2,1,1,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[],[],[[],[[[]]]],[]] => 0

[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[],[[[[[]],[]]]],[]] => 0

[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[[]]]],[],[],[]] => 0

[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[[]],[[]],[],[]] => 0

[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[[]],[[]]],[],[]] => 0

[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[],[[],[[]]],[],[]] => 0

[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[[],[]]]],[],[]] => 0

[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[[],[[[]]],[]],[]] => 0

[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[[]],[]] => 0

[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[],[]],[],[[]],[]] => 0

[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[],[],[]],[[]],[]] => 0

[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[],[],[[[]],[]],[]] => 0

[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[],[[[]]],[[[]],[]]] => 0

[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[[]]],[]]],[]] => 0

[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[[],[],[],[[]]],[]] => 0

[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[],[[[]],[]]],[]] => 0

[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[[]],[[[],[]]],[]] => 0

[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[],[[],[[],[]]],[]] => 0

[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[],[],[],[[[[]]],[]]] => 0

[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[[],[],[]]]],[]] => 0

[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[],[[[],[[[]]]],[]]] => 0

[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[],[[[]]],[],[]]] => 1

[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[[]],[],[[]],[]]] => 1

[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[[],[[]],[[]],[]]] => 1

[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[[],[],[[]]],[]]] => 1

[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[[],[[],[]]],[]]] => 1

[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[]],[]],[[],[]]] => 0

[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[[],[[]]],[[],[]]] => 0

[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[[]]],[],[[],[]]] => 0

[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[]] => 0

[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[],[[]],[],[[],[]]] => 0

[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[[]],[[]],[[],[]]] => 0

[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[],[[],[]],[[],[]]] => 0

[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[],[],[[]],[[[],[]]]] => 0

[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[[],[]],[[[]],[]]] => 0

[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[[]],[[],[[]],[]]] => 0

[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[],[[],[],[[]],[]]] => 0

[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[],[[[[]],[[]],[]]]] => 0

[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[],[],[[[],[]],[]]] => 0

[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[],[],[[],[[[]],[]]]] => 0

[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[[]],[[[[[]]],[]]]] => 0

[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[],[[],[[[[]]],[]]]] => 0

[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[[[[[]]],[],[]]]] => 2

[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[[],[],[[]],[]]]] => 2

[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[[[],[]]],[]]]] => 2

[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[[],[]],[[],[]]]] => 1

[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[[]],[],[[],[]]]] => 1

[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[[],[],[],[[],[]]]] => 1

[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[[],[[],[]],[]]]] => 2

[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[[]],[[[],[],[]]]] => 0

[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[],[[[[]],[],[]]]] => 0

[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[],[[],[[],[],[]]]] => 0

[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[],[[[],[],[[],[]]]]] => 0

[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[]],[],[[[[],[]]]]] => 0

[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[],[],[[[],[[],[]]]]] => 0

[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[],[[[[[],[]],[]]]]] => 0

[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[[],[],[],[]]]]] => 3

[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[],[],[[[[]]]],[],[]] => 0

[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[],[[]],[[]],[[]],[]] => 0

[7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[],[[[],[]]],[[]],[]] => 0

[7,4,3,2] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[[]],[],[],[[[]]],[]] => 0

[7,4,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[],[[],[]],[[[]]],[]] => 0

[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[],[[[[[]]],[]]],[]] => 0

[7,3,2,2,2] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[[]],[[[],[[]]]],[]] => 0

[7,3,2,2,1,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[],[[],[[],[[]]]],[]] => 0

[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[],[],[[[[],[]]]],[]] => 0

[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[]] => 0

[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[[]],[],[]] => 0

[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[],[]],[[]],[],[]] => 0

[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[],[],[[]]],[],[]] => 0

[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[],[[[],[]]],[],[]] => 0

[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[],[[[[]]]],[[],[]]] => 0

[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[[]],[[]],[]],[]] => 0

[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[[],[[]]],[]],[]] => 0

[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[[]]],[[],[]],[]] => 0

[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[[]],[]] => 0

[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[],[[]],[[],[]],[]] => 0

[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[[]],[[[]],[]],[]] => 0

[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[],[[],[[]],[]],[]] => 0

[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[],[],[[]],[[[]],[]]] => 0

[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[[],[[]],[]]],[]] => 0

[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[[]],[[],[]]],[]] => 0

[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[[],[],[[],[]]],[]] => 0

[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[],[[[[]],[[]]],[]]] => 0

[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[],[[[],[],[]]],[]] => 0

[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[],[],[[],[[[]]],[]]] => 0

[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[[]],[[[[[]]]],[]]] => 0

[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[],[[],[[[[]]]],[]]] => 0

[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[[]],[[]],[],[]]] => 1

[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[[],[[]]],[],[]]] => 1

[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[[[[[]]],[]],[]]] => 1

[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[],[[]],[]]] => 1

[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[[],[[[]],[]],[]]] => 1

[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[[[]],[]]],[]]] => 1

[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[[],[[[],[]]],[]]] => 1

[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[[]]],[[],[],[]]] => 0

[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[],[],[]],[[],[]]] => 0

[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[],[[[[]]],[],[]]] => 0

[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[],[]],[],[[],[]]] => 0

[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[[],[]]] => 0

[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[[],[]]] => 0

[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[],[[]],[],[[[],[]]]] => 0

[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[],[],[[[]],[],[]]] => 0

[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[],[[],[]],[[[],[]]]] => 0

[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[]],[[[],[]],[]]] => 0

[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[],[[[[]],[]],[]]] => 0

[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[],[[],[[],[]],[]]] => 0

[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[],[[[],[],[[]],[]]]] => 0

[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[[]],[],[[[[]],[]]]] => 0

[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[],[],[[[],[[]],[]]]] => 0

[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[],[[[[[],[]]],[]]]] => 0

[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[[],[[]],[],[]]]] => 2

[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[[[]],[]],[]]]] => 2

[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[[],[[[],[]],[]]]] => 1

[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[[[]],[[],[],[]]]] => 1

[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[[],[[[]],[],[]]]] => 1

[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[[],[],[[],[],[]]]] => 1

[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[]]]] => 0

[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[],[[[]],[[[],[]]]]] => 0

[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[[]],[[[],[[],[]]]]] => 0

[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[],[[],[[],[[],[]]]]] => 0

[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[],[],[[[[],[],[]]]]] => 0

[9,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[],[]]]]]]]],[]] => 0

[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[],[[]],[[[]]],[],[]] => 0

[7,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[],[[],[[[]]]],[],[]] => 0

[7,5,4,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[],[[[]]],[],[[]],[]] => 0

[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[[]],[],[[]],[[]],[]] => 0

[7,5,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[],[[],[[]]],[[]],[]] => 0

[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[],[[[[[]]]],[]],[]] => 0

[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[],[],[],[],[[[]]],[]] => 0

[7,4,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[],[[]],[[],[[]]],[]] => 0

[7,4,2,2,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[[]],[[[]],[[]]],[]] => 0

[7,4,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[],[[],[[]],[[]]],[]] => 0

[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[],[],[[[[]],[]]],[]] => 0

[7,3,2,2,2,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[],[[[],[],[[]]]],[]] => 0

[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[],[[[],[[],[]]]],[]] => 0

[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[[]],[]]]]],[]] => 0

[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[]] => 0

[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[],[[]]],[],[],[]] => 0

[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[[]]],[]],[],[]] => 0

[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[[]],[],[]] => 0

[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[],[[[]],[]],[],[]] => 0

[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[[]],[]]],[],[]] => 0

[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[],[[],[]]],[],[]] => 0

[6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[],[],[[[]]],[[],[]]] => 0

[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[[]]],[],[]],[]] => 0

[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[[],[],[[]],[]],[]] => 0

[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[[],[]]],[]],[]] => 0

[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[],[]],[[],[]],[]] => 0

[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[[]],[],[[],[]],[]] => 0

[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[],[],[],[[],[]],[]] => 0

[6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[],[[]],[],[[[]],[]]] => 0

[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[],[[[],[]],[]],[]] => 0

[6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[],[[],[]],[[[]],[]]] => 0

[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[[]],[],[]]],[]] => 0

[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[[],[]],[]]],[]] => 0

[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[[],[[],[],[]]],[]] => 0

[6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[],[[[],[],[[]]],[]]] => 0

[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[]],[],[[[[]]],[]]] => 0

[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[],[],[[[],[[]]],[]]] => 0

[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[],[[[[[],[]]]],[]]] => 0

[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[]]] => 1

[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[[],[],[[]],[],[]]] => 1

[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[[],[]]],[],[]]] => 1

[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[[],[[]],[]],[]]] => 1

[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[[[]],[[],[]],[]]] => 1

[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[[],[],[[],[]],[]]] => 1

[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[[],[],[]]],[]]] => 1

[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[],[]],[[],[],[]]] => 0

[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[[]],[[[]],[],[]]] => 0

[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[],[[],[[]],[],[]]] => 0

[5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[],[[[[]]],[[],[]]]] => 0

[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[[]],[],[[],[],[]]] => 0

[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[],[[]],[[],[],[]]] => 0

[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[],[[],[],[]]] => 0

[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[],[],[],[],[[[],[]]]] => 0

[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[[]],[[]],[[[],[]]]] => 0

[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[],[],[[[]],[[],[]]]] => 0

[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[],[[[],[],[]],[]]] => 0

[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[],[[[]],[[[]],[]]]] => 0

[5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[[]],[[[],[[]],[]]]] => 0

[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[],[[],[[],[[]],[]]]] => 0

[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[],[],[[[[],[]],[]]]] => 0

[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[[]],[],[],[]]]] => 2

[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[[],[]],[],[]]]] => 2

[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[[],[],[]],[]]]] => 2

[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[[],[[],[],[],[]]]] => 1

[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[[]],[[],[[[],[]]]]] => 0

[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[],[[],[],[[[],[]]]]] => 0

[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[],[[],[[[],[],[]]]]] => 0

[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[]] => 0

[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[]]] => 1

[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[],[],[],[],[]],[]] => 0

[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[],[]]] => 0

[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[],[],[],[],[]]]] => 2

[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[],[],[],[]],[],[]] => 0

[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[[],[],[],[]],[]]] => 1

[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[],[[],[],[],[]],[]] => 0

[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[],[],[[],[],[],[]]] => 0

[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[[],[],[],[]]],[]] => 0

[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[],[],[]],[],[],[]] => 0

[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[[],[],[]],[],[]]] => 1

[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[[],[],[]],[]],[]] => 0

[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[],[[[],[]],[],[]]] => 0

[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[],[[],[],[]],[],[]] => 0

[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[[],[[],[],[]],[]]] => 1

[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[],[],[[],[],[]],[]] => 0

[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[[],[],[]]],[],[]] => 0

[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[],[]],[],[],[],[]] => 0

[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[[],[]],[],[],[]]] => 1

[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[[],[]],[],[]],[]] => 0

[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[],[[[]],[],[],[]]] => 0

[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[[],[]],[]],[],[]] => 0

[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[[],[]],[]],[]]] => 1

[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[],[[[]],[],[]],[]] => 0

[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[],[[],[]],[],[],[]] => 0

[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[[],[[],[]],[],[]]] => 1

[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[[],[[],[]],[]],[]] => 0

[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[],[],[[],[]],[],[]] => 0

[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[[],[]]],[],[],[]] => 0

[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[]] => 0

[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[]]] => 1

[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[[]],[],[],[]],[]] => 0

[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[]],[[],[],[],[]]] => 0

[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[[]],[],[]],[],[]] => 0

[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[[]],[],[]],[]]] => 1

[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[[]],[[],[],[]],[]] => 0

[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[[]],[]],[],[],[]] => 0

[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[[]],[]],[],[]]] => 1

[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[[]],[]],[]],[]] => 0

[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[[]],[[],[]],[],[]] => 0

[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[]] => 0

[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[[],[[]],[],[],[]]] => 1

[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[[],[[]],[],[]],[]] => 0

[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[],[[]],[]],[],[]] => 0

[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[]] => 0

[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[]] => 0

[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[],[],[],[],[],[],[],[]] => 0

[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[],[[],[],[],[],[],[]]] => 0

[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[],[[],[],[],[],[]],[]] => 0

[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[],[],[[],[],[],[],[]]] => 0

[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[],[[[],[],[],[]],[]]] => 0

[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[],[[[],[],[],[],[]]]] => 0

[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[],[],[],[[],[],[],[]]] => 0

[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[],[],[[[],[]],[],[]]] => 0

[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[],[],[[[],[],[]],[]]] => 0

[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[],[],[[[],[],[],[]]]] => 0

[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[],[[[[],[],[]]],[]]] => 0

[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[],[[[],[]],[],[],[]]] => 0

[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[],[],[[[]],[],[],[]]] => 0

[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[],[],[],[],[[],[],[]]] => 0

[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[],[],[[]],[[],[],[]]] => 0

[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[],[],[],[[[]],[],[]]] => 0

[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[],[],[],[[[],[]],[]]] => 0

[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[],[],[],[[[],[],[]]]] => 0

[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[],[],[[[[]]],[],[]]] => 0

[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[[],[],[]]]]],[]] => 0

[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[],[]],[],[],[],[],[]] => 0

[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[],[[[]],[],[],[],[]]] => 0

[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[],[[],[[]],[],[],[]]] => 0

[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[],[],[],[],[],[[],[]]] => 0

[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[],[[[[]]],[],[],[]]] => 0

[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[],[[]],[],[],[[],[]]] => 0

[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[],[[[],[]]],[],[],[]] => 0

[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[],[],[[]],[[],[]],[]] => 0

[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[],[],[[]],[],[[],[]]] => 0

[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[],[],[[[],[]]],[],[]] => 0

[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[],[],[],[[[],[]]],[]] => 0

[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[],[],[],[],[[[]],[]]] => 0

[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[],[[[]]],[],[[],[]]] => 0

[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[]],[],[],[],[],[],[]] => 0

[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[]],[[],[],[],[],[]]] => 0

[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[]],[],[[],[],[],[]]] => 0

[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[]],[],[],[[],[],[]]] => 0

[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[]],[],[[[],[],[]]]] => 0

[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[]],[[[[],[],[]]]]] => 0

[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[]],[],[],[],[[],[]]] => 0

[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[[]],[[]],[],[[],[]]] => 0

[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[]],[],[],[[[],[]]]] => 0

[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[],[[]],[],[],[],[],[]] => 0

[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[],[],[[]],[],[],[],[]] => 0

[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[],[],[],[[]],[],[],[]] => 0

[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[],[],[],[],[[]],[],[]] => 0

[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[],[],[],[],[],[[]],[]] => 0

[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[],[],[[],[[]]],[],[]] => 0

[7,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[],[],[],[[],[[]]],[]] => 0

[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[]]],[],[],[],[],[]] => 0

[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[[]]],[]]]],[]] => 0

[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[]],[[]],[],[],[],[]] => 0

[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[[]],[],[[]],[],[],[]] => 0

[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[[]],[],[],[[]],[],[]] => 0

[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[]],[],[],[],[[]],[]] => 0

[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[],[[[]]],[],[],[],[]] => 0

[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[],[[]],[],[],[[]],[]] => 0

[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[],[],[[[]]],[],[],[]] => 0

[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[],[],[[]],[[]],[],[]] => 0

[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[],[],[[]],[],[[]],[]] => 0

[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[],[],[],[[[]]],[],[]] => 0

[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[[]]],[],[[]],[],[]] => 0

[7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[[]]],[],[],[[]],[]] => 0

[7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[[]],[[[]]],[],[],[]] => 0

[8,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[[]],[]]]]]],[]] => 0

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 2 + q^{2}$

$F_{4} = 3 + q + q^{3}$

$F_{5} = 5 + q + q^{4}$

$F_{6} = 7 + 2\ q + q^{2} + q^{5}$

Description

The length of the trunk of an ordered tree.
This is the length of the path from the root to the first vertex which has not exactly one child.

Map

switch returns and last double rise

Description

An alternative to the Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and exchanging the number of components with the position of the last double rise.

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.

Map

to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.