Identifier
Mp00048:
Ordered trees
—left-right symmetry⟶
Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Images
=>
Cc0021;cc-rep-0Cc0021;cc-rep-1Cc0005;cc-rep-2Cc0002;cc-rep-3
[]=>[]=>[]=>[]
[[]]=>[[]]=>[1,0]=>[]
[[],[]]=>[[],[]]=>[1,0,1,0]=>[1]
[[[]]]=>[[[]]]=>[1,1,0,0]=>[]
[[],[],[]]=>[[],[],[]]=>[1,0,1,0,1,0]=>[2,1]
[[],[[]]]=>[[[]],[]]=>[1,1,0,0,1,0]=>[2]
[[[]],[]]=>[[],[[]]]=>[1,0,1,1,0,0]=>[1,1]
[[[],[]]]=>[[[],[]]]=>[1,1,0,1,0,0]=>[1]
[[[[]]]]=>[[[[]]]]=>[1,1,1,0,0,0]=>[]
[[],[],[],[]]=>[[],[],[],[]]=>[1,0,1,0,1,0,1,0]=>[3,2,1]
[[],[],[[]]]=>[[[]],[],[]]=>[1,1,0,0,1,0,1,0]=>[3,2]
[[],[[]],[]]=>[[],[[]],[]]=>[1,0,1,1,0,0,1,0]=>[3,1,1]
[[],[[],[]]]=>[[[],[]],[]]=>[1,1,0,1,0,0,1,0]=>[3,1]
[[],[[[]]]]=>[[[[]]],[]]=>[1,1,1,0,0,0,1,0]=>[3]
[[[]],[],[]]=>[[],[],[[]]]=>[1,0,1,0,1,1,0,0]=>[2,2,1]
[[[]],[[]]]=>[[[]],[[]]]=>[1,1,0,0,1,1,0,0]=>[2,2]
[[[],[]],[]]=>[[],[[],[]]]=>[1,0,1,1,0,1,0,0]=>[2,1,1]
[[[[]]],[]]=>[[],[[[]]]]=>[1,0,1,1,1,0,0,0]=>[1,1,1]
[[[],[],[]]]=>[[[],[],[]]]=>[1,1,0,1,0,1,0,0]=>[2,1]
[[[],[[]]]]=>[[[[]],[]]]=>[1,1,1,0,0,1,0,0]=>[2]
[[[[]],[]]]=>[[[],[[]]]]=>[1,1,0,1,1,0,0,0]=>[1,1]
[[[[],[]]]]=>[[[[],[]]]]=>[1,1,1,0,1,0,0,0]=>[1]
[[[[[]]]]]=>[[[[[]]]]]=>[1,1,1,1,0,0,0,0]=>[]
[[],[],[],[],[]]=>[[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]
[[],[],[],[[]]]=>[[[]],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]
[[],[],[[]],[]]=>[[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]
[[],[],[[],[]]]=>[[[],[]],[],[]]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]
[[],[],[[[]]]]=>[[[[]]],[],[]]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]
[[],[[]],[],[]]=>[[],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]
[[],[[]],[[]]]=>[[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]
[[],[[],[]],[]]=>[[],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]
[[],[[[]]],[]]=>[[],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]
[[],[[],[],[]]]=>[[[],[],[]],[]]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]
[[],[[],[[]]]]=>[[[[]],[]],[]]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]
[[],[[[]],[]]]=>[[[],[[]]],[]]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]
[[],[[[],[]]]]=>[[[[],[]]],[]]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]
[[],[[[[]]]]]=>[[[[[]]]],[]]=>[1,1,1,1,0,0,0,0,1,0]=>[4]
[[[]],[],[],[]]=>[[],[],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]
[[[]],[],[[]]]=>[[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]
[[[]],[[]],[]]=>[[],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]
[[[]],[[],[]]]=>[[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]
[[[]],[[[]]]]=>[[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]
[[[],[]],[],[]]=>[[],[],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]
[[[[]]],[],[]]=>[[],[],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]
[[[],[]],[[]]]=>[[[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]
[[[[]]],[[]]]=>[[[]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]
[[[],[],[]],[]]=>[[],[[],[],[]]]=>[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]
[[[],[[]]],[]]=>[[],[[[]],[]]]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]
[[[[]],[]],[]]=>[[],[[],[[]]]]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]
[[[[],[]]],[]]=>[[],[[[],[]]]]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]
[[[[[]]]],[]]=>[[],[[[[]]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]
[[[],[],[],[]]]=>[[[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]
[[[],[],[[]]]]=>[[[[]],[],[]]]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]
[[[],[[]],[]]]=>[[[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]
[[[],[[],[]]]]=>[[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]
[[[],[[[]]]]]=>[[[[[]]],[]]]=>[1,1,1,1,0,0,0,1,0,0]=>[3]
[[[[]],[],[]]]=>[[[],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]
[[[[]],[[]]]]=>[[[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]
[[[[],[]],[]]]=>[[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]
[[[[[]]],[]]]=>[[[],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]
[[[[],[],[]]]]=>[[[[],[],[]]]]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]
[[[[],[[]]]]]=>[[[[[]],[]]]]=>[1,1,1,1,0,0,1,0,0,0]=>[2]
[[[[[]],[]]]]=>[[[[],[[]]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]
[[[[[],[]]]]]=>[[[[[],[]]]]]=>[1,1,1,1,0,1,0,0,0,0]=>[1]
[[[[[[]]]]]]=>[[[[[[]]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>[]
[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]
[[],[],[],[],[[]]]=>[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2]
[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,1]
[[],[],[],[[],[]]]=>[[[],[]],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,1]
[[],[],[],[[[]]]]=>[[[[]]],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]
[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[5,4,2,2,1]
[[],[],[[]],[[]]]=>[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[5,4,2,2]
[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,1]
[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]
[[],[],[[],[],[]]]=>[[[],[],[]],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]
[[],[],[[],[[]]]]=>[[[[]],[]],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]
[[],[],[[[]],[]]]=>[[[],[[]]],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]
[[],[],[[[],[]]]]=>[[[[],[]]],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]
[[],[],[[[[]]]]]=>[[[[[]]]],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]
[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,3,3,2,1]
[[],[[]],[],[[]]]=>[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[5,3,3,2]
[[],[[]],[[]],[]]=>[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,3,1,1]
[[],[[]],[[],[]]]=>[[[],[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]
[[],[[]],[[[]]]]=>[[[[]]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]
[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[5,3,2,2,1]
[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]
[[],[[],[]],[[]]]=>[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]
[[],[[[]]],[[]]]=>[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]
[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]
[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]
[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]
[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]
[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]
[[],[[],[],[],[]]]=>[[[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]
[[],[[],[],[[]]]]=>[[[[]],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]
[[],[[],[[]],[]]]=>[[[],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]
[[],[[],[[],[]]]]=>[[[[],[]],[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]
[[],[[],[[[]]]]]=>[[[[[]]],[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]
[[],[[[]],[],[]]]=>[[[],[],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]
[[],[[[]],[[]]]]=>[[[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]
[[],[[[],[]],[]]]=>[[[],[[],[]]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]
[[],[[[[]]],[]]]=>[[[],[[[]]]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]
[[],[[[],[],[]]]]=>[[[[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]
[[],[[[],[[]]]]]=>[[[[[]],[]]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]
[[],[[[[]],[]]]]=>[[[[],[[]]]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]
[[],[[[[],[]]]]]=>[[[[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]
[[],[[[[[]]]]]]=>[[[[[[]]]]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5]
[[[]],[],[],[],[]]=>[[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[4,4,3,2,1]
[[[]],[],[],[[]]]=>[[[]],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[4,4,3,2]
[[[]],[],[[]],[]]=>[[],[[]],[],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[4,4,3,1,1]
[[[]],[],[[],[]]]=>[[[],[]],[],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]
[[[]],[],[[[]]]]=>[[[[]]],[],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]
[[[]],[[]],[],[]]=>[[],[],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,4,2,2,1]
[[[]],[[]],[[]]]=>[[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]
[[[]],[[],[]],[]]=>[[],[[],[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[4,4,2,1,1]
[[[]],[[[]]],[]]=>[[],[[[]]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]
[[[]],[[],[],[]]]=>[[[],[],[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]
[[[]],[[],[[]]]]=>[[[[]],[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]
[[[]],[[[]],[]]]=>[[[],[[]]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]
[[[]],[[[],[]]]]=>[[[[],[]]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]
[[[]],[[[[]]]]]=>[[[[[]]]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]
[[[],[]],[],[],[]]=>[[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[4,3,3,2,1]
[[[[]]],[],[],[]]=>[[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]
[[[],[]],[],[[]]]=>[[[]],[],[[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]
[[[[]]],[],[[]]]=>[[[]],[],[[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]
[[[],[]],[[]],[]]=>[[],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]
[[[[]]],[[]],[]]=>[[],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]
[[[],[]],[[],[]]]=>[[[],[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]
[[[],[]],[[[]]]]=>[[[[]]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]
[[[[]]],[[],[]]]=>[[[],[]],[[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]
[[[[]]],[[[]]]]=>[[[[]]],[[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]
[[[],[],[]],[],[]]=>[[],[],[[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[4,3,2,2,1]
[[[],[[]]],[],[]]=>[[],[],[[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]
[[[[]],[]],[],[]]=>[[],[],[[],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]
[[[[],[]]],[],[]]=>[[],[],[[[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]
[[[[[]]]],[],[]]=>[[],[],[[[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]
[[[],[],[]],[[]]]=>[[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]
[[[],[[]]],[[]]]=>[[[]],[[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]
[[[[]],[]],[[]]]=>[[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]
[[[[],[]]],[[]]]=>[[[]],[[[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]
[[[[[]]]],[[]]]=>[[[]],[[[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]
[[[],[],[],[]],[]]=>[[],[[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,1]
[[[],[],[[]]],[]]=>[[],[[[]],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]
[[[],[[]],[]],[]]=>[[],[[],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]
[[[],[[],[]]],[]]=>[[],[[[],[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]
[[[],[[[]]]],[]]=>[[],[[[[]]],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]
[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]
[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]
[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]
[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]
[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]
[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]
[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]
[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]
[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]
[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]
[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]
[[[],[],[[]],[]]]=>[[[],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]
[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]
[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]
[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]
[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]
[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]
[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]
[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]
[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]
[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]
[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]
[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[4]
[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]
[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]
[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]
[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]
[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]
[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]
[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]
[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]
[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]
[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]
[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]
[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]
[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]
[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]
[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]
[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]
[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]
[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]
[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[3]
[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]
[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]
[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]
[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]
[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]
[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2]
[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]
[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1]
[[[[[[[]]]]]]]=>[[[[[[[]]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[]
[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]
[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2]
[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,1]
[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1]
[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3]
[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2,1]
[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,2]
[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,1]
[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1,1]
[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1]
[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]
[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1]
[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1]
[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]
[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2,1]
[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,2]
[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1,1]
[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3,1]
[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]
[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2,1]
[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2,1]
[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,2]
[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2]
[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,1]
[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]
[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1,1]
[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1,1]
[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]
[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1]
[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]
[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]
[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]
[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]
[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1]
[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]
[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1]
[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]
[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1]
[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]
[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]
[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]
[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]
[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2,1]
[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,2]
[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1,1]
[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3,1]
[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]
[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2,1]
[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,2]
[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1,1]
[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]
[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1]
[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]
[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]
[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]
[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]
[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2,1]
[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2,1]
[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,2]
[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2]
[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1,1]
[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1,1]
[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1]
[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]
[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1]
[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]
[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2,1]
[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]
[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2,1]
[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2,1]
[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]
[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2]
[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]
[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2]
[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2]
[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]
[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,1]
[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]
[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]
[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]
[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]
[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1,1]
[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]
[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1,1]
[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]
[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1,1]
[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]
[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]
[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]
[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]
[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1]
[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]
[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]
[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]
[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]
[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]
[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]
[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]
[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]
[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]
[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]
[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]
[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]
[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]
[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1]
[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]
[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]
[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]
[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]
[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1]
[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]
[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]
[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]
[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1]
[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]
[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]
[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]
[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]
[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]
[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]
[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]
[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]
[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]
[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]
[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]
[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]
[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]
[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]
[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]
[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]
[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]
[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6]
[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2,1]
[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2]
[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1,1]
[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,1]
[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]
[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2,1]
[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,2]
[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1,1]
[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]
[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1]
[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]
[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]
[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]
[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]
[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2,1]
[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,2]
[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1,1]
[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1]
[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]
[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2,1]
[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]
[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2]
[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]
[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1,1]
[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]
[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]
[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]
[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]
[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1]
[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]
[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]
[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]
[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]
[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]
[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]
[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]
[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]
[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]
[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]
[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]
[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]
[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]
[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2,1]
[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2,1]
[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2]
[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2]
[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1,1]
[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1,1]
[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1]
[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]
[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1]
[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]
[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2,1]
[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2,1]
[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2]
[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2]
[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1,1]
[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]
[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1,1]
[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]
[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1]
[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]
[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]
[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]
[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]
[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1]
[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]
[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]
[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]
[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]
[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2,1]
[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2,1]
[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2,1]
[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2,1]
[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]
[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2]
[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]
[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2]
[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2]
[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]
[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1,1]
[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]
[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1,1]
[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1,1]
[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]
[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1]
[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]
[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]
[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]
[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1]
[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]
[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1]
[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]
[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]
[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]
[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2,1]
[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2,1]
[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2,1]
[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2,1]
[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]
[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2,1]
[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]
[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2,1]
[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]
[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2,1]
[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]
[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]
[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]
[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]
[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2]
[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]
[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]
[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]
[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]
[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2]
[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]
[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2]
[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]
[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2]
[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]
[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]
[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]
[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]
[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,1]
[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1,1]
[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1,1]
[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1,1]
[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]
[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1,1]
[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]
[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1,1]
[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]
[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1,1]
[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]
[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]
[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]
[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]
[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1,1]
[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]
[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]
[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]
[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]
[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1,1]
[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]
[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]
[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]
[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1,1]
[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]
[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]
[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]
[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]
[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]
[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]
[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]
[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]
[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]
[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]
[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]
[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]
[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]
[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]
[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]
[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]
[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]
[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1]
[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2]
[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1]
[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1]
[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]
[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1]
[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]
[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1]
[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]
[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]
[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]
[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]
[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]
[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]
[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1]
[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]
[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]
[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]
[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]
[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1]
[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]
[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]
[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]
[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]
[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]
[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]
[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]
[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]
[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]
[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]
[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]
[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]
[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]
[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]
[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]
[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]
[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]
[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]
[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]
[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]
[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]
[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5]
[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1]
[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]
[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]
[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]
[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]
[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]
[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]
[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]
[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]
[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]
[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]
[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]
[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]
[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]
[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1]
[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]
[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]
[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]
[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]
[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]
[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]
[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]
[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]
[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]
[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]
[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]
[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]
[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]
[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]
[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]
[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]
[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]
[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]
[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]
[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]
[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]
[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]
[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]
[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]
[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]
[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]
[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]
[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]
[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]
[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]
[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]
[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]
[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]
[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]
[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]
[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]
[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]
[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]
[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]
[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]
[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]
[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]
[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]
[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]
[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]
[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]
[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4]
[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]
[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]
[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]
[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]
[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]
[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]
[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]
[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]
[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]
[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]
[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]
[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]
[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]
[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]
[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]
[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]
[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]
[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]
[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3]
[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]
[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]
[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]
[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]
[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]
[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2]
[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]
[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1]
[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[]
[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]
[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2]
[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,1]
[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1]
[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3]
[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,2,1]
[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,2]
[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,1]
[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1,1]
[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1]
[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2]
[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,1]
[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1]
[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4]
[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,2,1]
[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,2]
[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,1,1]
[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3,1]
[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,3]
[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,2,1]
[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2,1]
[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,2]
[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,2]
[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,1]
[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,1,1]
[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1,1]
[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1,1]
[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1,1]
[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1]
[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2]
[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,1]
[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1]
[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3]
[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2,1]
[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,2]
[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,1]
[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1,1]
[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1]
[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2]
[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,1]
[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1]
[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5]
[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2,1]
[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,2]
[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,1,1]
[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3,1]
[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,3]
[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,2,1]
[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,2]
[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,1,1]
[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1,1,1]
[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2,1]
[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,2]
[[],[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1,1]
[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4,1]
[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,4]
[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,2,1]
[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,2,1]
[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,2]
[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,2]
[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,1,1]
[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,1,1]
[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3,1]
[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,3]
[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3,1]
[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,3]
[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,2,1]
[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,2,1]
[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,2,1]
[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,2,1]
[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,2,1]
[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,2]
[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,2]
[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,2]
[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,2]
[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,2]
[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,1]
[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,1,1]
[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,1,1]
[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,1,1]
[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1,1,1]
[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1,1]
[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1,1,1]
[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1,1]
[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1,1]
[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1,1]
[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1,1,1]
[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1,1,1]
[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1,1,1]
[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1,1]
[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1]
[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2]
[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,1]
[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1]
[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3]
[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2,1]
[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,2]
[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,1]
[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1,1]
[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1]
[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2]
[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,1]
[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1]
[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]
[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2,1]
[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,2]
[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1,1]
[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3,1]
[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,3]
[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2,1]
[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2,1]
[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,2]
[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,2]
[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,1]
[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1,1]
[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1,1]
[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1,1]
[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]
[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1]
[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2]
[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,1]
[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]
[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]
[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2,1]
[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]
[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]
[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]
[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]
[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]
[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]
[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]
[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]
[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2,1]
[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,2]
[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,1,1]
[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3,1]
[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,3]
[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,2,1]
[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,2]
[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,1,1]
[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1,1,1]
[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2,1]
[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,2]
[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1,1]
[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4,1]
[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,5,4]
[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,2,1]
[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,2]
[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,1,1]
[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3,1]
[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,3]
[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,2,1]
[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,2,1]
[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,2]
[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,2]
[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,1,1]
[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1,1,1]
[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,1,1]
[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1,1,1]
[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1,1,1]
[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2,1]
[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,2]
[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1,1]
[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3,1]
[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,5,3]
[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2,1]
[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,2]
[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1,1]
[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1,1]
[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2,1]
[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,5,2]
[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1,1]
[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,5,1]
[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]
[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,2,1]
[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,2,1]
[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,2]
[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,2]
[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,1,1]
[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,1,1]
[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3,1]
[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,3]
[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3,1]
[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,3]
[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,2,1]
[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,2,1]
[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,2]
[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,2]
[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,1,1]
[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1,1,1]
[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,1,1]
[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1,1,1]
[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2,1]
[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,2]
[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1,1]
[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4,1]
[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,4]
[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2,1]
[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,2]
[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1,1]
[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4,1]
[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,4,4]
[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,2,1]
[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,2,1]
[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,2,1]
[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,2,1]
[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,2,1]
[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,2]
[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,2]
[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,2]
[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,2]
[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,2]
[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,1,1]
[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,1,1]
[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,1,1]
[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,1,1]
[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,1,1]
[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3,1]
[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,3]
[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3,1]
[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,3]
[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3,1]
[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,3]
[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3,1]
[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,3]
[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3,1]
[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,3]
[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,2,1]
[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,2,1]
[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,2,1]
[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,2,1]
[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,2,1]
[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,2,1]
[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,2,1]
[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,2,1]
[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,2,1]
[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,2,1]
[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,2,1]
[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,2,1]
[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,2,1]
[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2,1]
[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,2]
[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,2]
[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,2]
[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,2]
[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,2]
[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,2]
[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,2]
[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,2]
[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,2]
[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,2]
[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,2]
[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,2]
[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,2]
[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]
[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,1]
[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,1,1]
[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,1,1]
[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1,1]
[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1,1,1]
[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,1,1]
[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1,1,1]
[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,1,1]
[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,1,1]
[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,1,1]
[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1,1,1]
[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1,1,1]
[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1,1]
[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]
[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1,1]
[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1,1,1]
[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,1,1]
[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1,1,1]
[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1,1,1]
[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1,1]
[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1,1]
[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1,1,1]
[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1,1,1]
[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,1,1]
[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,1,1]
[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,1,1]
[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1,1]
[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]
[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1,1]
[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1,1]
[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1,1]
[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]
[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]
[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1,1]
[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]
[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]
[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]
[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]
[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]
[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]
[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]
[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]
[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1]
[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2]
[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,1]
[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1]
[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3]
[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2,1]
[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,2]
[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,1]
[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1,1]
[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1]
[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2]
[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,1]
[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]
[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]
[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2,1]
[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,2]
[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1,1]
[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3,1]
[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,3]
[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2,1]
[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2,1]
[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,2]
[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,2]
[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,1]
[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1,1]
[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1,1]
[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]
[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]
[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1]
[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]
[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]
[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]
[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]
[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]
[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]
[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]
[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]
[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]
[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]
[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]
[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]
[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]
[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2,1]
[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,2]
[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1,1]
[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3,1]
[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,4,3]
[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2,1]
[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,2]
[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1,1]
[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1,1]
[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2,1]
[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]
[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]
[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]
[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]
[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2,1]
[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2,1]
[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,2]
[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,2]
[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1,1]
[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1,1]
[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3,1]
[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]
[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]
[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]
[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2,1]
[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2,1]
[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2,1]
[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]
[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]
[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,2]
[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]
[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]
[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]
[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]
[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,1]
[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]
[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1]
[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]
[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]
[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1]
[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]
[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1]
[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]
[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1]
[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]
[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]
[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]
[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]
[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1]
[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]
[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1]
[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]
[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]
[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1]
[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]
[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]
[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]
[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]
[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]
[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]
[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]
[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]
[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1]
[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]
[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]
[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]
[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]
[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1]
[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]
[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]
[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]
[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]
[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]
[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]
[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]
[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]
[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]
[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]
[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]
[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]
[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]
[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]
[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]
[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]
[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]
[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]
[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]
[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]
[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]
[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7]
[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2,1]
[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2]
[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1,1]
[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,1]
[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3]
[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,2,1]
[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,2]
[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,1,1]
[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1,1,1]
[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2,1]
[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,2]
[[[]],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1,1]
[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,1]
[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[6,6,5,4]
[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,2,1]
[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,2]
[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,1,1]
[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3,1]
[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,3]
[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,2,1]
[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,2,1]
[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,2]
[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,2]
[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1,1]
[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1,1,1]
[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,1,1]
[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1,1,1]
[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1,1,1]
[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2,1]
[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,2]
[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1,1]
[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3,1]
[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[6,6,5,3]
[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2,1]
[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,2]
[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1,1]
[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1,1]
[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2,1]
[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[6,6,5,2]
[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1,1]
[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[6,6,5,1]
[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]
[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,2,1]
[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,2]
[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,1,1]
[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3,1]
[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,3]
[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,2,1]
[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,2]
[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,1,1]
[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1,1,1]
[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,1]
[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2]
[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1,1]
[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1]
[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4]
[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,2,1]
[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,2,1]
[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,2]
[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,2]
[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,1,1]
[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,1,1]
[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3,1]
[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,3]
[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3,1]
[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,3]
[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,2,1]
[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,2,1]
[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,2,1]
[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,2,1]
[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2,1]
[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,2]
[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,2]
[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,2]
[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,2]
[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,2]
[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1,1]
[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1,1,1]
[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,1,1]
[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1,1,1]
[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1,1,1]
[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,1,1]
[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1,1,1]
[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,1,1]
[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,1,1]
[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1,1,1]
[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1,1,1]
[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1,1,1]
[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1,1]
[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]
[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2,1]
[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,2]
[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1,1]
[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3,1]
[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[6,6,4,3]
[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2,1]
[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,2]
[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1,1]
[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1,1]
[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2,1]
[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,6,4,2]
[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1,1]
[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]
[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]
[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2,1]
[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,2]
[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1,1]
[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3,1]
[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[6,6,3,3]
[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,1]
[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2,1]
[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2]
[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,2]
[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1,1]
[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1,1]
[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1,1]
[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]
[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]
[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,1]
[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]
[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]
[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]
[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]
[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]
[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]
[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]
[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]
[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]
[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]
[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]
[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]
[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]
[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2,1]
[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,2,1]
[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2]
[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,2]
[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1,1]
[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,1,1]
[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,1]
[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3]
[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,1]
[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3]
[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,2,1]
[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,2,1]
[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,2]
[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,2]
[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,1,1]
[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1,1]
[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1,1]
[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1,1,1]
[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2,1]
[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,2]
[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1,1]
[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,1]
[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,5,4]
[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2,1]
[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,2]
[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1,1]
[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,1]
[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,5,5,4]
[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,2,1]
[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,2,1]
[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,2]
[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,2]
[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,1,1]
[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,1,1]
[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3,1]
[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,3]
[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3,1]
[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,3]
[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,2,1]
[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,2,1]
[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,2,1]
[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,2,1]
[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,2]
[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,2]
[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,2]
[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,2]
[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,1,1]
[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1,1,1]
[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,1,1]
[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1,1,1]
[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1,1,1]
[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1,1]
[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1,1,1]
[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,1,1]
[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1,1]
[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1,1,1]
[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2,1]
[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,2]
[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1,1]
[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3,1]
[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,5,3]
[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2,1]
[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,2]
[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1,1]
[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1,1]
[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2,1]
[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,5,2]
[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1,1]
[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1]
[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]
[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2,1]
[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,2]
[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1,1]
[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3,1]
[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,5,5,3]
[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2,1]
[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,2]
[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1,1]
[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1,1]
[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2,1]
[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]
[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]
[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]
[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]
[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2,1]
[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,2,1]
[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,2,1]
[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,2,1]
[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2,1]
[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2]
[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,2]
[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,2]
[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,2]
[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2]
[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,1,1]
[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,1,1]
[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,1,1]
[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,1,1]
[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1,1]
[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,1]
[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3]
[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,1]
[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3]
[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3,1]
[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,3]
[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,1]
[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3]
[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]
[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3]
[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,2,1]
[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,2,1]
[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,2,1]
[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,2,1]
[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2,1]
[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,2]
[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,2]
[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,2]
[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,2]
[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2]
[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,1,1]
[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1,1,1]
[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,1,1]
[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1,1,1]
[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,1,1]
[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1,1,1]
[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,1,1]
[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1,1,1]
[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]
[[[[[]]]],[[[]]],[]]=>[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1,1]
[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2,1]
[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,2]
[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1,1]
[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,1]
[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,4]
[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2,1]
[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,2]
[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1,1]
[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,1]
[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,4,4]
[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2,1]
[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,2]
[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1,1]
[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4,1]
[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,5,4,4]
[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,1]
[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2]
[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1,1]
[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1]
[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]
[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]
[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]
[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1]
[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]
[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]
[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2,1]
[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2,1]
[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,2,1]
[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2,1]
[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]
[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,2,1]
[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,2,1]
[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,2,1]
[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,2,1]
[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2,1]
[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,2,1]
[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,2,1]
[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2,1]
[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2,1]
[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2]
[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2]
[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,2]
[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2]
[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2]
[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,2]
[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,2]
[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,2]
[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,2]
[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,2]
[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,2]
[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,2]
[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,2]
[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]
[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,1,1]
[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,1,1]
[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,1,1]
[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,1,1]
[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,1,1]
[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,1,1]
[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,1,1]
[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,1,1]
[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,1,1]
[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,1,1]
[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,1,1]
[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,1,1]
[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1,1]
[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]
[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,1]
[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3]
[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,1]
[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3]
[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3,1]
[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,3]
[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,1]
[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3]
[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,1]
[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3]
[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3,1]
[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,3]
[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3,1]
[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,3]
[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3,1]
[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,3]
[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3,1]
[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,3]
[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3,1]
[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,3]
[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3,1]
[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]
[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3,1]
[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]
[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]
[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]
[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]
[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]
[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2,1]
[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2,1]
[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,2,1]
[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2,1]
[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]
[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,2,1]
[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,2,1]
[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,2,1]
[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,2,1]
[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2,1]
[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,2,1]
[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,2,1]
[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2,1]
[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]
[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2,1]
[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,2,1]
[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,2,1]
[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,2,1]
[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,2,1]
[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,2,1]
[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2,1]
[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,2,1]
[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,2,1]
[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,2,1]
[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,2,1]
[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,2,1]
[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2,1]
[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]
[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2,1]
[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2,1]
[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2,1]
[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]
[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]
[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2,1]
[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]
[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]
[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]
[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]
[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]
[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]
[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]
[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]
[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2]
[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2]
[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,2]
[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2]
[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2]
[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,2]
[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,2]
[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,2]
[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,2]
[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,2]
[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,2]
[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,2]
[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]
[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]
[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,2]
[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,2]
[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,2]
[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,2]
[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,2]
[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,2]
[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,2]
[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,2]
[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,2]
[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,2]
[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,2]
[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,2]
[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]
[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]
[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,2]
[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]
[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]
[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]
[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]
[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]
[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]
[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]
[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]
[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]
[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]
[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]
[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]
[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]
[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,1]
[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1,1]
[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1,1]
[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1,1]
[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]
[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1,1]
[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1,1]
[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1,1]
[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1,1]
[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1,1]
[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1,1]
[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1,1]
[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]
[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]
[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1,1]
[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1,1]
[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1,1]
[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1,1]
[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1,1]
[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,1,1]
[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1,1]
[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1,1]
[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1,1]
[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1,1]
[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1,1]
[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1,1]
[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]
[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]
[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1,1]
[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1,1]
[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]
[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1,1]
[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]
[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]
[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]
[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]
[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]
[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]
[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]
[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]
[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]
[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]
[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1,1]
[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1,1]
[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,1,1]
[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1,1]
[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1,1]
[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1,1]
[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1,1]
[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1,1]
[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1,1]
[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1,1]
[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]
[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]
[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]
[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]
[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1,1]
[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1,1]
[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1,1,1]
[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1,1]
[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,1,1]
[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1,1]
[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1,1]
[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]
[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]
[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]
[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1,1]
[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1,1]
[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1,1]
[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1,1]
[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]
[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1,1]
[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]
[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]
[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]
[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]
[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1,1]
[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]
[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]
[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]
[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]
[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]
[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]
[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]
[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]
[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]
[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]
[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]
[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]
[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]
[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1,1]
[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]
[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1,1]
[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]
[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]
[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]
[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]
[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]
[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]
[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]
[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]
[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]
[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]
[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]
[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]
[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]
[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]
[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]
[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]
[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]
[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]
[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]
[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]
[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]
[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]
[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]
[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]
[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]
[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]
[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]
[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]
[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]
[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]
[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]
[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]
[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]
[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]
[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]
[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]
[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]
[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]
[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]
[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1]
[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2]
[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1]
[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1]
[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]
[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,1]
[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2]
[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1]
[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1]
[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1]
[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]
[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]
[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]
[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]
[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2,1]
[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,2]
[[[],[],[[]],[[]],[]]]=>[[[],[[]],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1,1]
[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,1]
[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]
[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,1]
[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,1]
[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2]
[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]
[[[],[],[[],[],[]],[]]]=>[[[],[[],[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,1]
[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]
[[[],[],[[[]],[]],[]]]=>[[[],[[],[[]]],[],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]
[[[],[],[[[],[]]],[]]]=>[[[],[[[],[]]],[],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]
[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]
[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1]
[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]
[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]
[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1]
[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]
[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]
[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]
[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]
[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]
[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]
[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]
[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]
[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]
[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]
[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2,1]
[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,2]
[[[],[[]],[],[[]],[]]]=>[[[],[[]],[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1,1]
[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3,1]
[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]
[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2,1]
[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,2]
[[[],[[]],[[],[]],[]]]=>[[[],[[],[]],[[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1,1]
[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]
[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1]
[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]
[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]
[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]
[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]
[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2,1]
[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2,1]
[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,2]
[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]
[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1,1]
[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]
[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1]
[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]
[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]
[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]
[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2,1]
[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]
[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]
[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]
[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]
[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]
[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]
[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]
[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]
[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]
[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1]
[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]
[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]
[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]
[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]
[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]
[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]
[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]
[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]
[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]
[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]
[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]
[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]
[[[],[[[[[]]]]],[]]]=>[[[],[[[[[]]]]],[]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]
[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1]
[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]
[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]
[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]
[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]
[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]
[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]
[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]
[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]
[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]
[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]
[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]
[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]
[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]
[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]
[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]
[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]
[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]
[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]
[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]
[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]
[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]
[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]
[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]
[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]
[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]
[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]
[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]
[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]
[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]
[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]
[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]
[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]
[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]
[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]
[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]
[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]
[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]
[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]
[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]
[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]
[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[6]
[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1]
[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2]
[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1,1]
[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,1]
[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]
[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2,1]
[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,2]
[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1,1]
[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]
[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1]
[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]
[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]
[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]
[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]
[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2,1]
[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,2]
[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1,1]
[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]
[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]
[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2,1]
[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]
[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]
[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]
[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]
[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]
[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]
[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]
[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]
[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]
[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]
[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]
[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]
[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]
[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]
[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]
[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]
[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]
[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]
[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]
[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]
[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]
[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]
[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1]
[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]
[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2]
[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]
[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1,1]
[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]
[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1]
[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]
[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]
[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]
[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2,1]
[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]
[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]
[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]
[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]
[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]
[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]
[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]
[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]
[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]
[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]
[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]
[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]
[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]
[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]
[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]
[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]
[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]
[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1]
[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]
[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]
[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]
[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]
[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]
[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]
[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]
[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]
[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]
[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]
[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]
[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]
[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]
[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]
[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]
[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]
[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]
[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]
[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]
[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]
[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]
[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]
[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]
[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]
[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1]
[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]
[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]
[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]
[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]
[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]
[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]
[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]
[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]
[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]
[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]
[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]
[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]
[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]
[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]
[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]
[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]
[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]
[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]
[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]
[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]
[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]
[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]
[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]
[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]
[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]
[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]
[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]
[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1]
[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]
[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]
[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]
[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]
[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]
[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]
[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]
[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]
[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]
[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]
[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]
[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]
[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]
[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]
[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]
[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]
[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]
[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]
[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]
[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]
[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]
[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]
[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]
[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]
[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]
[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]
[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]
[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]
[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]
[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]
[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]
[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]
[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]
[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]
[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]
[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]
[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]
[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]
[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]
[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]
[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]
[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]
[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]
[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]
[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]
[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]
[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]
[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]
[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]
[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]
[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]
[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]
[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]
[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]
[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]
[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]
[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]
[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]
[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]
[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]
[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]
[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]
[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]
[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]
[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]
[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]
[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]
[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]
[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]
[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]
[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]
[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]
[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]
[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]
[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]
[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]
[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]
[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]
[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]
[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]
[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]
[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]
[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5]
[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]
[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]
[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]
[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]
[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]
[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]
[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]
[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]
[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]
[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]
[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]
[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]
[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]
[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]
[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]
[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]
[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]
[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]
[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]
[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]
[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]
[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]
[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]
[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]
[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]
[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]
[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]
[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]
[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]
[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]
[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]
[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]
[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]
[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]
[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]
[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]
[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]
[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]
[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]
[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]
[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]
[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]
[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]
[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]
[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]
[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]
[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]
[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]
[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]
[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]
[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]
[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]
[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]
[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]
[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]
[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]
[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]
[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]
[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]
[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]
[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]
[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4]
[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]
[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]
[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]
[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]
[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]
[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]
[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]
[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]
[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]
[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]
[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]
[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]
[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]
[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]
[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]
[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]
[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]
[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]
[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3]
[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]
[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]
[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]
[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]
[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]
[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2]
[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]
[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[]
[[],[[],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1]
[[],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,2,1,1]
[[],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,7,4,3,3,1]
[[],[[],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[9,7,4,2,1,1,1]
[[],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[9,7,3,2,2,1,1]
[[],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[9,6,5,5,3,1]
[[],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[9,6,5,5,2,1,1]
[[],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[9,6,4,3,3,3,1]
[[],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[9,5,4,4,3,3,1]
[[],[[[],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[9,6,4,2,1,1,1,1]
[[],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[9,6,3,2,2,1,1,1]
[[],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[9,5,4,4,2,1,1,1]
[[],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[9,5,3,2,2,2,1,1]
[[],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,3,2,2,1,1]
[[[],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[8,7,7,5,3,1]
[[[],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[8,7,7,5,2,1,1]
[[[],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[8,7,7,4,3,3,1]
[[[],[]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[8,7,7,4,2,1,1,1]
[[[],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[8,7,7,3,2,2,1,1]
[[[],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[8,6,5,5,5,3,1]
[[[],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[8,6,5,5,5,2,1,1]
[[[[],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,6,6,5,5,3,1]
[[[[],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,6,6,5,5,2,1,1]
[[[],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,3,3,3,3,1]
[[[],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,4,3,3,3,1]
[[[[],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7,6,6,4,3,3,3,1]
[[[[],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[7,5,4,4,4,3,3,1]
[[[[[],[]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,5,5,4,4,3,3,1]
[[[],[[],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,1,1,1,1,1]
[[[],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[8,6,3,2,2,1,1,1,1]
[[[],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[8,5,4,4,2,1,1,1,1]
[[[],[[[],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[8,5,3,2,2,2,1,1,1]
[[[],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[8,4,3,3,2,2,1,1,1]
[[[[],[]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[7,6,6,4,2,1,1,1,1]
[[[[],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[7,6,6,3,2,2,1,1,1]
[[[[],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[7,5,4,4,4,2,1,1,1]
[[[[[],[]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[6,5,5,4,4,2,1,1,1]
[[[[],[[],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[7,5,3,2,2,2,2,1,1]
[[[[],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[7,4,3,3,2,2,2,1,1]
[[[[[],[]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[6,5,5,3,2,2,2,1,1]
[[[[[],[[],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,4,3,3,3,2,2,1,1]
[[[[[[],[]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,4,3,3,2,2,1,1]
[[],[[],[[],[[],[[],[[],[]]]]]]]=>[[[[[[[],[]],[]],[]],[]],[]],[]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[11,9,7,5,3,1]
[[],[[],[[],[[],[[[],[]],[]]]]]]=>[[[[[[],[[],[]]],[]],[]],[]],[]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[11,9,7,5,2,1,1]
[[],[[],[[],[[[],[]],[[],[]]]]]]=>[[[[[[],[]],[[],[]]],[]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[11,9,7,4,3,3,1]
[[],[[],[[],[[[],[[],[]]],[]]]]]=>[[[[[],[[[],[]],[]]],[]],[]],[]]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[11,9,7,4,2,1,1,1]
[[],[[],[[],[[[[],[]],[]],[]]]]]=>[[[[[],[[],[[],[]]]],[]],[]],[]]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[11,9,7,3,2,2,1,1]
[[],[[],[[[],[]],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[[],[]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[11,9,6,5,5,3,1]
[[],[[],[[[],[]],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[[],[]]],[]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[11,9,6,5,5,2,1,1]
[[],[[],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[11,9,6,4,3,3,3,1]
[[],[[],[[[[],[]],[]],[[],[]]]]]=>[[[[[],[]],[[],[[],[]]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[11,9,5,4,4,3,3,1]
[[],[[],[[[],[[],[[],[]]]],[]]]]=>[[[[],[[[[],[]],[]],[]]],[]],[]]=>[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[11,9,6,4,2,1,1,1,1]
[[],[[],[[[],[[[],[]],[]]],[]]]]=>[[[[],[[[],[[],[]]],[]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[11,9,6,3,2,2,1,1,1]
[[],[[],[[[[],[]],[[],[]]],[]]]]=>[[[[],[[[],[]],[[],[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[11,9,5,4,4,2,1,1,1]
[[],[[],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[11,9,5,3,2,2,2,1,1]
[[],[[],[[[[[],[]],[]],[]],[]]]]=>[[[[],[[],[[],[[],[]]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[11,9,4,3,3,2,2,1,1]
[[],[[[],[]],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[[],[]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[11,8,7,7,5,3,1]
[[],[[[],[]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[],[]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[11,8,7,7,5,2,1,1]
[[],[[[],[]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[11,8,7,7,4,3,3,1]
[[],[[[],[]],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[[],[]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[11,8,7,7,4,2,1,1,1]
[[],[[[],[]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[],[]]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[11,8,7,7,3,2,2,1,1]
[[],[[[],[[],[]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[11,8,6,5,5,5,3,1]
[[],[[[],[[],[]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[11,8,6,5,5,5,2,1,1]
[[],[[[[],[]],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[11,7,6,6,5,5,3,1]
[[],[[[[],[]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[11,7,6,6,5,5,2,1,1]
[[],[[[],[[],[[],[]]]],[[],[]]]]=>[[[[],[]],[[[[],[]],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[11,8,6,4,3,3,3,3,1]
[[],[[[],[[[],[]],[]]],[[],[]]]]=>[[[[],[]],[[[],[[],[]]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[11,8,5,4,4,3,3,3,1]
[[],[[[[],[]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[11,7,6,6,4,3,3,3,1]
[[],[[[[],[[],[]]],[]],[[],[]]]]=>[[[[],[]],[[],[[[],[]],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[11,7,5,4,4,4,3,3,1]
[[],[[[[[],[]],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[[],[]]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[11,6,5,5,4,4,3,3,1]
[[],[[[],[[],[[],[[],[]]]]],[]]]=>[[[],[[[[[],[]],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[11,8,6,4,2,1,1,1,1,1]
[[],[[[],[[],[[[],[]],[]]]],[]]]=>[[[],[[[[],[[],[]]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[11,8,6,3,2,2,1,1,1,1]
[[],[[[],[[[],[]],[[],[]]]],[]]]=>[[[],[[[[],[]],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[11,8,5,4,4,2,1,1,1,1]
[[],[[[],[[[],[[],[]]],[]]],[]]]=>[[[],[[[],[[[],[]],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[11,8,5,3,2,2,2,1,1,1]
[[],[[[],[[[[],[]],[]],[]]],[]]]=>[[[],[[[],[[],[[],[]]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[11,8,4,3,3,2,2,1,1,1]
[[],[[[[],[]],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[[],[]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[11,7,6,6,4,2,1,1,1,1]
[[],[[[[],[]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[11,7,6,6,3,2,2,1,1,1]
[[],[[[[],[[],[]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[],[]],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[11,7,5,4,4,4,2,1,1,1]
[[],[[[[[],[]],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[[],[]]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[11,6,5,5,4,4,2,1,1,1]
[[],[[[[],[[],[[],[]]]],[]],[]]]=>[[[],[[],[[[[],[]],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[11,7,5,3,2,2,2,2,1,1]
[[],[[[[],[[[],[]],[]]],[]],[]]]=>[[[],[[],[[[],[[],[]]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[11,7,4,3,3,2,2,2,1,1]
[[],[[[[[],[]],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[11,6,5,5,3,2,2,2,1,1]
[[],[[[[[],[[],[]]],[]],[]],[]]]=>[[[],[[],[[],[[[],[]],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[11,6,4,3,3,3,2,2,1,1]
[[],[[[[[[],[]],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[[],[]]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[11,5,4,4,3,3,2,2,1,1]
[[[],[]],[[],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[]],[[],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[10,9,9,7,5,3,1]
[[[],[]],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[[],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[10,9,9,7,5,2,1,1]
[[[],[]],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[10,9,9,7,4,3,3,1]
[[[],[]],[[],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[]],[[],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[10,9,9,7,4,2,1,1,1]
[[[],[]],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[[],[]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[10,9,9,7,3,2,2,1,1]
[[[],[]],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[10,9,9,6,5,5,3,1]
[[[],[]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[10,9,9,6,5,5,2,1,1]
[[[],[]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[10,9,9,6,4,3,3,3,1]
[[[],[]],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[10,9,9,5,4,4,3,3,1]
[[[],[]],[[[],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[]]],[[],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[10,9,9,6,4,2,1,1,1,1]
[[[],[]],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[[],[]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[10,9,9,6,3,2,2,1,1,1]
[[[],[]],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[[],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[10,9,9,5,4,4,2,1,1,1]
[[[],[]],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[10,9,9,5,3,2,2,2,1,1]
[[[],[]],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[10,9,9,4,3,3,2,2,1,1]
[[[],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[10,8,7,7,7,5,3,1]
[[[],[[],[]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[10,8,7,7,7,5,2,1,1]
[[[],[[],[]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[10,8,7,7,7,4,3,3,1]
[[[],[[],[]]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[[],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[10,8,7,7,7,4,2,1,1,1]
[[[],[[],[]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[],[]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[10,8,7,7,7,3,2,2,1,1]
[[[[],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[9,8,8,7,7,5,3,1]
[[[[],[]],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[9,8,8,7,7,5,2,1,1]
[[[[],[]],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[9,8,8,7,7,4,3,3,1]
[[[[],[]],[]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[],[[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[9,8,8,7,7,4,2,1,1,1]
[[[[],[]],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[[],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[9,8,8,7,7,3,2,2,1,1]
[[[],[[],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,5,5,5,5,3,1]
[[[],[[],[[],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[]],[]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,5,5,5,5,2,1,1]
[[[],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[10,7,6,6,5,5,5,3,1]
[[[],[[[],[]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[10,7,6,6,5,5,5,2,1,1]
[[[[],[]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[9,8,8,6,5,5,5,3,1]
[[[[],[]],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[9,8,8,6,5,5,5,2,1,1]
[[[[],[[],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[]],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,7,6,6,6,5,5,3,1]
[[[[],[[],[]]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[[],[]],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,7,6,6,6,5,5,2,1,1]
[[[[[],[]],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[[],[]]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[8,7,7,6,6,5,5,3,1]
[[[[[],[]],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[8,7,7,6,6,5,5,2,1,1]
[[[],[[],[[],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,3,3,3,3,3,1]
[[[],[[],[[[],[]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[],[]]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[10,8,5,4,4,3,3,3,3,1]
[[[],[[[],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[10,7,6,6,4,3,3,3,3,1]
[[[],[[[],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[10,7,5,4,4,4,3,3,3,1]
[[[],[[[[],[]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[],[]]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[10,6,5,5,4,4,3,3,3,1]
[[[[],[]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[9,8,8,6,4,3,3,3,3,1]
[[[[],[]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[9,8,8,5,4,4,3,3,3,1]
[[[[],[[],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[]],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,7,6,6,6,4,3,3,3,1]
[[[[[],[]],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[8,7,7,6,6,4,3,3,3,1]
[[[[],[[],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[9,7,5,4,4,4,4,3,3,1]
[[[[],[[[],[]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[],[]]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[9,6,5,5,4,4,4,3,3,1]
[[[[[],[]],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[[],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[8,7,7,5,4,4,4,3,3,1]
[[[[[],[[],[]]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[[],[]],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,6,5,5,5,4,4,3,3,1]
[[[[[[],[]],[]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[],[[],[]]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,6,6,5,5,4,4,3,3,1]
[[[],[[],[[],[[],[[],[]]]]]],[]]=>[[],[[[[[[],[]],[]],[]],[]],[]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,4,2,1,1,1,1,1,1]
[[[],[[],[[],[[[],[]],[]]]]],[]]=>[[],[[[[[],[[],[]]],[]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[10,8,6,3,2,2,1,1,1,1,1]
[[[],[[],[[[],[]],[[],[]]]]],[]]=>[[],[[[[[],[]],[[],[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[10,8,5,4,4,2,1,1,1,1,1]
[[[],[[],[[[],[[],[]]],[]]]],[]]=>[[],[[[[],[[[],[]],[]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[10,8,5,3,2,2,2,1,1,1,1]
[[[],[[],[[[[],[]],[]],[]]]],[]]=>[[],[[[[],[[],[[],[]]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[10,8,4,3,3,2,2,1,1,1,1]
[[[],[[[],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[10,7,6,6,4,2,1,1,1,1,1]
[[[],[[[],[]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[10,7,6,6,3,2,2,1,1,1,1]
[[[],[[[],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[10,7,5,4,4,4,2,1,1,1,1]
[[[],[[[[],[]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[],[]]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[10,6,5,5,4,4,2,1,1,1,1]
[[[],[[[],[[],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[10,7,5,3,2,2,2,2,1,1,1]
[[[],[[[],[[[],[]],[]]],[]]],[]]=>[[],[[[],[[[],[[],[]]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[10,7,4,3,3,2,2,2,1,1,1]
[[[],[[[[],[]],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[[],[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[10,6,5,5,3,2,2,2,1,1,1]
[[[],[[[[],[[],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[]],[]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[10,6,4,3,3,3,2,2,1,1,1]
[[[],[[[[[],[]],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[[],[]]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[10,5,4,4,3,3,2,2,1,1,1]
[[[[],[]],[[],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[]],[[],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[9,8,8,6,4,2,1,1,1,1,1]
[[[[],[]],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[[],[]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[9,8,8,6,3,2,2,1,1,1,1]
[[[[],[]],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[9,8,8,5,4,4,2,1,1,1,1]
[[[[],[]],[[[],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[9,8,8,5,3,2,2,2,1,1,1]
[[[[],[]],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[9,8,8,4,3,3,2,2,1,1,1]
[[[[],[[],[]]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,7,6,6,6,4,2,1,1,1,1]
[[[[],[[],[]]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[9,7,6,6,6,3,2,2,1,1,1]
[[[[[],[]],[]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[],[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[8,7,7,6,6,4,2,1,1,1,1]
[[[[[],[]],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[8,7,7,6,6,3,2,2,1,1,1]
[[[[],[[],[[],[]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[],[]],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[9,7,5,4,4,4,4,2,1,1,1]
[[[[],[[[],[]],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[[],[]]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[9,6,5,5,4,4,4,2,1,1,1]
[[[[[],[]],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[8,7,7,5,4,4,4,2,1,1,1]
[[[[[],[[],[]]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[[],[]],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,6,5,5,5,4,4,2,1,1,1]
[[[[[[],[]],[]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[],[[],[]]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,6,6,5,5,4,4,2,1,1,1]
[[[[],[[],[[],[[],[]]]]],[]],[]]=>[[],[[],[[[[[],[]],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[9,7,5,3,2,2,2,2,2,1,1]
[[[[],[[],[[[],[]],[]]]],[]],[]]=>[[],[[],[[[[],[[],[]]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[9,7,4,3,3,2,2,2,2,1,1]
[[[[],[[[],[]],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[9,6,5,5,3,2,2,2,2,1,1]
[[[[],[[[],[[],[]]],[]]],[]],[]]=>[[],[[],[[[],[[[],[]],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[9,6,4,3,3,3,2,2,2,1,1]
[[[[],[[[[],[]],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[[],[]]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[9,5,4,4,3,3,2,2,2,1,1]
[[[[[],[]],[[],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[8,7,7,5,3,2,2,2,2,1,1]
[[[[[],[]],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[8,7,7,4,3,3,2,2,2,1,1]
[[[[[],[[],[]]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8,6,5,5,5,3,2,2,2,1,1]
[[[[[[],[]],[]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,6,6,5,5,3,2,2,2,1,1]
[[[[[],[[],[[],[]]]],[]],[]],[]]=>[[],[[],[[],[[[[],[]],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[8,6,4,3,3,3,3,2,2,1,1]
[[[[[],[[[],[]],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[[],[]]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[8,5,4,4,3,3,3,2,2,1,1]
[[[[[[],[]],[[],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[]],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[7,6,6,4,3,3,3,2,2,1,1]
[[[[[[],[[],[]]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[[],[]],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[7,5,4,4,4,3,3,2,2,1,1]
[[[[[[[],[]],[]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[],[[],[]]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,5,5,4,4,3,3,2,2,1,1]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path is the depth of the tree.
This sends the maximal height of the Dyck path is the depth of the tree.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
searching the database
Sorry, this map was not found in the database.