Identifier
Mp00048:
Ordered trees
—left-right symmetry⟶
Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Images
=>
Cc0021;cc-rep-0Cc0021;cc-rep-1Cc0005;cc-rep-2
[]=>[]=>[]=>[]
[[]]=>[[]]=>[1,0]=>[1]
[[],[]]=>[[],[]]=>[1,0,1,0]=>[2,1]
[[[]]]=>[[[]]]=>[1,1,0,0]=>[1,2]
[[],[],[]]=>[[],[],[]]=>[1,0,1,0,1,0]=>[2,1,3]
[[],[[]]]=>[[[]],[]]=>[1,1,0,0,1,0]=>[3,1,2]
[[[]],[]]=>[[],[[]]]=>[1,0,1,1,0,0]=>[2,3,1]
[[[],[]]]=>[[[],[]]]=>[1,1,0,1,0,0]=>[1,3,2]
[[[[]]]]=>[[[[]]]]=>[1,1,1,0,0,0]=>[1,2,3]
[[],[],[],[]]=>[[],[],[],[]]=>[1,0,1,0,1,0,1,0]=>[2,1,4,3]
[[],[],[[]]]=>[[[]],[],[]]=>[1,1,0,0,1,0,1,0]=>[3,1,4,2]
[[],[[]],[]]=>[[],[[]],[]]=>[1,0,1,1,0,0,1,0]=>[2,1,3,4]
[[],[[],[]]]=>[[[],[]],[]]=>[1,1,0,1,0,0,1,0]=>[3,1,2,4]
[[],[[[]]]]=>[[[[]]],[]]=>[1,1,1,0,0,0,1,0]=>[4,1,2,3]
[[[]],[],[]]=>[[],[],[[]]]=>[1,0,1,0,1,1,0,0]=>[2,4,1,3]
[[[]],[[]]]=>[[[]],[[]]]=>[1,1,0,0,1,1,0,0]=>[3,4,1,2]
[[[],[]],[]]=>[[],[[],[]]]=>[1,0,1,1,0,1,0,0]=>[2,3,1,4]
[[[[]]],[]]=>[[],[[[]]]]=>[1,0,1,1,1,0,0,0]=>[2,3,4,1]
[[[],[],[]]]=>[[[],[],[]]]=>[1,1,0,1,0,1,0,0]=>[1,3,2,4]
[[[],[[]]]]=>[[[[]],[]]]=>[1,1,1,0,0,1,0,0]=>[1,4,2,3]
[[[[]],[]]]=>[[[],[[]]]]=>[1,1,0,1,1,0,0,0]=>[1,3,4,2]
[[[[],[]]]]=>[[[[],[]]]]=>[1,1,1,0,1,0,0,0]=>[1,2,4,3]
[[[[[]]]]]=>[[[[[]]]]]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]
[[],[],[],[],[]]=>[[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]
[[],[],[],[[]]]=>[[[]],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]
[[],[],[[]],[]]=>[[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]
[[],[],[[],[]]]=>[[[],[]],[],[]]=>[1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]
[[],[],[[[]]]]=>[[[[]]],[],[]]=>[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]
[[],[[]],[],[]]=>[[],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]
[[],[[]],[[]]]=>[[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]
[[],[[],[]],[]]=>[[],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]
[[],[[[]]],[]]=>[[],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]
[[],[[],[],[]]]=>[[[],[],[]],[]]=>[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]
[[],[[],[[]]]]=>[[[[]],[]],[]]=>[1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]
[[],[[[]],[]]]=>[[[],[[]]],[]]=>[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]
[[],[[[],[]]]]=>[[[[],[]]],[]]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]
[[],[[[[]]]]]=>[[[[[]]]],[]]=>[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]
[[[]],[],[],[]]=>[[],[],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]
[[[]],[],[[]]]=>[[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]
[[[]],[[]],[]]=>[[],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]
[[[]],[[],[]]]=>[[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]
[[[]],[[[]]]]=>[[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]
[[[],[]],[],[]]=>[[],[],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]
[[[[]]],[],[]]=>[[],[],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]
[[[],[]],[[]]]=>[[[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]
[[[[]]],[[]]]=>[[[]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]
[[[],[],[]],[]]=>[[],[[],[],[]]]=>[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]
[[[],[[]]],[]]=>[[],[[[]],[]]]=>[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]
[[[[]],[]],[]]=>[[],[[],[[]]]]=>[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]
[[[[],[]]],[]]=>[[],[[[],[]]]]=>[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]
[[[[[]]]],[]]=>[[],[[[[]]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]
[[[],[],[],[]]]=>[[[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]
[[[],[],[[]]]]=>[[[[]],[],[]]]=>[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]
[[[],[[]],[]]]=>[[[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]
[[[],[[],[]]]]=>[[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]
[[[],[[[]]]]]=>[[[[[]]],[]]]=>[1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]
[[[[]],[],[]]]=>[[[],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]
[[[[]],[[]]]]=>[[[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]
[[[[],[]],[]]]=>[[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]
[[[[[]]],[]]]=>[[[],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]
[[[[],[],[]]]]=>[[[[],[],[]]]]=>[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]
[[[[],[[]]]]]=>[[[[[]],[]]]]=>[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]
[[[[[]],[]]]]=>[[[[],[[]]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]
[[[[[],[]]]]]=>[[[[[],[]]]]]=>[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]
[[[[[[]]]]]]=>[[[[[[]]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]
[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]
[[],[],[],[],[[]]]=>[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]
[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]
[[],[],[],[[],[]]]=>[[[],[]],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]
[[],[],[],[[[]]]]=>[[[[]]],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]
[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]
[[],[],[[]],[[]]]=>[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]
[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]
[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]
[[],[],[[],[],[]]]=>[[[],[],[]],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]
[[],[],[[],[[]]]]=>[[[[]],[]],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]
[[],[],[[[]],[]]]=>[[[],[[]]],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]
[[],[],[[[],[]]]]=>[[[[],[]]],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]
[[],[],[[[[]]]]]=>[[[[[]]]],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]
[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]
[[],[[]],[],[[]]]=>[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]
[[],[[]],[[]],[]]=>[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]
[[],[[]],[[],[]]]=>[[[],[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]
[[],[[]],[[[]]]]=>[[[[]]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]
[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]
[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]
[[],[[],[]],[[]]]=>[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]
[[],[[[]]],[[]]]=>[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]
[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]
[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]
[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]
[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]
[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]
[[],[[],[],[],[]]]=>[[[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]
[[],[[],[],[[]]]]=>[[[[]],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]
[[],[[],[[]],[]]]=>[[[],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]
[[],[[],[[],[]]]]=>[[[[],[]],[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]
[[],[[],[[[]]]]]=>[[[[[]]],[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]
[[],[[[]],[],[]]]=>[[[],[],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]
[[],[[[]],[[]]]]=>[[[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]
[[],[[[],[]],[]]]=>[[[],[[],[]]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]
[[],[[[[]]],[]]]=>[[[],[[[]]]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]
[[],[[[],[],[]]]]=>[[[[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]
[[],[[[],[[]]]]]=>[[[[[]],[]]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]
[[],[[[[]],[]]]]=>[[[[],[[]]]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]
[[],[[[[],[]]]]]=>[[[[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]
[[],[[[[[]]]]]]=>[[[[[[]]]]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]
[[[]],[],[],[],[]]=>[[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]
[[[]],[],[],[[]]]=>[[[]],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]
[[[]],[],[[]],[]]=>[[],[[]],[],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]
[[[]],[],[[],[]]]=>[[[],[]],[],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]
[[[]],[],[[[]]]]=>[[[[]]],[],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]
[[[]],[[]],[],[]]=>[[],[],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]
[[[]],[[]],[[]]]=>[[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]
[[[]],[[],[]],[]]=>[[],[[],[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]
[[[]],[[[]]],[]]=>[[],[[[]]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]
[[[]],[[],[],[]]]=>[[[],[],[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]
[[[]],[[],[[]]]]=>[[[[]],[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]
[[[]],[[[]],[]]]=>[[[],[[]]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]
[[[]],[[[],[]]]]=>[[[[],[]]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]
[[[]],[[[[]]]]]=>[[[[[]]]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]
[[[],[]],[],[],[]]=>[[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]
[[[[]]],[],[],[]]=>[[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]
[[[],[]],[],[[]]]=>[[[]],[],[[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]
[[[[]]],[],[[]]]=>[[[]],[],[[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]
[[[],[]],[[]],[]]=>[[],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]
[[[[]]],[[]],[]]=>[[],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]
[[[],[]],[[],[]]]=>[[[],[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]
[[[],[]],[[[]]]]=>[[[[]]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]
[[[[]]],[[],[]]]=>[[[],[]],[[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]
[[[[]]],[[[]]]]=>[[[[]]],[[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]
[[[],[],[]],[],[]]=>[[],[],[[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]
[[[],[[]]],[],[]]=>[[],[],[[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]
[[[[]],[]],[],[]]=>[[],[],[[],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]
[[[[],[]]],[],[]]=>[[],[],[[[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]
[[[[[]]]],[],[]]=>[[],[],[[[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]
[[[],[],[]],[[]]]=>[[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]
[[[],[[]]],[[]]]=>[[[]],[[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]
[[[[]],[]],[[]]]=>[[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]
[[[[],[]]],[[]]]=>[[[]],[[[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]
[[[[[]]]],[[]]]=>[[[]],[[[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]
[[[],[],[],[]],[]]=>[[],[[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]
[[[],[],[[]]],[]]=>[[],[[[]],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]
[[[],[[]],[]],[]]=>[[],[[],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]
[[[],[[],[]]],[]]=>[[],[[[],[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]
[[[],[[[]]]],[]]=>[[],[[[[]]],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]
[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]
[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]
[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]
[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]
[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]
[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]
[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]
[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]
[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]
[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]
[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]
[[[],[],[[]],[]]]=>[[[],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]
[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]
[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]
[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]
[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]
[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]
[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]
[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]
[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]
[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]
[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]
[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]
[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]
[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]
[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]
[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]
[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]
[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]
[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]
[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]
[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]
[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]
[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]
[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]
[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]
[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]
[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]
[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]
[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]
[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]
[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]
[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]
[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]
[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]
[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]
[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]
[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]
[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]
[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]
[[[[[[[]]]]]]]=>[[[[[[[]]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]
[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]
[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]
[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]
[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]
[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]
[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]
[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]
[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]
[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]
[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]
[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]
[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]
[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]
[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]
[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]
[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]
[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]
[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]
[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]
[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]
[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]
[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]
[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]
[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]
[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]
[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]
[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]
[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]
[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]
[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]
[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]
[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]
[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]
[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]
[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]
[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]
[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]
[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]
[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]
[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]
[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]
[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]
[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]
[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]
[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]
[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]
[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]
[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]
[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]
[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]
[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]
[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]
[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]
[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]
[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]
[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]
[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]
[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]
[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]
[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]
[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]
[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]
[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]
[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]
[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]
[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]
[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]
[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]
[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]
[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]
[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]
[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]
[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]
[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]
[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]
[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]
[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]
[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]
[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]
[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]
[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]
[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]
[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]
[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]
[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]
[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]
[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]
[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]
[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]
[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]
[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]
[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]
[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]
[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]
[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]
[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]
[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]
[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]
[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]
[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]
[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]
[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]
[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]
[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]
[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]
[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]
[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]
[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]
[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]
[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]
[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]
[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]
[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]
[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]
[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]
[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]
[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]
[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]
[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]
[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]
[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]
[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]
[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]
[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]
[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]
[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]
[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]
[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]
[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]
[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]
[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]
[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]
[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]
[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]
[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]
[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]
[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]
[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]
[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]
[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]
[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]
[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]
[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]
[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]
[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]
[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]
[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]
[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]
[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]
[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]
[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]
[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]
[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]
[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]
[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]
[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]
[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]
[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]
[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]
[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]
[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]
[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]
[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]
[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]
[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]
[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]
[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]
[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]
[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]
[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]
[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]
[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]
[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]
[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]
[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]
[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]
[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]
[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]
[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]
[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]
[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]
[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]
[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]
[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]
[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]
[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]
[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]
[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]
[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]
[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]
[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]
[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]
[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]
[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]
[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]
[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]
[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]
[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]
[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]
[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]
[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]
[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]
[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]
[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]
[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]
[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]
[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]
[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]
[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]
[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]
[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]
[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]
[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]
[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]
[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]
[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]
[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]
[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]
[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]
[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]
[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]
[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]
[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]
[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]
[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]
[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]
[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]
[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]
[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]
[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]
[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]
[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]
[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]
[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]
[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]
[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]
[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]
[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]
[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]
[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]
[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]
[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]
[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]
[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]
[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]
[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]
[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]
[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]
[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]
[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]
[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]
[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]
[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]
[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]
[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]
[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]
[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]
[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]
[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]
[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]
[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]
[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]
[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]
[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]
[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]
[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]
[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]
[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]
[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]
[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]
[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]
[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]
[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]
[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]
[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]
[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]
[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]
[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]
[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]
[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]
[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]
[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]
[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]
[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]
[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]
[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]
[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]
[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]
[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]
[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]
[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]
[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]
[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]
[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]
[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]
[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]
[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]
[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]
[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]
[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]
[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]
[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]
[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]
[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]
[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]
[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]
[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]
[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]
[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]
[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]
[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]
[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]
[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]
[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]
[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]
[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]
[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]
[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]
[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]
[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]
[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]
[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]
[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]
[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]
[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]
[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]
[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]
[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]
[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]
[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]
[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]
[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]
[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]
[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]
[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]
[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]
[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]
[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]
[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]
[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]
[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]
[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]
[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]
[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]
[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]
[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]
[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]
[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]
[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]
[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]
[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]
[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]
[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]
[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]
[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]
[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]
[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]
[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]
[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]
[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]
[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]
[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]
[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]
[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]
[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]
[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]
[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]
[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]
[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]
[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]
[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]
[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]
[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]
[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]
[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]
[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]
[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]
[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]
[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]
[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]
[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]
[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]
[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]
[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]
[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]
[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]
[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]
[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]
[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]
[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]
[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]
[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]
[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]
[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]
[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]
[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]
[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]
[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]
[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]
[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]
[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]
[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]
[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]
[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]
[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]
[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]
[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]
[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]
[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]
[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]
[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]
[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]
[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]
[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]
[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]
[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]
[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]
[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]
[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]
[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]
[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]
[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]
[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]
[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]
[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]
[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]
[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]
[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]
[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]
[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]
[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]
[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]
[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]
[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]
[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]
[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]
[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]
[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]
[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]
[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6]
[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]
[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]
[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]
[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]
[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]
[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7,8]
[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7,8]
[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8]
[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6,8]
[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,6,7]
[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6,8]
[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,6,7]
[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6,8]
[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5,8]
[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,8,4,6,7]
[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,8,4,5,7]
[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,7,3,8,4,5,6]
[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8]
[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6,8]
[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5,8]
[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5,8]
[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4,8]
[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]
[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,8,3,6,7]
[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,8,4,5,7]
[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,7,2,8,4,5,6]
[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,5,7]
[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,8,3,4,7]
[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,5,6]
[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,8,3,4,6]
[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,5]
[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,8,5,7]
[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]
[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,8,4,7]
[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,8,4,7]
[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,8,3,7]
[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]
[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,7,8,5,6]
[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,7,8,4,6]
[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,6,3,7,8,4,5]
[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,8,4,6]
[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,7,8,3,6]
[[],[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,6,2,7,8,4,5]
[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,6,2,7,8,3,5]
[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,1,6,2,7,8,3,4]
[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5,8]
[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]
[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5,8]
[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]
[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4,8]
[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]
[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4,8]
[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3,8]
[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,6,7,8,4]
[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]
[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6,8]
[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,8,6,7]
[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]
[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,8,7]
[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]
[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6,8]
[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,8,6,7]
[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]
[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,8,7]
[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]
[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6,8]
[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5,8]
[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,8,6,7]
[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,8,5,7]
[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,7,3,4,8,5,6]
[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,7,8,6]
[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]
[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,8,7]
[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]
[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,8,7]
[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,8,6]
[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7,8]
[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6,8]
[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7]
[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,8]
[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6,8]
[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,8]
[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5,8]
[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4,8]
[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,8,6,7]
[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,8,6,7]
[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,8,5,7]
[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,7,2,4,8,5,6]
[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,8,5,7]
[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,8,4,7]
[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,7,2,3,8,5,6]
[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,7,2,3,8,4,6]
[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,7,2,3,8,4,5]
[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]
[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]
[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,7,8,5]
[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]
[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]
[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,8,7]
[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7,8]
[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,8,7]
[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7,8]
[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,8,7]
[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,8,6]
[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]
[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6,8]
[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]
[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,8,7]
[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,8,7]
[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,8,6]
[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,8,6]
[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,8,5]
[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7,8]
[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7,8]
[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6,8]
[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,8,2,3,5,6,7]
[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6,8]
[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5,8]
[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,8,2,3,4,6,7]
[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]
[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6]
[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,8,7]
[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,8,7]
[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]
[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,8,7]
[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,8,7]
[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,8,6]
[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,8,6]
[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,8,6]
[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,8,5]
[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,8,6]
[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,8,6]
[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,8,5]
[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,8,5]
[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,8,4]
[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7,8]
[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7,8]
[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7,8]
[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7,8]
[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7,8]
[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6,8]
[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,4,8,3,5,6,7]
[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6,8]
[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,8,2,5,6,7]
[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6,8]
[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5,8]
[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,8,3,4,6,7]
[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,8,3,4,5,7]
[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,7,8,3,4,5,6]
[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,8]
[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6,8]
[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8]
[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5,8]
[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4,8]
[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,8,2,4,6,7]
[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,8,2,3,6,7]
[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,8,2,4,5,7]
[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6]
[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,8,2,3,5,7]
[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,1,6,8,2,3,4,7]
[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,7,8,2,3,5,6]
[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,7,8,2,3,4,6]
[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,4,5]
[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,8,5,7]
[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,8,3,5,7]
[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]
[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,8,2,5,7]
[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,8,4,7]
[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,8,3,4,7]
[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]
[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,8,3,7]
[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,8,2,4,7]
[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]
[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,7,3,8,5,6]
[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,7,8,3,5,6]
[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,7,2,8,5,6]
[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,7,8,2,5,6]
[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]
[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,6,7,3,8,4,5]
[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,7,8,3,4,6]
[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]
[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,7,2,8,4,6]
[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,7,2,8,3,6]
[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,6,7,2,8,4,5]
[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,6,7,2,8,3,5]
[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[5,1,6,7,2,8,3,4]
[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,7,8,2,4,6]
[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,7,8,2,3,6]
[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,6,7,8,2,4,5]
[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,6,7,8,2,3,5]
[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,6,7,8,2,3,4]
[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5,8]
[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,3,7,8,5]
[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5,8]
[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,3,8,5]
[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,6,7,8,3,5]
[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5,8]
[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,6,2,7,8,5]
[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5,8]
[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,6,7,2,8,5]
[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,6,7,8,2,5]
[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4,8]
[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,8,4]
[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4,8]
[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,8,4]
[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,5,6,7,8,3,4]
[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4,8]
[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3,8]
[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,6,2,7,8,4]
[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[4,1,5,6,2,7,8,3]
[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4,8]
[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3,8]
[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,8,4]
[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,8,3]
[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,6,7,8,2,4]
[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,5,6,7,8,2,3]
[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6,8]
[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,8,6,7]
[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,7,8,6]
[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,8,7]
[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7,8]
[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6,8]
[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,4,5,8,3,6,7]
[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,7,3,8,6]
[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,7,8,3,6]
[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7]
[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7,8]
[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,8,3,7]
[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3,8]
[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3]
[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]
[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,8,6,7]
[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,7,8,6]
[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,8,7]
[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7,8]
[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6,8]
[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,4,5,8,2,6,7]
[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,7,2,8,6]
[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,7,8,2,6]
[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,8,7]
[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7,8]
[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]
[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2,8]
[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2]
[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6,8]
[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5,8]
[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,8,6,7]
[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,8,5,7]
[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,7,4,8,5,6]
[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,7,8,6]
[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,8,5]
[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,8,7]
[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7,8]
[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,8,7]
[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,8,6]
[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7,8]
[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6,8]
[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,8,4,5,6,7]
[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6,8]
[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5,8]
[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,5,8,4,6,7]
[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,8,4,5,7]
[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,7,8,4,5,6]
[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,7,4,8,6]
[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,7,8,4,6]
[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,8,5]
[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,6,7,8,4,5]
[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,8,7]
[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7,8]
[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,8,4,7]
[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4,8]
[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,5,6,7,8,4]
[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,8,7]
[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,8,6]
[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7,8]
[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6,8]
[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,4,8,5,6,7]
[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,8,5,7]
[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,7,8,5,6]
[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5,8]
[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,6,7,8,5]
[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6,8]
[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,8,6,7]
[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,8,6]
[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]
[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8]
[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]
[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]
[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5,8]
[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]
[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4,8]
[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,8,6,7]
[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,8,6,7]
[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,8,5,7]
[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,7,4,8,5,6]
[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]
[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,8,4,7]
[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,7,3,8,5,6]
[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,7,3,8,4,6]
[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[6,1,2,7,3,8,4,5]
[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,7,8,6]
[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,7,8,6]
[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,8,5]
[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,8,5]
[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,8,4]
[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,8,7]
[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7,8]
[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,8,7]
[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7,8]
[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,8,7]
[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,8,6]
[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7,8]
[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6,8]
[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,8,4,5,6,7]
[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,8,7]
[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,8,7]
[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,8,6]
[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,6]
[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,8,5]
[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7,8]
[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7,8]
[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8]
[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,7]
[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6,8]
[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5,8]
[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]
[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,5,7]
[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,8,3,4,5,6]
[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]
[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]
[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5,8]
[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]
[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4,8]
[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,5,8,4,6,7]
[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,8,3,6,7]
[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,8,4,5,7]
[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,7,8,4,5,6]
[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,8,3,5,7]
[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,8,3,4,7]
[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,8,3,5,6]
[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,7,8,3,4,6]
[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[6,1,2,7,8,3,4,5]
[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,7,4,8,6]
[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,7,8,4,6]
[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,7,3,8,6]
[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,7,8,3,6]
[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,5]
[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,6,7,8,4,5]
[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,5]
[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,8,4]
[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,6,7,8,3,5]
[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,1,2,6,7,8,3,4]
[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,8,7]
[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7,8]
[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,8,4,7]
[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4,8]
[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,4]
[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,8,7]
[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7,8]
[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]
[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3,8]
[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,3]
[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7]
[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,8,6]
[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7,8]
[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]
[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,7]
[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,8,5,7]
[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,7,8,5,6]
[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8]
[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,8,5]
[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6,8]
[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]
[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,8,6]
[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]
[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8]
[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7]
[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,8,7]
[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,8,6]
[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,8,6]
[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,8,5]
[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7,8]
[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7,8]
[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]
[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]
[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6,8]
[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5,8]
[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,3,8,4,6,7]
[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,8,4,5,7]
[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1,2,3,8,4,5,6]
[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,8,5,7]
[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,8,4,7]
[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,7,8,5,6]
[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,7,8,4,6]
[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[6,1,2,3,7,8,4,5]
[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5,8]
[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,6,7,8,5]
[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4,8]
[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,6,7,8,4]
[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6,8]
[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,8,6,7]
[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,8,6]
[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]
[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8]
[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6,8]
[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5,8]
[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,8,6,7]
[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,8,5,7]
[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1,2,3,4,8,5,6]
[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,8,6]
[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,8,5]
[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]
[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8]
[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]
[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]
[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8]
[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]
[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]
[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]
[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]
[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,8,7]
[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,8,7]
[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]
[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]
[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,8,6]
[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]
[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,8,5]
[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,8,6]
[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,8,6]
[[[]],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,8,5]
[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,8,5]
[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,8,4]
[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7,8]
[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7,8]
[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7,8]
[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7,8]
[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7,8]
[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6,8]
[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,8,5,6,7]
[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6,8]
[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,8,5,6,7]
[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6,8]
[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5,8]
[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,8,4,6,7]
[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,8,4,5,7]
[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,7,1,3,8,4,5,6]
[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6,8]
[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6,8]
[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5,8]
[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5,8]
[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4,8]
[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,8,4,6,7]
[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,8,3,6,7]
[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,8,4,5,7]
[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,7,1,2,8,4,5,6]
[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,8,3,5,7]
[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,8,3,4,7]
[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,7,1,2,8,3,5,6]
[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,7,1,2,8,3,4,6]
[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,7,1,2,8,3,4,5]
[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7]
[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,8,5,7]
[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,7]
[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,8,4,7]
[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,8,3,7]
[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6]
[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]
[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,8,4,6]
[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,1,3,7,8,4,5]
[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,7,8,4,6]
[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,7,8,3,6]
[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,8,4,5]
[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,6,1,2,7,8,3,5]
[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,6,1,2,7,8,3,4]
[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5,8]
[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,7,8,5]
[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5,8]
[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,7,8,5]
[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4,8]
[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,7,8,4]
[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]
[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]
[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,7,8,4]
[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,7,8,3]
[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6,8]
[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,8,6,7]
[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,8,6]
[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,8,7]
[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8]
[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]
[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,8,6,7]
[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,8,6]
[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,8,7]
[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8]
[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6,8]
[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5,8]
[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,8,6,7]
[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,8,5,7]
[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,7,1,3,4,8,5,6]
[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,8,6]
[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,7,8,5]
[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,8,7]
[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7,8]
[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,8,7]
[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]
[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7,8]
[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6,8]
[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7]
[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]
[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]
[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]
[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]
[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4,8]
[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,8,6,7]
[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,8,6,7]
[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,8,5,7]
[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,7,1,2,4,8,5,6]
[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,8,5,7]
[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,7]
[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,7,1,2,3,8,5,6]
[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,8,4,6]
[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,7,1,2,3,8,4,5]
[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,8,6]
[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,8,6]
[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,8,5]
[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,8,5]
[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,8,4]
[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]
[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7,8]
[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,8,7]
[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7,8]
[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,8,7]
[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,8,6]
[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7,8]
[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6,8]
[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,8,1,2,4,5,6,7]
[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7]
[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,8,7]
[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,8,6]
[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]
[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,5]
[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7,8]
[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7,8]
[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6,8]
[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,8,1,2,3,5,6,7]
[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,8]
[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5,8]
[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,8,1,2,3,4,6,7]
[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,8,1,2,3,4,5,7]
[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]
[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7]
[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7]
[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,8,7]
[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,8,7]
[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,8,7]
[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,8,7]
[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]
[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,8,7]
[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,8,7]
[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]
[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,8,6]
[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,8,6]
[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,8,6]
[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,8,6]
[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]
[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,8,5]
[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,8,6]
[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]
[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,8,6]
[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,8,6]
[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,8,5]
[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,8,5]
[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,8,4]
[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,8,6]
[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,8,6]
[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,8,5]
[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,8,5]
[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,8,4]
[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7,8]
[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7,8]
[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7,8]
[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7,8]
[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7,8]
[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7,8]
[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7,8]
[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7,8]
[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7,8]
[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8]
[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6,8]
[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,5,6,7]
[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6,8]
[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,8,1,3,5,6,7]
[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6,8]
[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,8,2,5,6,7]
[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6,8]
[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,8,1,2,5,6,7]
[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6,8]
[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5,8]
[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,8,3,4,6,7]
[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,8,3,4,5,7]
[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]
[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6,8]
[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5,8]
[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,5,8,1,3,4,6,7]
[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,6,8,1,3,4,5,7]
[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,7,8,1,3,4,5,6]
[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6,8]
[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6,8]
[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5,8]
[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8]
[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4,8]
[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,8,2,4,6,7]
[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,8,2,3,6,7]
[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,8,2,4,5,7]
[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,7,1,8,2,4,5,6]
[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,8,2,3,5,7]
[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[5,6,1,8,2,3,4,7]
[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,7,1,8,2,3,5,6]
[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,6]
[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,7,1,8,2,3,4,5]
[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,8]
[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6,8]
[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5,8]
[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5,8]
[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4,8]
[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,5,8,1,2,4,6,7]
[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,7]
[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,6,8,1,2,4,5,7]
[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,7,8,1,2,4,5,6]
[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,8,1,2,3,5,7]
[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,8,1,2,3,4,7]
[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,7,8,1,2,3,5,6]
[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,8,1,2,3,4,6]
[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]
[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7]
[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7]
[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]
[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]
[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]
[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,8,5,7]
[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,8,2,5,7]
[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,8,5,7]
[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,8,2,5,7]
[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]
[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,8,4,7]
[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,8,3,4,7]
[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,8,4,7]
[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,8,3,4,7]
[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]
[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,8,4,7]
[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,8,3,7]
[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,8,2,4,7]
[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,8,2,3,7]
[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]
[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]
[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]
[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]
[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]
[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]
[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6]
[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,8,3,5,6]
[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,7,1,3,8,5,6]
[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]
[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]
[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,7,2,8,5,6]
[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,7,8,2,5,6]
[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,7,1,2,8,5,6]
[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]
[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]
[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,7,3,8,4,6]
[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,5]
[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,7,8,3,4,6]
[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,6,1,7,8,3,4,5]
[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,7,1,3,8,4,6]
[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,6,7,1,3,8,4,5]
[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,7,1,8,3,4,6]
[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,6,7,1,8,3,4,5]
[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]
[[[[[]]]],[[[]]],[]]=>[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]
[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]
[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,7,2,8,3,6]
[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,6,1,7,2,8,4,5]
[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,6,1,7,2,8,3,5]
[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,6,1,7,2,8,3,4]
[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,7,8,2,4,6]
[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]
[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]
[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,6,1,7,8,2,3,5]
[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,6,1,7,8,2,3,4]
[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,7,1,2,8,4,6]
[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]
[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]
[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,6,7,1,2,8,3,5]
[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,7,1,2,8,3,4]
[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,7,1,8,2,4,6]
[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,5,7,1,8,2,3,6]
[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,6,7,1,8,2,4,5]
[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]
[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]
[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]
[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]
[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]
[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]
[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]
[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8]
[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]
[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5,8]
[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]
[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,6,7,8,3,5]
[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5,8]
[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,6,1,3,7,8,5]
[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5,8]
[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]
[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,6,1,7,3,8,5]
[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]
[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,8,5]
[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,8,3,5]
[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,7,8,1,3,5]
[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5,8]
[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,2,7,8,5]
[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5,8]
[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,6,7,2,8,5]
[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,6,7,8,2,5]
[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5,8]
[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,6,1,2,7,8,5]
[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5,8]
[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5,8]
[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,6,1,7,2,8,5]
[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]
[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,6,7,1,2,8,5]
[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,8,2,5]
[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,7,8,1,2,5]
[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4,8]
[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]
[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4,8]
[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]
[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,6,7,8,3,4]
[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4,8]
[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,7,8,4]
[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4,8]
[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4,8]
[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,7,3,8,4]
[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]
[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,6,7,1,3,8,4]
[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5,6,7,1,8,3,4]
[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,6,7,8,1,3,4]
[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4,8]
[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3,8]
[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]
[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]
[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4,8]
[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3,8]
[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]
[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]
[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,4]
[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5,1,6,7,8,2,3]
[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4,8]
[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3,8]
[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5,6,1,2,7,8,4]
[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,6,1,2,7,8,3]
[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8]
[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3,8]
[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]
[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]
[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,7,2,8,4]
[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5,6,1,7,2,8,3]
[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]
[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,5,6,1,7,8,2,3]
[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,8,4]
[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,6,7,1,2,8,3]
[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,8,2,4]
[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,3]
[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5,6,7,8,1,2,4]
[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]
[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,8]
[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7]
[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]
[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,8,7]
[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8]
[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6,8]
[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,5,8,3,6,7]
[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]
[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,7,8,3,6]
[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,8,7]
[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7,8]
[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,8,3,7]
[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3,8]
[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,7,8,3]
[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6,8]
[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,8,6,7]
[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,7,8,6]
[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,8,7]
[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7,8]
[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6,8]
[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6,8]
[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]
[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,8,1,3,6,7]
[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,7,3,8,6]
[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,7,8,3,6]
[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,8,6]
[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,5,7,1,8,3,6]
[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,7,8,1,3,6]
[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,8,7]
[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7,8]
[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,8,3,7]
[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3,8]
[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,5,1,6,7,8,3]
[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,8,7]
[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]
[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,8,3,7]
[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,5,6,8,1,3,7]
[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3,8]
[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,5,6,1,7,8,3]
[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3,8]
[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]
[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,3]
[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6,8]
[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,8,6,7]
[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,7,8,6]
[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,8,7]
[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7,8]
[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6,8]
[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,5,8,2,6,7]
[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,7,2,8,6]
[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,7,8,2,6]
[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,8,7]
[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7,8]
[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,8,2,7]
[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2,8]
[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,5,6,7,8,2]
[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6,8]
[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]
[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,7,8,6]
[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,8,7]
[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7,8]
[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6,8]
[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6,8]
[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,1,8,2,6,7]
[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]
[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,7,2,8,6]
[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,7,8,2,6]
[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,8,6]
[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,7,1,8,2,6]
[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,7,8,1,2,6]
[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7]
[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7,8]
[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,8,2,7]
[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2,8]
[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,1,6,7,8,2]
[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,8,7]
[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]
[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,8,2,7]
[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,6,8,1,2,7]
[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8]
[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,5,6,1,7,8,2]
[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]
[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2]
[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]
[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,8]
[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,8]
[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,8,6,7]
[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7]
[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,7,4,8,5,6]
[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,7,8,6]
[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,7,8,5]
[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,8,7]
[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7,8]
[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,8,7]
[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,8,6]
[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7,8]
[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6,8]
[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,8,4,5,6,7]
[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6,8]
[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5,8]
[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,5,8,4,6,7]
[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,8,4,5,7]
[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,1,7,8,4,5,6]
[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,7,4,8,6]
[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,7,8,4,6]
[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,4,8,5]
[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,6,7,8,4,5]
[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,8,7]
[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7,8]
[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,8,4,7]
[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4,8]
[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,4]
[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,8,7]
[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,8,6]
[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7,8]
[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8]
[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,7]
[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,8,5,7]
[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,8,5,6]
[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8]
[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,8,5]
[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6,8]
[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]
[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]
[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,8,7]
[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8]
[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6,8]
[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5,8]
[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]
[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,8,5,7]
[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,3,7,1,4,8,5,6]
[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,7,8,6]
[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]
[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,8,7]
[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7,8]
[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,8,7]
[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,8,6]
[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7,8]
[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6,8]
[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,8,1,4,5,6,7]
[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6,8]
[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6,8]
[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5,8]
[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5,8]
[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]
[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,8,1,4,6,7]
[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]
[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,8,4,5,6]
[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,8,1,4,5,7]
[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]
[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,7,4,8,6]
[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,7,8,4,6]
[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,8,6]
[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,7,1,8,4,6]
[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,7,8,1,4,6]
[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,6,1,7,4,8,5]
[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]
[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,3,6,7,1,4,8,5]
[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,8,4,5]
[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,3,6,7,8,1,4,5]
[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,8,7]
[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7,8]
[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,8,4,7]
[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8]
[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]
[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,8,7]
[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]
[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,8,4,7]
[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,6,8,1,4,7]
[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4,8]
[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]
[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4,8]
[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4]
[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,6,7,8,1,4]
[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7]
[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6]
[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8]
[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6,8]
[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]
[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,8,5,7]
[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]
[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5,8]
[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]
[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6,8]
[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,8,6,7]
[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,7,8,6]
[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,8,7]
[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8]
[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,8,7]
[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,8,6]
[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]
[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]
[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]
[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,8,5,7]
[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,8,1,5,7]
[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,4,7,1,8,5,6]
[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,7,8,1,5,6]
[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5,8]
[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,6,1,7,8,5]
[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5,8]
[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,6,7,1,8,5]
[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,7,8,1,5]
[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6,8]
[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,8,6,7]
[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,7,8,6]
[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,8,7]
[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]
[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6,8]
[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,8,1,6,7]
[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,6]
[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,8,1,6]
[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7]
[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]
[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,7]
[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]
[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]
[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8]
[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,8]
[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,8]
[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,8]
[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8]
[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,8,6,7]
[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,8,6,7]
[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,8,5,7]
[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,7,4,8,5,6]
[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,7]
[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,8,4,7]
[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,2,7,3,8,5,6]
[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,7,3,8,4,6]
[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,5]
[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]
[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,7,8,6]
[[[],[],[[]],[[]],[]]]=>[[[],[[]],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]
[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,7,8,5]
[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]
[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,8,7]
[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7,8]
[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,8,7]
[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8]
[[[],[],[[],[],[]],[]]]=>[[[],[[],[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,8,7]
[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,8,6]
[[[],[],[[[]],[]],[]]]=>[[[],[[],[[]]],[],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7,8]
[[[],[],[[[],[]]],[]]]=>[[[],[[[],[]]],[],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6,8]
[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,2,8,4,5,6,7]
[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,8,7]
[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,8,7]
[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,8,6]
[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,8,6]
[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,8,5]
[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7,8]
[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7,8]
[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6,8]
[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,8,3,5,6,7]
[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]
[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5,8]
[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,2,8,3,4,6,7]
[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,8,3,4,5,7]
[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,7,2,8,3,4,5,6]
[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,8]
[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6,8]
[[[],[[]],[],[[]],[]]]=>[[[],[[]],[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8]
[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5,8]
[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4,8]
[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,8,4,6,7]
[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,8,3,6,7]
[[[],[[]],[[],[]],[]]]=>[[[],[[],[]],[[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,8,4,5,7]
[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,3,2,7,8,4,5,6]
[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,8,3,5,7]
[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,8,3,4,7]
[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,7,8,3,5,6]
[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,7,8,3,4,6]
[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,6,2,7,8,3,4,5]
[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]
[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,7,8,4,6]
[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]
[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,7,8,3,6]
[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,4,8,5]
[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,6,7,8,4,5]
[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,6,7,3,8,5]
[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,5,2,6,7,3,8,4]
[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,6,7,8,3,5]
[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,5,2,6,7,8,3,4]
[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,8,7]
[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7,8]
[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,8,4,7]
[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4,8]
[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,5,6,7,8,4]
[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,8,7]
[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7,8]
[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,8,3,7]
[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3,8]
[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,3]
[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7]
[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]
[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,8]
[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6,8]
[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,3,2,4,8,5,6,7]
[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,8,5,7]
[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,8,5,6]
[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5,8]
[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,6,7,8,5]
[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]
[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]
[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,7,8,6]
[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,8,7]
[[[],[[[[[]]]]],[]]]=>[[[],[[[[[]]]]],[]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8]
[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7]
[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,8,7]
[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]
[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]
[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]
[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7,8]
[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7,8]
[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]
[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,3,8,5,6,7]
[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6,8]
[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5,8]
[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,2,3,8,4,6,7]
[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,8,4,5,7]
[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,7,2,3,8,4,5,6]
[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,8,5,7]
[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,8,4,7]
[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,8,5,6]
[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,8,4,6]
[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,6,2,3,7,8,4,5]
[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5,8]
[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,6,7,8,5]
[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4,8]
[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,6,7,8,4]
[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6,8]
[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]
[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,7,8,6]
[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,8,7]
[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8]
[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6,8]
[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5,8]
[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]
[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]
[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]
[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,7,8,6]
[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,8,5]
[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,8,7]
[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8]
[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,8,7]
[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,8,6]
[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8]
[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8]
[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7]
[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,8]
[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,8]
[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5,8]
[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5,8]
[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4,8]
[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]
[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]
[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]
[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,3,7,2,4,8,5,6]
[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]
[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]
[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,7,2,3,8,5,6]
[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,7,2,3,8,4,6]
[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,6,7,2,3,8,4,5]
[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,7,8,6]
[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,7,8,6]
[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,7,8,5]
[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,7,8,5]
[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,7,8,4]
[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,8,7]
[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8]
[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,8,7]
[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7,8]
[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,8,7]
[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,8,6]
[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7,8]
[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6,8]
[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7]
[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,8,7]
[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,8,7]
[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,8,6]
[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,8,6]
[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,8,5]
[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7,8]
[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7,8]
[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6,8]
[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,4,8,2,3,5,6,7]
[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6,8]
[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]
[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,8,2,3,4,6,7]
[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,6,8,2,3,4,5,7]
[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,8,2,3,4,5,6]
[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,8]
[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]
[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6,8]
[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]
[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5,8]
[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]
[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5,8]
[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4,8]
[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]
[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4,8]
[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]
[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]
[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]
[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]
[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]
[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]
[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,8,2,4,5,7]
[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]
[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]
[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]
[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]
[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]
[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,6,7,2,8,3,4,5]
[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]
[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]
[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,4,7,8,2,3,5,6]
[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,7,8,2,3,4,6]
[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]
[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6]
[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]
[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,8,6]
[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,6]
[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,8,2,4,6]
[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,7,3,8,6]
[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]
[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,8,6]
[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,7,2,8,3,6]
[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,7,8,2,3,6]
[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,6,2,7,4,8,5]
[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]
[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,8,5]
[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,8,4,5]
[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,6,7,8,2,4,5]
[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,2,7,3,8,5]
[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,5,6,2,7,3,8,4]
[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]
[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,5,6,2,7,8,3,4]
[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,8,5]
[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,8,4]
[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,8,3,5]
[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,5,6,7,2,8,3,4]
[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,6,7,8,2,3,5]
[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,6,7,8,2,3,4]
[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,8,7]
[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,8]
[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,8,4,7]
[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4,8]
[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,5,2,6,7,8,4]
[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,8,7]
[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]
[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,8,4,7]
[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,6,8,2,4,7]
[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]
[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,5,6,2,7,8,4]
[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4,8]
[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,5,6,7,2,8,4]
[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,6,7,8,2,4]
[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,8,7]
[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7,8]
[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,8,3,7]
[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3,8]
[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,5,2,6,7,8,3]
[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,8,7]
[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]
[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,8,3,7]
[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,6,8,2,3,7]
[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3,8]
[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,5,6,2,7,8,3]
[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]
[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,5,6,7,2,8,3]
[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,5,6,7,8,2,3]
[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,8,7]
[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,8,6]
[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7,8]
[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6,8]
[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]
[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,8,5,7]
[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]
[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]
[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,6,7,8,5]
[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6,8]
[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,8,6,7]
[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6]
[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,8,7]
[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8]
[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,8,7]
[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,8,6]
[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]
[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]
[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]
[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,8,5,7]
[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,8,2,5,7]
[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,3,4,7,2,8,5,6]
[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,3,4,7,8,2,5,6]
[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5,8]
[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,6,2,7,8,5]
[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5,8]
[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,6,7,2,8,5]
[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,6,7,8,2,5]
[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6,8]
[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,8,6,7]
[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,7,8,6]
[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,8,7]
[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]
[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6,8]
[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,3,4,5,8,2,6,7]
[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,7,2,8,6]
[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,7,8,2,6]
[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,8,7]
[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7,8]
[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,8,2,7]
[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8]
[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2]
[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7]
[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7]
[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,8,6]
[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6]
[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5]
[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]
[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7,8]
[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6,8]
[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]
[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6,8]
[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5,8]
[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]
[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]
[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]
[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,8,5,7]
[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,8,4,7]
[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]
[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]
[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]
[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5,8]
[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,6,7,8,5]
[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4,8]
[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,6,7,8,4]
[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6,8]
[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,8,6,7]
[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,7,8,6]
[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,8,7]
[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8]
[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6,8]
[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,8]
[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,8,6,7]
[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,8,5,7]
[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]
[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,7,8,6]
[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,7,8,5]
[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,8,7]
[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7,8]
[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,8,7]
[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,8,6]
[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8]
[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6,8]
[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,7]
[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,8,7]
[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,8,7]
[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,8,6]
[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,8,6]
[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,8,5]
[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]
[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]
[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]
[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]
[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]
[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]
[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]
[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]
[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]
[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,8,5,7]
[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7]
[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,8,4,7]
[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,8,3,4,7]
[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,4,7,3,8,5,6]
[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,8,3,5,6]
[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,3,8,4,6]
[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,8,4,5]
[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,7,8,3,4,6]
[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,7,8,3,4,5]
[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5,8]
[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,6,3,7,8,5]
[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5,8]
[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,6,7,3,8,5]
[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,6,7,8,3,5]
[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,8]
[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,5,6,3,7,8,4]
[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4,8]
[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,6,7,3,8,4]
[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,5,6,7,8,3,4]
[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6,8]
[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,8,6,7]
[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,7,8,6]
[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,8,7]
[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]
[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6,8]
[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,4,5,8,3,6,7]
[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,7,3,8,6]
[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,7,8,3,6]
[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,8,7]
[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7,8]
[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,8,3,7]
[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3,8]
[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,3]
[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,8]
[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,8]
[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,8,6,7]
[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,8,5,7]
[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,6]
[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,7,8,6]
[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,7,8,5]
[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,8,7]
[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]
[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,8,7]
[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6]
[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]
[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]
[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]
[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,8]
[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5,8]
[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,8,4,6,7]
[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,8,4,5,7]
[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,6]
[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,7,4,8,6]
[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,8,4,6]
[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,6,7,4,8,5]
[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,7,8,4,5]
[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,8,7]
[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7,8]
[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,8,4,7]
[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4,8]
[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4]
[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7]
[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6]
[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8]
[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8]
[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,7]
[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7]
[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6]
[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8]
[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5]
[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8]
[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7]
[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6]
[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]
[[],[[],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,9,5,7,10]
[[],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,10,6,7,9]
[[],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,9,6,10]
[[],[[],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,10,7,9]
[[],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8,10,9]
[[],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,7,8,3,10,4,6,9]
[[],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,7,9,3,10,5,6,8]
[[],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,9,5,10]
[[],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,6,7,8,3,10,5,9]
[[],[[[],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,10,7,9]
[[],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8,10,9]
[[],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,7,9,5,10,6,8]
[[],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8,10,9]
[[],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,9,5,10,8]
[[[],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,10,6,9]
[[[],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,7,1,9,2,3,5,10,6,8]
[[[],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8,10,9]
[[[],[]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,7,1,9,2,4,5,6,10,8]
[[[],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,6,1,9,2,4,5,7,8,10]
[[[],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,6,1,7,9,2,10,3,5,8]
[[[],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,6,1,8,9,2,10,4,5,7]
[[[[],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,6,7,1,9,2,3,10,5,8]
[[[[],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,6,8,1,9,2,4,10,5,7]
[[[],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,9,4,10]
[[[],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,10,4,9]
[[[[],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8,10,9]
[[[[],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,9,2,10,4,8]
[[[[[],[]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,9,2,4,10,8]
[[[],[[],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,10,7,9]
[[[],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8,10,9]
[[[],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,7,9,5,10,6,8]
[[[],[[[],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8,10,9]
[[[],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,9,5,10,8]
[[[[],[]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,9,4,5,6,10,8]
[[[[],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,9,4,5,7,8,10]
[[[[],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,1,8,9,4,10,5,7]
[[[[[],[]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,6,8,1,9,4,5,10,7]
[[[[],[[],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8,10,9]
[[[[],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,9,4,10,8]
[[[[[],[]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,9,4,7,8,10]
[[[[[],[[],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,8,9,4,10,7]
[[[[[[],[]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,8,1,9,4,7,10]
[[],[[],[[],[[],[[],[[],[]]]]]]]=>[[[[[[[],[]],[]],[]],[]],[]],[]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1,2,9,3,4,10,5,6,12,8,11]
[[],[[],[[],[[],[[[],[]],[]]]]]]=>[[[[[[],[[],[]]],[]],[]],[]],[]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,9,3,4,11,5,7,12,8,10]
[[],[[],[[],[[[],[]],[[],[]]]]]]=>[[[[[[],[]],[[],[]]],[]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,9,5,7,10,12,11]
[[],[[],[[],[[[],[[],[]]],[]]]]]=>[[[[[],[[[],[]],[]]],[]],[]],[]]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,9,3,4,11,6,7,8,12,10]
[[],[[],[[],[[[[],[]],[]],[]]]]]=>[[[[[],[[],[[],[]]]],[]],[]],[]]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,11,6,7,9,10,12]
[[],[[],[[[],[]],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[[],[]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,9,11,5,12,7,10]
[[],[[],[[[],[]],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[[],[]]],[]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,10,11,6,12,7,9]
[[],[[],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,9,6,10,12,11]
[[],[[],[[[[],[]],[]],[[],[]]]]]=>[[[[[],[]],[[],[[],[]]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,9,11,6,12,10]
[[],[[],[[[],[[],[[],[]]]],[]]]]=>[[[[],[[[[],[]],[]],[]]],[]],[]]=>[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,9,3,5,6,11,7,8,12,10]
[[],[[],[[[],[[[],[]],[]]],[]]]]=>[[[[],[[[],[[],[]]],[]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,11,7,9,10,12]
[[],[[],[[[[],[]],[[],[]]],[]]]]=>[[[[],[[[],[]],[[],[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,10,11,7,12,9]
[[],[[],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8,11,9,10,12]
[[],[[],[[[[[],[]],[]],[]],[]]]]=>[[[[],[[],[[],[[],[]]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8,10,11,9,12]
[[],[[[],[]],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[[],[]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,1,2,8,9,3,11,4,5,7,12,10]
[[],[[[],[]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[],[]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,8,10,3,11,4,6,7,12,9]
[[],[[[],[]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,7,8,3,11,4,6,9,10,12]
[[],[[[],[]],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[[],[]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,8,10,3,11,5,6,7,9,12]
[[],[[[],[]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[],[]]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,7,10,3,12,5,6,8,9,11]
[[],[[[],[[],[]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,7,8,3,10,11,4,12,6,9]
[[],[[[],[[],[]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,7,9,3,10,11,5,12,6,8]
[[],[[[[],[]],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,7,8,10,3,11,4,6,12,9]
[[],[[[[],[]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,7,9,10,3,11,5,6,12,8]
[[],[[[],[[],[[],[]]]],[[],[]]]]=>[[[[],[]],[[[[],[]],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,9,5,10,12,11]
[[],[[[],[[[],[]],[]]],[[],[]]]]=>[[[[],[]],[[[],[[],[]]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,6,7,3,8,9,11,5,12,10]
[[],[[[[],[]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,6,7,8,3,11,5,9,10,12]
[[],[[[[],[[],[]]],[]],[[],[]]]]=>[[[[],[]],[[],[[[],[]],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,6,7,8,3,10,11,5,12,9]
[[],[[[[[],[]],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[[],[]]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,6,7,8,10,3,11,5,9,12]
[[],[[[],[[],[[],[[],[]]]]],[]]]=>[[[],[[[[[],[]],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,9,5,6,11,7,8,12,10]
[[],[[[],[[],[[[],[]],[]]]],[]]]=>[[[],[[[[],[[],[]]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,11,7,9,10,12]
[[],[[[],[[[],[]],[[],[]]]],[]]]=>[[[],[[[[],[]],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,10,11,7,12,9]
[[],[[[],[[[],[[],[]]],[]]],[]]]=>[[[],[[[],[[[],[]],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8,11,9,10,12]
[[],[[[],[[[[],[]],[]],[]]],[]]]=>[[[],[[[],[[],[[],[]]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8,10,11,9,12]
[[],[[[[],[]],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[[],[]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,8,10,5,11,6,7,9,12]
[[],[[[[],[]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,7,10,5,12,6,8,9,11]
[[],[[[[],[[],[]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[],[]],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,7,9,5,10,11,6,12,8]
[[],[[[[[],[]],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[[],[]]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,7,9,10,5,11,6,8,12]
[[],[[[[],[[],[[],[]]]],[]],[]]]=>[[[],[[],[[[[],[]],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8,11,9,10,12]
[[],[[[[],[[[],[]],[]]],[]],[]]]=>[[[],[[],[[[],[[],[]]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5,8,10,11,9,12]
[[],[[[[[],[]],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,10,5,12,8,9,11]
[[],[[[[[],[[],[]]],[]],[]],[]]]=>[[[],[[],[[],[[[],[]],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,9,5,10,11,8,12]
[[],[[[[[[],[]],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[[],[]]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,9,10,5,12,8,11]
[[[],[]],[[],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[]],[[],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,8,1,9,2,3,4,11,5,7,12,10]
[[[],[]],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[[],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,8,1,10,2,3,4,11,6,7,12,9]
[[[],[]],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,11,6,9,10,12]
[[[],[]],[[],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[]],[[],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,8,1,10,2,3,5,11,6,7,9,12]
[[[],[]],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[[],[]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,7,1,10,2,3,5,12,6,8,9,11]
[[[],[]],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,10,11,6,12,9]
[[[],[]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,7,1,9,2,3,5,10,11,6,12,8]
[[[],[]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8,11,9,10,12]
[[[],[]],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8,10,11,9,12]
[[[],[]],[[[],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[]]],[[],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,8,1,10,2,4,5,6,11,7,9,12]
[[[],[]],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[[],[]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,7,1,10,2,4,5,6,12,8,9,11]
[[[],[]],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[[],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,7,1,9,2,4,5,6,10,11,8,12]
[[[],[]],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,6,1,10,2,4,5,7,8,12,9,11]
[[[],[]],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[3,6,1,9,2,4,5,7,8,10,12,11]
[[[],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,7,1,8,10,2,11,3,4,6,9,12]
[[[],[[],[]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,7,1,9,10,2,11,3,5,6,8,12]
[[[],[[],[]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,6,1,7,10,2,12,3,5,8,9,11]
[[[],[[],[]]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[[],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,7,1,9,10,2,12,4,5,6,8,11]
[[[],[[],[]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[],[]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,6,1,9,11,2,12,4,5,7,8,10]
[[[[],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,7,8,1,10,2,3,11,4,6,9,12]
[[[[],[]],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,7,9,1,10,2,3,11,5,6,8,12]
[[[[],[]],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,6,7,1,10,2,3,12,5,8,9,11]
[[[[],[]],[]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[],[[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,7,9,1,10,2,4,12,5,6,8,11]
[[[[],[]],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[[],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,6,9,1,11,2,4,12,5,7,8,10]
[[[],[[],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,9,2,10,11,3,12,5,8]
[[[],[[],[[],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[]],[]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,8,9,2,10,11,4,12,5,7]
[[[],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,7,9,10,2,11,3,5,12,8]
[[[],[[[],[]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,8,9,10,2,11,4,5,12,7]
[[[[],[]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,6,7,1,9,2,3,10,11,5,12,8]
[[[[],[]],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,6,8,1,9,2,4,10,11,5,12,7]
[[[[],[[],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[]],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,9,10,2,11,3,5,8,12]
[[[[],[[],[]]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[[],[]],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,8,1,9,10,2,11,4,5,7,12]
[[[[[],[]],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[[],[]]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,7,9,1,10,2,3,11,5,8,12]
[[[[[],[]],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,6,8,9,1,10,2,4,11,5,7,12]
[[[],[[],[[],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,9,4,10,12,11]
[[[],[[],[[[],[]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[],[]]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,9,11,4,12,10]
[[[],[[[],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,11,4,9,10,12]
[[[],[[[],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,10,11,4,12,9]
[[[],[[[[],[]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[],[]]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[3,5,1,6,7,8,10,2,11,4,9,12]
[[[[],[]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8,11,9,10,12]
[[[[],[]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8,10,11,9,12]
[[[[],[[],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[]],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,10,2,12,4,8,9,11]
[[[[[],[]],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,10,2,4,12,8,9,11]
[[[[],[[],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,9,2,10,11,4,12,8]
[[[[],[[[],[]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[],[]]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[3,5,6,1,7,9,10,2,11,4,8,12]
[[[[[],[]],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[[],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,9,2,4,10,11,8,12]
[[[[[],[[],[]]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[[],[]],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,5,6,7,1,9,10,2,12,4,8,11]
[[[[[[],[]],[]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[],[[],[]]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,6,7,9,1,10,2,4,12,8,11]
[[[],[[],[[],[[],[[],[]]]]]],[]]=>[[],[[[[[[],[]],[]],[]],[]],[]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,9,5,6,11,7,8,12,10]
[[[],[[],[[],[[[],[]],[]]]]],[]]=>[[],[[[[[],[[],[]]],[]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,11,7,9,10,12]
[[[],[[],[[[],[]],[[],[]]]]],[]]=>[[],[[[[[],[]],[[],[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,10,11,7,12,9]
[[[],[[],[[[],[[],[]]],[]]]],[]]=>[[],[[[[],[[[],[]],[]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8,11,9,10,12]
[[[],[[],[[[[],[]],[]],[]]]],[]]=>[[],[[[[],[[],[[],[]]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6,8,10,11,9,12]
[[[],[[[],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,8,10,5,11,6,7,9,12]
[[[],[[[],[]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,7,10,5,12,6,8,9,11]
[[[],[[[],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,7,9,5,10,11,6,12,8]
[[[],[[[[],[]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[],[]]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,7,9,10,5,11,6,8,12]
[[[],[[[],[[],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8,11,9,10,12]
[[[],[[[],[[[],[]],[]]],[]]],[]]=>[[],[[[],[[[],[[],[]]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8,10,11,9,12]
[[[],[[[[],[]],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[[],[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,10,5,12,8,9,11]
[[[],[[[[],[[],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[]],[]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,9,5,10,11,8,12]
[[[],[[[[[],[]],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[[],[]]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,9,10,5,12,8,11]
[[[[],[]],[[],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[]],[[],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,8,1,10,4,5,6,11,7,9,12]
[[[[],[]],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[[],[]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,10,4,5,6,12,8,9,11]
[[[[],[]],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,7,1,9,4,5,6,10,11,8,12]
[[[[],[]],[[[],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,10,4,5,7,8,12,9,11]
[[[[],[]],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,9,4,5,7,8,10,12,11]
[[[[],[[],[]]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,7,1,9,10,4,12,5,6,8,11]
[[[[],[[],[]]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,1,9,11,4,12,5,7,8,10]
[[[[[],[]],[]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[],[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,7,9,1,10,4,5,12,6,8,11]
[[[[[],[]],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,6,9,1,11,4,5,12,7,8,10]
[[[[],[[],[[],[]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[],[]],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[2,3,6,1,8,9,4,10,11,5,12,7]
[[[[],[[[],[]],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[[],[]]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,6,1,8,9,10,4,11,5,7,12]
[[[[[],[]],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,6,8,1,9,4,5,10,11,7,12]
[[[[[],[[],[]]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[[],[]],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,6,8,1,9,10,4,12,5,7,11]
[[[[[[],[]],[]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[],[[],[]]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,6,8,9,1,10,4,5,12,7,11]
[[[[],[[],[[],[[],[]]]]],[]],[]]=>[[],[[],[[[[[],[]],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8,11,9,10,12]
[[[[],[[],[[[],[]],[]]]],[]],[]]=>[[],[[],[[[[],[[],[]]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8,10,11,9,12]
[[[[],[[[],[]],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,10,4,12,8,9,11]
[[[[],[[[],[[],[]]],[]]],[]],[]]=>[[],[[],[[[],[[[],[]],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,9,4,10,11,8,12]
[[[[],[[[[],[]],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[[],[]]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,9,10,4,12,8,11]
[[[[[],[]],[[],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,10,4,7,8,12,9,11]
[[[[[],[]],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,9,4,7,8,10,12,11]
[[[[[],[[],[]]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,9,11,4,12,7,8,10]
[[[[[[],[]],[]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,9,1,11,4,7,12,8,10]
[[[[[],[[],[[],[]]]],[]],[]],[]]=>[[],[[],[[],[[[[],[]],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,8,9,4,10,11,7,12]
[[[[[],[[[],[]],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[[],[]]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[2,3,5,6,1,8,9,10,4,12,7,11]
[[[[[[],[]],[[],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[]],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,8,1,9,4,7,10,12,11]
[[[[[[],[[],[]]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[[],[]],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[2,3,5,6,8,1,9,11,4,12,7,10]
[[[[[[[],[]],[]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[],[[],[]]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,3,5,6,8,9,1,11,4,7,12,10]
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 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
searching the database
Sorry, this map was not found in the database.