Identifier
Mp00328:
Ordered trees
—DeBruijn-Morselt plane tree automorphism⟶
Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Images
=>
Cc0021;cc-rep-0Cc0021;cc-rep-1Cc0021;cc-rep-2Cc0005;cc-rep-3
[]=>[]=>[]=>[]
[[]]=>[[]]=>[[]]=>[1,0]
[[],[]]=>[[[]]]=>[[[]]]=>[1,1,0,0]
[[[]]]=>[[],[]]=>[[],[]]=>[1,0,1,0]
[[],[],[]]=>[[[[]]]]=>[[[[]]]]=>[1,1,1,0,0,0]
[[],[[]]]=>[[[],[]]]=>[[[],[]]]=>[1,1,0,1,0,0]
[[[]],[]]=>[[],[[]]]=>[[[]],[]]=>[1,1,0,0,1,0]
[[[],[]]]=>[[[]],[]]=>[[],[[]]]=>[1,0,1,1,0,0]
[[[[]]]]=>[[],[],[]]=>[[],[],[]]=>[1,0,1,0,1,0]
[[],[],[],[]]=>[[[[[]]]]]=>[[[[[]]]]]=>[1,1,1,1,0,0,0,0]
[[],[],[[]]]=>[[[[],[]]]]=>[[[[],[]]]]=>[1,1,1,0,1,0,0,0]
[[],[[]],[]]=>[[[],[[]]]]=>[[[[]],[]]]=>[1,1,1,0,0,1,0,0]
[[],[[],[]]]=>[[[[]],[]]]=>[[[],[[]]]]=>[1,1,0,1,1,0,0,0]
[[],[[[]]]]=>[[[],[],[]]]=>[[[],[],[]]]=>[1,1,0,1,0,1,0,0]
[[[]],[],[]]=>[[],[[[]]]]=>[[[[]]],[]]=>[1,1,1,0,0,0,1,0]
[[[]],[[]]]=>[[],[[],[]]]=>[[[],[]],[]]=>[1,1,0,1,0,0,1,0]
[[[],[]],[]]=>[[[]],[[]]]=>[[[]],[[]]]=>[1,1,0,0,1,1,0,0]
[[[[]]],[]]=>[[],[],[[]]]=>[[[]],[],[]]=>[1,1,0,0,1,0,1,0]
[[[],[],[]]]=>[[[[]]],[]]=>[[],[[[]]]]=>[1,0,1,1,1,0,0,0]
[[[],[[]]]]=>[[[],[]],[]]=>[[],[[],[]]]=>[1,0,1,1,0,1,0,0]
[[[[]],[]]]=>[[],[[]],[]]=>[[],[[]],[]]=>[1,0,1,1,0,0,1,0]
[[[[],[]]]]=>[[[]],[],[]]=>[[],[],[[]]]=>[1,0,1,0,1,1,0,0]
[[[[[]]]]]=>[[],[],[],[]]=>[[],[],[],[]]=>[1,0,1,0,1,0,1,0]
[[],[],[],[],[]]=>[[[[[[]]]]]]=>[[[[[[]]]]]]=>[1,1,1,1,1,0,0,0,0,0]
[[],[],[],[[]]]=>[[[[[],[]]]]]=>[[[[[],[]]]]]=>[1,1,1,1,0,1,0,0,0,0]
[[],[],[[]],[]]=>[[[[],[[]]]]]=>[[[[[]],[]]]]=>[1,1,1,1,0,0,1,0,0,0]
[[],[],[[],[]]]=>[[[[[]],[]]]]=>[[[[],[[]]]]]=>[1,1,1,0,1,1,0,0,0,0]
[[],[],[[[]]]]=>[[[[],[],[]]]]=>[[[[],[],[]]]]=>[1,1,1,0,1,0,1,0,0,0]
[[],[[]],[],[]]=>[[[],[[[]]]]]=>[[[[[]]],[]]]=>[1,1,1,1,0,0,0,1,0,0]
[[],[[]],[[]]]=>[[[],[[],[]]]]=>[[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0]
[[],[[],[]],[]]=>[[[[]],[[]]]]=>[[[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,0]
[[],[[[]]],[]]=>[[[],[],[[]]]]=>[[[[]],[],[]]]=>[1,1,1,0,0,1,0,1,0,0]
[[],[[],[],[]]]=>[[[[[]]],[]]]=>[[[],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,0]
[[],[[],[[]]]]=>[[[[],[]],[]]]=>[[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0]
[[],[[[]],[]]]=>[[[],[[]],[]]]=>[[[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,0]
[[],[[[],[]]]]=>[[[[]],[],[]]]=>[[[],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,0]
[[],[[[[]]]]]=>[[[],[],[],[]]]=>[[[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[]]=>[[],[[[[]]]]]=>[[[[[]]]],[]]=>[1,1,1,1,0,0,0,0,1,0]
[[[]],[],[[]]]=>[[],[[[],[]]]]=>[[[[],[]]],[]]=>[1,1,1,0,1,0,0,0,1,0]
[[[]],[[]],[]]=>[[],[[],[[]]]]=>[[[[]],[]],[]]=>[1,1,1,0,0,1,0,0,1,0]
[[[]],[[],[]]]=>[[],[[[]],[]]]=>[[[],[[]]],[]]=>[1,1,0,1,1,0,0,0,1,0]
[[[]],[[[]]]]=>[[],[[],[],[]]]=>[[[],[],[]],[]]=>[1,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[]]=>[[[]],[[[]]]]=>[[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,0,0]
[[[[]]],[],[]]=>[[],[],[[[]]]]=>[[[[]]],[],[]]=>[1,1,1,0,0,0,1,0,1,0]
[[[],[]],[[]]]=>[[[]],[[],[]]]=>[[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0]
[[[[]]],[[]]]=>[[],[],[[],[]]]=>[[[],[]],[],[]]=>[1,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[]]=>[[[[]]],[[]]]=>[[[]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[]]=>[[[],[]],[[]]]=>[[[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[]]=>[[],[[]],[[]]]=>[[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[]]=>[[[]],[],[[]]]=>[[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[]]=>[[],[],[],[[]]]=>[[[]],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]]]=>[[[[[]]]],[]]=>[[],[[[[]]]]]=>[1,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]]]=>[[[[],[]]],[]]=>[[],[[[],[]]]]=>[1,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]]]=>[[[],[[]]],[]]=>[[],[[[]],[]]]=>[1,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]]]=>[[[[]],[]],[]]=>[[],[[],[[]]]]=>[1,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]]]=>[[[],[],[]],[]]=>[[],[[],[],[]]]=>[1,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]]]=>[[],[[[]]],[]]=>[[],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]]]=>[[],[[],[]],[]]=>[[],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]]]=>[[[]],[[]],[]]=>[[],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]]]=>[[],[],[[]],[]]=>[[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]]]=>[[[[]]],[],[]]=>[[],[],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]]]=>[[[],[]],[],[]]=>[[],[],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]]]=>[[],[[]],[],[]]=>[[],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]]]=>[[[]],[],[],[]]=>[[],[],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]]]=>[[],[],[],[],[]]=>[[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[]]=>[[[[[[[]]]]]]]=>[[[[[[[]]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[]]]=>[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[],[],[],[[]],[]]=>[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[],[],[],[[],[]]]=>[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[]]]]=>[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[],[],[[]],[],[]]=>[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[]]]=>[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[[],[],[[],[]],[]]=>[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[]]=>[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[[],[],[[],[],[]]]=>[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]]]=>[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]]]=>[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]]]=>[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]]]=>[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[[],[[]],[],[],[]]=>[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[]]]=>[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[]],[]]=>[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[],[]]]=>[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]]]=>[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[[],[[],[]],[],[]]=>[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[]]=>[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[[]]]=>[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]]]=>[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[[],[[],[],[]],[]]=>[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[]]=>[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[]]=>[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[]]=>[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[]]=>[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]]]=>[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]]]=>[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]]]=>[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]]]=>[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]]]=>[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]]]=>[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]]]=>[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]]]=>[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]]]=>[[[],[],[[]],[]]]=>[[[],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]]]=>[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]]]=>[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]]]=>[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]]]=>[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]]]=>[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[],[]]=>[[],[[[[[]]]]]]=>[[[[[[]]]]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[]]]=>[[],[[[[],[]]]]]=>[[[[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[]],[]]=>[[],[[[],[[]]]]]=>[[[[[]],[]]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[],[]]]=>[[],[[[[]],[]]]]=>[[[[],[[]]]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[]]]]=>[[],[[[],[],[]]]]=>[[[[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[]],[],[]]=>[[],[[],[[[]]]]]=>[[[[[]]],[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[]]]=>[[],[[],[[],[]]]]=>[[[[],[]],[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[],[]],[]]=>[[],[[[]],[[]]]]=>[[[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[]]=>[[],[[],[],[[]]]]=>[[[[]],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]]]=>[[],[[[[]]],[]]]=>[[[],[[[]]]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]]]=>[[],[[[],[]],[]]]=>[[[],[[],[]]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]]]=>[[],[[],[[]],[]]]=>[[[],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]]]=>[[],[[[]],[],[]]]=>[[[],[],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]]]=>[[],[[],[],[],[]]]=>[[[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[],[]]=>[[[]],[[[[]]]]]=>[[[[[]]]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[]]=>[[],[],[[[[]]]]]=>[[[[[]]]],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[[]]]=>[[[]],[[[],[]]]]=>[[[[],[]]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]]]=>[[],[],[[[],[]]]]=>[[[[],[]]],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[[]],[]]=>[[[]],[[],[[]]]]=>[[[[]],[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[]]=>[[],[],[[],[[]]]]=>[[[[]],[]],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]]]=>[[[]],[[[]],[]]]=>[[[],[[]]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]]]=>[[[]],[[],[],[]]]=>[[[],[],[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]]]=>[[],[],[[[]],[]]]=>[[[],[[]]],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]]]=>[[],[],[[],[],[]]]=>[[[],[],[]],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[],[]]=>[[[[]]],[[[]]]]=>[[[[]]],[[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[]]=>[[[],[]],[[[]]]]=>[[[[]]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[]]=>[[],[[]],[[[]]]]=>[[[[]]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[]]=>[[[]],[],[[[]]]]=>[[[[]]],[],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[]]=>[[],[],[],[[[]]]]=>[[[[]]],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]]]=>[[[[]]],[[],[]]]=>[[[],[]],[[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]]]=>[[[],[]],[[],[]]]=>[[[],[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]]]=>[[],[[]],[[],[]]]=>[[[],[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]]]=>[[[]],[],[[],[]]]=>[[[],[]],[],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]]]=>[[],[],[],[[],[]]]=>[[[],[]],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[]]=>[[[[[]]]],[[]]]=>[[[]],[[[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[]]=>[[[[],[]]],[[]]]=>[[[]],[[[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[]]=>[[[],[[]]],[[]]]=>[[[]],[[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[]]=>[[[[]],[]],[[]]]=>[[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[]]=>[[[],[],[]],[[]]]=>[[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[]]=>[[],[[[]]],[[]]]=>[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[]]=>[[],[[],[]],[[]]]=>[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[]]=>[[[]],[[]],[[]]]=>[[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[]]=>[[],[],[[]],[[]]]=>[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[]]=>[[[[]]],[],[[]]]=>[[[]],[],[[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[]]=>[[[],[]],[],[[]]]=>[[[]],[],[[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[]]=>[[],[[]],[],[[]]]=>[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[]]=>[[[]],[],[],[[]]]=>[[[]],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[]]=>[[],[],[],[],[[]]]=>[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]]]=>[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]]]=>[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]]]=>[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]]]=>[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]]]=>[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]]]=>[[[],[[[]]]],[]]=>[[],[[[[]]],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]]]=>[[[],[[],[]]],[]]=>[[],[[[],[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]]]=>[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]]]=>[[[],[],[[]]],[]]=>[[],[[[]],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]]]=>[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]]]=>[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]]]=>[[[],[[]],[]],[]]=>[[],[[],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]]]=>[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]]]=>[[[],[],[],[]],[]]=>[[],[[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]]]=>[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]]]=>[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]]]=>[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]]]=>[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]]]=>[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]]]=>[[[]],[[[]]],[]]=>[[],[[[]]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]]]=>[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[]],[[]]]]=>[[[]],[[],[]],[]]=>[[],[[],[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[]]]]=>[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]]]=>[[[[]]],[[]],[]]=>[[],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[]]]=>[[[],[]],[[]],[]]=>[[],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[]]]=>[[],[[]],[[]],[]]=>[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]]]=>[[[]],[],[[]],[]]=>[[],[[]],[],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]]]=>[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]]]=>[[[[[]]]],[],[]]=>[[],[],[[[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]]]=>[[[[],[]]],[],[]]=>[[],[],[[[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]]]=>[[[],[[]]],[],[]]=>[[],[],[[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]]]=>[[[[]],[]],[],[]]=>[[],[],[[],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]]]=>[[[],[],[]],[],[]]=>[[],[],[[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]]]=>[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]]]=>[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]]]=>[[[]],[[]],[],[]]=>[[],[],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]]]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]]]=>[[[[]]],[],[],[]]=>[[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]]]=>[[[],[]],[],[],[]]=>[[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]]]]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]]]=>[[[]],[],[],[],[]]=>[[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]]]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[]]=>[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[]]]=>[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[],[],[],[],[[]],[]]=>[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[],[],[],[[],[]]]=>[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[],[],[],[[[]]]]=>[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[],[],[],[[]],[],[]]=>[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[[]]]=>[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[],[],[[],[]],[]]=>[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[],[],[[[]]],[]]=>[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[],[],[[],[],[]]]=>[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[],[[],[[]]]]=>[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[],[],[[[]],[]]]=>[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[],[],[],[[[],[]]]]=>[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[[]]]]]=>[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[],[],[[]],[],[],[]]=>[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[[]]]=>[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[[]],[]]=>[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[],[]]]=>[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[]]]]=>[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[],[],[[],[]],[],[]]=>[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[],[]]=>[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[[]]]=>[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[[]]]=>[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[],[],[[],[],[]],[]]=>[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[]]=>[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]],[]]=>[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]],[]]=>[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]],[]]=>[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[],[]]]=>[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[[],[],[[]]]]=>[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[],[],[[],[[]],[]]]=>[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[],[],[[],[[],[]]]]=>[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[],[[],[[[]]]]]=>[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[],[],[[[]],[],[]]]=>[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[]]]]=>[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[],[],[[[],[]],[]]]=>[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[]]]=>[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[],[],[[[],[],[]]]]=>[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[],[[]]]]]=>[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]]]]=>[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[]]]]]]=>[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[],[[]],[],[],[],[]]=>[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[[]]]=>[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[[]],[]]=>[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[],[]]]=>[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[]]]]=>[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[[]],[],[]]=>[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[]]]=>[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[],[]],[]]=>[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]],[]]=>[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[],[]]]=>[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[]]]]=>[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[]],[]]]=>[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[],[]]]]=>[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[]]]]]=>[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[],[[],[]],[],[],[]]=>[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[],[]]=>[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[[]]]=>[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[[]]]=>[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[[]],[]]=>[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]],[]]=>[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[],[]]]=>[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[]]]]=>[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[]]]=>[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[]]]]=>[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[],[[],[],[]],[],[]]=>[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[],[]]=>[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[],[]]=>[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[],[]]=>[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[],[]]=>[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[[]]]=>[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[[]]]=>[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[[]]]=>[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[[]]]=>[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[]]]=>[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]],[]]=>[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]],[]]=>[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]],[]]=>[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]],[]]=>[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[]]=>[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]],[]]=>[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]],[]]=>[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]],[]]=>[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[]]=>[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]],[]]=>[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]],[]]=>[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]],[]]=>[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]],[]]=>[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[]]=>[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[]]]=>[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[],[],[],[[]]]]=>[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[],[],[[]],[]]]=>[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[],[],[[],[]]]]=>[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[],[],[[[]]]]]=>[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[],[[]],[],[]]]=>[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[]]]]=>[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[],[[],[]],[]]]=>[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[]]]=>[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[],[]]]]=>[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[],[[],[[]]]]]=>[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[],[[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]]]]=>[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[]]]]]]=>[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[]],[],[],[]]]=>[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[]]]]=>[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[]],[]]]=>[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[],[]]]]=>[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[]]]]]=>[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[]],[],[]]]=>[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[],[[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]]]]=>[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[],[]],[]]]=>[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[]]]=>[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[]]]=>[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[]]]=>[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[]]]=>[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[]]]]=>[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]]]]=>[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[],[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]]]]=>[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[[]]]]]]=>[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[]]]]=>[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[[]],[[]]]]]=>[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]]]]=>[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[]]]]=>[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]]]]]=>[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]]]]=>[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]]]]]=>[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]]]]]=>[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]]]]=>[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[],[],[]]=>[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[[]]]=>[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[[]],[]]=>[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[],[]]]=>[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[]]]]=>[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[[]],[],[]]=>[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[]]]=>[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[],[]],[]]=>[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[]]],[]]=>[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[],[[],[],[]]]=>[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[]]]]=>[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[]],[]]]=>[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[],[]]]]=>[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[]]]]]=>[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[[]],[],[],[]]=>[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[]]]=>[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[]],[]]=>[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[],[]]]=>[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[]]]]=>[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[],[]],[],[]]=>[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[],[]]=>[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[[],[]],[[]]]=>[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[[]]]=>[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]],[]]=>[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]],[]]=>[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[]]=>[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]],[]]=>[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[],[]]]=>[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[]]]]=>[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[]],[]]]=>[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[],[]]]]=>[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[]]]]]=>[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[]],[],[]]]=>[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[]]]]=>[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[],[]],[]]]=>[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[]]]=>[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[]]]]=>[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[],[[]]]]]=>[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[]]]]=>[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]]]]]=>[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]]]]]=>[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[],[],[]]=>[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[],[]]=>[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[[]]]=>[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[[]]]=>[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[[]],[]]=>[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]],[]]=>[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[],[]]]=>[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[]]]]=>[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[],[]]]=>[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[]]]]=>[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[[]],[],[]]=>[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[],[]]=>[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[[]]]=>[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[[]]]=>[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]],[]]=>[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]],[]]=>[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]],[]]=>[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]],[]]=>[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[],[]]]=>[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[]]]]=>[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[]],[]]]=>[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[]]]]=>[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]]]]]=>[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[],[]]]=>[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[]]]]=>[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[]],[]]]=>[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[]]]]=>[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]]]]]=>[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[],[],[]]=>[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[],[]]=>[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[],[]]=>[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[],[]]=>[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[]]]=>[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[[]]]=>[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[[]]]=>[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[]]]=>[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]],[]]=>[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]],[]]=>[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[]]=>[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]],[]]=>[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[],[]]]=>[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]]]]=>[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[],[]]]=>[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[]]]]=>[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[],[]]]=>[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[]]]]=>[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[],[]]]=>[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[]]]]=>[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[]]=>[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[],[]]=>[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[],[]]=>[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[],[]]=>[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[],[]]=>[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[],[]]=>[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[],[]]=>[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[],[]]=>[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[],[]]=>[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[]]=>[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[],[]]=>[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[],[]]=>[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[],[]]=>[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[]]=>[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[[]]]=>[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[[]]]=>[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[[]]]=>[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[[]]]=>[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[[]]]=>[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[[]]]=>[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[[]]]=>[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[[]]]=>[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[[]]]=>[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[[]]]=>[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[[]]]=>[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[[]]]=>[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[[]]]=>[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[[]]]=>[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]],[]]=>[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]],[]]=>[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]],[]]=>[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]],[]]=>[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]],[]]=>[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]],[]]=>[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]],[]]=>[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]],[]]=>[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]],[]]=>[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]],[]]=>[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]],[]]=>[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]],[]]=>[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[]]=>[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]],[]]=>[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]],[]]=>[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]],[]]=>[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[]]=>[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]],[]]=>[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]],[]]=>[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]],[]]=>[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[]],[[]]],[]]=>[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[]]],[]]=>[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]],[]]=>[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[]],[]]=>[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[]],[]]=>[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]],[]]=>[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]],[]]=>[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]],[]]=>[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]],[]]=>[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]],[]]=>[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]],[]]=>[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]],[]]=>[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]],[]]=>[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]],[]]=>[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]],[]]=>[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]],[]]=>[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]],[]]=>[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]],[]]=>[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]]],[]]=>[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]],[]]=>[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]],[]]=>[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[],[]]]=>[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[],[],[],[],[[]]]]=>[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[],[],[],[[]],[]]]=>[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[],[],[],[[],[]]]]=>[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[],[],[],[[[]]]]]=>[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[]],[],[]]]=>[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[]]]]=>[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[],[]],[]]]=>[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[]]]=>[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[],[],[]]]]=>[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[],[[]]]]]=>[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]]]]=>[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[]]]]]]=>[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[]],[],[],[]]]=>[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[]]]]=>[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[]],[]]]=>[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[],[]]]]=>[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[]]]]]=>[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[]],[],[]]]=>[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[],[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[]]]]=>[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[],[]],[]]]=>[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[]]]=>[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[]]]=>[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[]]]=>[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[]]]=>[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[]]]]=>[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]]]]=>[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[],[[],[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]]]]=>[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[[]]]]]]=>[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[]]]]=>[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[[]],[[]]]]]=>[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]]]]=>[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[]]]]=>[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]]]]]=>[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]]]]=>[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]]]]]=>[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]]]]]=>[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]]]]=>[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[]]]=>[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]]]]=>[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[]]]=>[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[],[]]]]=>[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[]]]]]=>[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[]]]=>[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[]]]]=>[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[],[]],[]]]=>[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[]]]=>[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[]]]]=>[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[],[[]]]]]=>[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[]]]]=>[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]]]]]=>[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]]]]]=>[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[],[]]]=>[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[]]]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[[]]]]=>[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[]]]]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[],[]],[[]],[]]]=>[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[]]]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[]]]]=>[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]]]]]=>[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[]]]]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]]]]]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[],[]]]=>[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[]]]=>[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[]]]=>[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[]]]=>[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[]]]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[]]]]=>[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[]]]]=>[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[]]]]=>[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[]]]]=>[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[]]]]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]],[]]]=>[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[]]]=>[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[]]]=>[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[]]]=>[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[]]]=>[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[]]]=>[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[]]]=>[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[]]]=>[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[]]]=>[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[]]]=>[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]],[]]]=>[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]],[]]]=>[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[]]]=>[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[]]]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[]]]]=>[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[],[],[],[[]]]]]=>[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[],[],[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]]]]=>[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[],[],[[[]]]]]]=>[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[]]]]=>[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[[]]]]]=>[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[]]]]=>[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[]]]]=>[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]]]]]=>[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]]]]=>[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]]]]]=>[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]]]]]=>[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]]]]=>[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]]]]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[]],[],[[]]]]]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[]]]]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]]]]]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]]]]]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[]]]]=>[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[]]]]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]]]]]=>[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[]]]]]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[]]]]=>[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[]]]]=>[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[]]]]=>[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[]]]]=>[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[]]]]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]]]]]=>[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]]]]]=>[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]]]]]=>[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]]]]]=>[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]]]]]=>[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]]]]]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]]]]]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]]]]]=>[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]]]]]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]]]]]=>[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[],[[]]]]]]]=>[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[]],[]]]]]]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[],[]]]]]]]=>[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]]]]]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[],[]]=>[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[],[],[],[],[],[],[[]]]=>[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[]],[]]=>[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[],[],[],[],[],[[],[]]]=>[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[[]]]]=>[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[],[],[],[],[[]],[],[]]=>[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[],[],[],[],[[]],[[]]]=>[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[],[],[],[],[[],[]],[]]=>[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[],[],[],[],[[[]]],[]]=>[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[],[],[],[],[[],[],[]]]=>[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[[],[[]]]]=>[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[],[],[],[],[[[]],[]]]=>[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[],[],[],[],[[[],[]]]]=>[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[],[],[],[],[[[[]]]]]=>[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[],[],[],[[]],[],[],[]]=>[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[],[[]]]=>[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[[]],[]]=>[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[],[],[],[[]],[[],[]]]=>[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[[[]]]]=>[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[],[],[],[[],[]],[],[]]=>[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[],[],[],[[[]]],[],[]]=>[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[],[],[],[[],[]],[[]]]=>[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[[],[],[],[[[]]],[[]]]=>[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[],[],[],[[],[],[]],[]]=>[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[],[],[],[[],[[]]],[]]=>[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[],[],[],[[[]],[]],[]]=>[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[[],[],[],[[[],[]]],[]]=>[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[[]]]],[]]=>[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[[],[],[],[[],[],[],[]]]=>[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[[],[],[[]]]]=>[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[],[],[],[[],[[]],[]]]=>[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[],[],[],[[],[[],[]]]]=>[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[],[],[],[[],[[[]]]]]=>[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[],[],[],[[[]],[],[]]]=>[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[],[],[],[[[]],[[]]]]=>[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[],[],[],[[[],[]],[]]]=>[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[],[],[],[[[[]]],[]]]=>[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[[],[],[],[[[],[],[]]]]=>[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[],[[[],[[]]]]]=>[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[],[],[],[[[[]],[]]]]=>[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[[],[],[],[[[[],[]]]]]=>[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[],[],[],[[[[[]]]]]]=>[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[],[],[[]],[],[],[],[]]=>[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[],[[]]]=>[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[[]],[]]=>[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[],[[],[]]]=>[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[],[[[]]]]=>[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[[]],[],[]]=>[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[]],[[]]]=>[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[],[]],[]]=>[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[]]],[]]=>[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[],[],[[]],[[],[],[]]]=>[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[],[],[[]],[[],[[]]]]=>[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[]],[]]]=>[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[[],[]]]]=>[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[[[]]]]]=>[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[],[],[[],[]],[],[],[]]=>[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[],[],[]]=>[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[],[[]]]=>[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[],[[]]]=>[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[[]],[]]=>[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[[]],[]]=>[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[[],[]]]=>[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[],[],[[],[]],[[[]]]]=>[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[[],[]]]=>[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[[],[],[[[]]],[[[]]]]=>[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[[],[],[[],[],[]],[],[]]=>[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[],[]]=>[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]],[],[]]=>[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]],[],[]]=>[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]],[],[]]=>[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[]],[[]]]=>[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[[]]]=>[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[]],[]],[[]]]=>[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[]]],[[]]]=>[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]],[[]]]=>[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[],[]],[]]=>[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[[],[],[[]]],[]]=>[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[],[],[[],[[]],[]],[]]=>[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[[],[],[[],[[],[]]],[]]=>[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[],[],[[],[[[]]]],[]]=>[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[[],[],[[[]],[],[]],[]]=>[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[]]],[]]=>[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[[],[],[[[],[]],[]],[]]=>[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[]],[]]=>[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[[],[],[[[],[],[]]],[]]=>[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[],[[]]]],[]]=>[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[[]],[]]],[]]=>[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]]],[]]=>[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[]]]]],[]]=>[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[],[],[]]]=>[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[[],[],[],[[]]]]=>[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[[],[],[[],[],[[]],[]]]=>[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[],[[],[],[[],[]]]]=>[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[],[[],[],[[[]]]]]=>[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[],[],[[],[[]],[],[]]]=>[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[],[[],[[]],[[]]]]=>[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[],[[],[[],[]],[]]]=>[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[],[[],[[[]]],[]]]=>[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[],[[],[[],[],[]]]]=>[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[],[[],[[],[[]]]]]=>[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[],[[],[[[]],[]]]]=>[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[],[],[[],[[[],[]]]]]=>[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[],[[],[[[[]]]]]]=>[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[],[],[[[]],[],[],[]]]=>[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[],[[[]],[],[[]]]]=>[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[]],[]]]=>[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[],[[[]],[[],[]]]]=>[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[],[],[[[]],[[[]]]]]=>[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[],[],[[[],[]],[],[]]]=>[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[],[]]]=>[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[],[],[[[],[]],[[]]]]=>[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[],[[[[]]],[[]]]]=>[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[],[],[[[],[],[]],[]]]=>[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[],[[[],[[]]],[]]]=>[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[[]],[]],[]]]=>[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]],[]]]=>[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[]]]],[]]]=>[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[],[[[],[],[],[]]]]=>[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[],[[[],[],[[]]]]]=>[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[],[],[[[],[[]],[]]]]=>[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[],[],[[[],[[],[]]]]]=>[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[],[[[],[[[]]]]]]=>[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[],[],[[[[]],[],[]]]]=>[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[],[],[[[[]],[[]]]]]=>[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[],[],[[[[],[]],[]]]]=>[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[[[]]],[]]]]=>[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[],[],[[[[],[],[]]]]]=>[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[[],[[]]]]]]=>[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[[[]],[]]]]]=>[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[[[],[]]]]]]=>[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[[[[]]]]]]]=>[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[],[[]],[],[],[],[],[]]=>[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[],[[]]]=>[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[[]],[]]=>[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[],[[],[]]]=>[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[],[[[]]]]=>[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[[]],[],[]]=>[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[]],[[]]]=>[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[],[]],[]]=>[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[]]],[]]=>[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[],[[],[],[]]]=>[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[],[[],[[]]]]=>[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[]],[]]]=>[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[[],[]]]]=>[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[],[[[[]]]]]=>[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[[]],[],[],[]]=>[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[],[[]]]=>[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[]],[]]=>[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[],[]]]=>[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[[]]]]=>[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[],[]],[],[]]=>[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]],[],[]]=>[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[]],[[]]]=>[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[]]],[[]]]=>[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[],[]],[]]=>[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[]]],[]]=>[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[]],[]],[]]=>[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[],[]]],[]]=>[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[]]]],[]]=>[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[[],[[]],[[],[],[],[]]]=>[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[[]],[[],[],[[]]]]=>[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[]],[]]]=>[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[[],[[],[]]]]=>[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[],[[]],[[],[[[]]]]]=>[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[]],[],[]]]=>[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[[]],[[[]],[[]]]]=>[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[],[]],[]]]=>[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[]]],[]]]=>[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[]],[[[],[],[]]]]=>[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[],[[]],[[[],[[]]]]]=>[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[[],[[]],[[[[]],[]]]]=>[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[[[],[]]]]]=>[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[],[[]],[[[[[]]]]]]=>[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[[],[[],[]],[],[],[],[]]=>[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[],[],[]]=>[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[],[[]]]=>[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[],[[]]]=>[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[[]],[]]=>[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[[]],[]]=>[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[],[[],[]]]=>[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[]],[],[[[]]]]=>[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[]]],[],[[],[]]]=>[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[[],[[[]]],[],[[[]]]]=>[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[[],[[],[]],[[]],[],[]]=>[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]],[],[]]=>[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[]],[[]]]=>[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[]],[[]]]=>[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[],[]],[]]=>[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[]]],[]]=>[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[]],[]]=>[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[]]],[]]=>[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[],[],[]]]=>[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[],[]],[[],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[]],[]]]=>[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[],[]],[[[],[]]]]=>[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[[]]]]]=>[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[[[]]],[[],[[]]]]=>[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[]],[]]]=>[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[[]]],[[[],[]]]]=>[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[[[]]]]]=>[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[[],[[],[],[]],[],[],[]]=>[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[],[],[]]=>[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[],[],[]]=>[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[],[],[]]=>[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[],[],[]]=>[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[],[[]]]=>[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[],[[]]]=>[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[],[[]]]=>[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[],[[]]]=>[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[],[[]]]=>[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[[]],[]]=>[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[[]],[]]=>[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[[]],[]]=>[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[[]],[]]=>[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[]],[]]=>[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[]],[[],[]]]=>[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[[],[],[]],[[[]]]]=>[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[[],[]]]=>[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[[],[[]]],[[[]]]]=>[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[]],[[],[]]]=>[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[]],[]],[[[]]]]=>[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[],[]]],[[],[]]]=>[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[]]],[[[]]]]=>[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[[],[]]]=>[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[[[[]]]],[[[]]]]=>[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]],[],[]]=>[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]],[],[]]=>[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]],[],[]]=>[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]],[],[]]=>[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[],[]]=>[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]],[],[]]=>[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]],[],[]]=>[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]],[],[]]=>[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[],[]]=>[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]],[],[]]=>[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]],[],[]]=>[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]],[],[]]=>[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]],[],[]]=>[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[],[]]=>[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]],[[]]]=>[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]],[[]]]=>[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[]],[]],[[]]]=>[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]],[[]]]=>[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[[]]]=>[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[],[]],[[]]]=>[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[]]],[[]]]=>[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]],[[]]]=>[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[]]],[]],[[]]]=>[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[],[],[]]],[[]]]=>[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]],[[]]]=>[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[]],[]]],[[]]]=>[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[],[]]]],[[]]]=>[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[[]]]=>[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[]],[]]=>[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[],[],[],[[]]],[]]=>[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[],[],[[]],[]],[]]=>[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[],[],[[],[]]],[]]=>[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[],[],[[[]]]],[]]=>[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[],[[]],[],[]],[]]=>[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[]]],[]]=>[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[],[[],[]],[]],[]]=>[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[]],[]]=>[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[],[]]],[]]=>[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[],[[],[[]]]],[]]=>[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[],[[[]],[]]],[]]=>[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]]],[]]=>[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[]]]]],[]]=>[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[]],[],[],[]],[]]=>[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[]]],[]]=>[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[]],[]],[]]=>[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[],[]]],[]]=>[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[]]]],[]]=>[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[]],[],[]],[]]=>[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[]],[]]=>[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[[],[[[],[]],[[]]],[]]=>[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]]],[]]=>[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[],[]],[]],[]]=>[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[]],[]]=>[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[]],[]]=>[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[]],[]]=>[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[]],[]]=>[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[]]],[]]=>[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]]],[]]=>[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[],[[]],[]]],[]]=>[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]]],[]]=>[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[[]]]]],[]]=>[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[]]],[]]=>[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[[]],[[]]]],[]]=>[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]]],[]]=>[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[]]],[]]=>[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]]]],[]]=>[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]]],[]]=>[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]]]],[]]=>[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]]]],[]]=>[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]]],[]]=>[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[],[]]]=>[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[[],[],[],[],[[]]]]=>[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[],[[],[],[],[[]],[]]]=>[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[[],[],[],[[],[]]]]=>[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[[],[],[],[[[]]]]]=>[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[],[[],[],[[]],[],[]]]=>[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[[],[],[[]],[[]]]]=>[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[[],[],[[],[]],[]]]=>[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[],[],[[[]]],[]]]=>[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[[],[],[[],[],[]]]]=>[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[[],[],[[],[[]]]]]=>[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[[],[],[[[]],[]]]]=>[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[],[[],[],[[[],[]]]]]=>[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[[],[],[[[[]]]]]]=>[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[],[[],[[]],[],[],[]]]=>[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[[],[[]],[],[[]]]]=>[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[]],[]]]=>[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[[],[[]],[[],[]]]]=>[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[],[[],[[]],[[[]]]]]=>[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[],[[],[[],[]],[],[]]]=>[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[],[]]]=>[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[],[[],[[],[]],[[]]]]=>[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[[]]]]=>[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[],[]],[]]]=>[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[[],[[],[[]]],[]]]=>[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[[],[[[]],[]],[]]]=>[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]],[]]]=>[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[]]]],[]]]=>[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[[],[[],[],[],[]]]]=>[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[[],[[],[],[[]]]]]=>[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[],[[],[[],[[]],[]]]]=>[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[],[[],[[],[[],[]]]]]=>[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[],[[],[[[]]]]]]=>[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[],[[],[[[]],[],[]]]]=>[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[[]],[[]]]]]=>[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[],[[],[[[],[]],[]]]]=>[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[[]]],[]]]]=>[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[[],[],[]]]]]=>[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[[],[[[],[[]]]]]]=>[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[],[[],[[[[]],[]]]]]=>[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[],[[],[[[[],[]]]]]]=>[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[[],[[[[[]]]]]]]=>[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[],[[[]],[],[],[],[]]]=>[[[],[[[[[]]]]],[]]]=>[[[],[[[[[]]]]],[]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[[[]],[],[],[[]]]]=>[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[]],[]]]=>[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[[]],[],[[],[]]]]=>[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[],[[[]],[],[[[]]]]]=>[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[]],[],[]]]=>[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[[[]],[[]],[[]]]]=>[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[],[]],[]]]=>[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[]]],[]]]=>[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[[]],[[],[],[]]]]=>[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[],[[[]],[[],[[]]]]]=>[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[[]],[]]]]=>[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[],[[[]],[[[],[]]]]]=>[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[],[[[]],[[[[]]]]]]=>[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[]],[],[],[]]]=>[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[[[],[]],[],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[[]]],[],[[]]]]=>[[[],[],[[[],[]]],[]]]=>[[[],[[[],[]]],[],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[],[[[],[]],[[]],[]]]=>[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]],[]]]=>[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[[],[]],[[],[]]]]=>[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[[],[]],[[[]]]]]=>[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[],[]]]]=>[[[],[],[[[]],[]],[]]]=>[[[],[[],[[]]],[],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[[]]],[[[]]]]]=>[[[],[],[[],[],[]],[]]]=>[[[],[[],[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[],[]],[],[]]]=>[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[],[]]]=>[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[],[]]]=>[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[],[]]]=>[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[]],[[]]]]=>[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[[]]]]=>[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[[]],[]],[[]]]]=>[[[],[[]],[[],[]],[]]]=>[[[],[[],[]],[[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[[],[]]],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[[]]]]=>[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[]],[]]]=>[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]],[]]]=>[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[[],[[]],[]],[]]]=>[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]],[]]]=>[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[[]]]],[]]]=>[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[]],[]]]=>[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[[]],[[]]],[]]]=>[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]],[]]]=>[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[]],[]]]=>[[[],[],[[]],[[]],[]]]=>[[[],[[]],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]]],[]]]=>[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]],[]]]=>[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]]],[]]]=>[[[],[[]],[],[[]],[]]]=>[[[],[[]],[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]]],[]]]=>[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]],[]]]=>[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[],[]]]]=>[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[[],[],[],[[]]]]]=>[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[[],[],[[]],[]]]]=>[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[[],[],[[],[]]]]]=>[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[[],[],[[[]]]]]]=>[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[[],[[]],[],[]]]]=>[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[[],[[]],[[]]]]]=>[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[],[[],[]],[]]]]=>[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[],[[[]]],[]]]]=>[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[[],[[],[],[]]]]]=>[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[[],[[],[[]]]]]]=>[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[],[[[]],[]]]]]=>[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[[],[[[],[]]]]]]=>[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[],[[[[]]]]]]]=>[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[],[]]]]=>[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[[]],[],[[]]]]]=>[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[[]],[[]],[]]]]=>[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[[]],[[],[]]]]]=>[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[[]],[[[]]]]]]=>[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[],[]]]]=>[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[[[]]],[],[]]]]=>[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[],[[[[],[]],[[]]]]]=>[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[[[]]],[[]]]]]=>[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[[],[],[]],[]]]]=>[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]],[]]]]=>[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[[[]],[]],[]]]]=>[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[[[],[]]],[]]]]=>[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]],[]]]]=>[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[[],[],[],[]]]]]=>[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[[],[],[[]]]]]]=>[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[[],[[]],[]]]]]=>[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[[],[[],[]]]]]]=>[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[[],[[[]]]]]]]=>[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[[]],[],[]]]]]=>[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[[[]],[[]]]]]]=>[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[[],[]],[]]]]]=>[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[[[[]]],[]]]]]=>[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[[],[],[]]]]]]=>[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[[],[[]]]]]]]=>[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[[]],[]]]]]]=>[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[[],[]]]]]]]=>[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[[]]]]]]]]=>[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[],[],[],[],[],[]]=>[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[],[[]]]=>[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[[]],[]]=>[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[],[[],[]]]=>[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[[[]]]]=>[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[[]],[],[]]=>[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[]],[[]]]=>[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[],[]],[]]=>[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[]]],[]]=>[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[],[[],[],[]]]=>[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[[],[[]]]]=>[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[]],[]]]=>[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[],[[[],[]]]]=>[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[],[[[[]]]]]=>[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[[]],[],[],[]]=>[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[],[[]]]=>[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[]],[]]=>[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[],[]]]=>[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[[]]]]=>[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[],[]],[],[]]=>[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[]]],[],[]]=>[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[[[]],[],[[],[]],[[]]]=>[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[]]],[[]]]=>[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[],[[],[],[]],[]]=>[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[]]],[]]=>[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[]],[]],[]]=>[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[],[]]],[]]=>[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[]]]],[]]=>[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[],[[],[],[],[]]]=>[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[],[[],[],[[]]]]=>[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[]],[]]]=>[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[],[[],[[],[]]]]=>[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[],[[],[[[]]]]]=>[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[]],[],[]]]=>[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[[]],[[]]]]=>[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[],[]],[]]]=>[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[]]],[]]]=>[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[],[[[],[],[]]]]=>[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[],[[[],[[]]]]]=>[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[[[]],[]]]]=>[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[],[[[[],[]]]]]=>[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[],[[[[[]]]]]]=>[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[[]],[],[],[],[]]=>[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[],[[]]]=>[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[]],[]]=>[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[],[]]]=>[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[],[[[]]]]=>[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[]],[],[]]=>[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[]],[[]]]=>[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[]]],[]]=>[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[],[],[]]]=>[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[]],[[],[[]]]]=>[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[]],[]]]=>[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[[],[]]]]=>[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[]],[[[[]]]]]=>[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[],[]],[],[],[]]=>[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[],[],[]]=>[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[[]],[[],[]],[],[[]]]=>[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[],[[]]]=>[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[[],[]],[[]],[]]=>[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[[]],[]]=>[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[]],[[],[]]]=>[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[],[]],[[[]]]]=>[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[[],[]]]=>[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[[[]]],[[[]]]]=>[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]],[],[]]=>[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]],[],[]]=>[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]],[],[]]=>[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[],[]]=>[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]],[],[]]=>[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]],[[]]]=>[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]],[[]]]=>[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[]],[[]]]=>[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[[]]]=>[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]],[[]]]=>[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[],[]],[]]=>[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[]]],[]]=>[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[]],[]],[]]=>[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[],[]]],[]]=>[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[]]]],[]]=>[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[]],[],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[]]],[]]=>[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[],[]],[]],[]]=>[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[]]],[]]=>[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[],[[]]]],[]]=>[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[]]],[]]=>[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]]]],[]]=>[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]]]],[]]=>[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[],[],[]]]=>[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[]],[[],[],[],[[]]]]=>[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[]],[]]]=>[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[]],[[],[],[[],[]]]]=>[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[[[]]]]]=>[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[]],[],[]]]=>[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[]],[[],[[]],[[]]]]=>[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[],[]],[]]]=>[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[]]],[]]]=>[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[[],[[],[],[]]]]=>[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[[],[[]]]]]=>[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[]],[[],[[[]],[]]]]=>[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[]],[[],[[[],[]]]]]=>[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[]],[[],[[[[]]]]]]=>[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[]],[],[],[]]]=>[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[]],[[[]],[],[[]]]]=>[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[]],[]]]=>[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[[]],[[],[]]]]=>[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[]],[[[]]]]]=>[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[],[]],[],[]]]=>[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[],[]]]=>[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[]],[[]]]]=>[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[[]]]]=>[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[]],[]]]=>[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[],[[]]],[]]]=>[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[]],[]]]=>[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]]],[]]]=>[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]]],[]]]=>[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[],[]]]]=>[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[[],[],[[]]]]]=>[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[[],[[]],[]]]]=>[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[[],[[],[]]]]]=>[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[[],[[[]]]]]]=>[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[[]],[],[]]]]=>[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[[]],[[]]]]]=>[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[[],[]],[]]]]=>[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[[[]]],[]]]]=>[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[[],[],[]]]]]=>[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[[],[[]]]]]]=>[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[[[]],[]]]]]=>[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[[[],[]]]]]]=>[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[[[]]]]]]]=>[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[]],[],[],[],[],[]]=>[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[],[],[]]=>[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[],[[]]]=>[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[],[[]]]=>[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[[]],[]]=>[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[[]],[]]=>[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[],[[],[]]]=>[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[],[]],[],[],[[[]]]]=>[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[[],[]]]=>[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[[]]],[],[],[[[]]]]=>[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[[]],[],[]]=>[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[]],[[]]]=>[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[],[]],[]]=>[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[]]],[]]=>[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[],[]],[]]=>[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[]]],[]]=>[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[],[[],[],[]]]=>[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[]],[],[[],[[]]]]=>[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[]],[]]]=>[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[]],[],[[[],[]]]]=>[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[[]]]]]=>[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[],[],[]]]=>[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[]]],[],[[],[[]]]]=>[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[]],[]]]=>[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[]]],[],[[[],[]]]]=>[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[[[]]]]]=>[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[[]],[],[],[]]=>[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[],[],[]]=>[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[],[[]]]=>[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[],[[]]]=>[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[[]],[]]=>[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[[]],[]]=>[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[]],[[],[]]]=>[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[]],[[]],[[[]]]]=>[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[[],[]]]=>[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[]]],[[]],[[[]]]]=>[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]],[],[]]=>[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]],[],[]]=>[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[]],[[]]]=>[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[]]],[[]]]=>[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[],[]],[]]=>[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[]]],[]]=>[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[]],[]],[]]=>[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[]]],[]]=>[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]]]],[]]=>[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[],[]],[]]=>[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[]]],[]]=>[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[]],[]],[]]=>[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[]]],[]]=>[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]]]],[]]=>[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[]],[[],[],[],[]]]=>[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[]],[[],[],[[]]]]=>[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[]],[]]]=>[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[]],[[],[[],[]]]]=>[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[],[[[]]]]]=>[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[]],[],[]]]=>[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[]],[[]]]]=>[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[]],[]]]=>[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]]],[]]]=>[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[],[]],[[[],[],[]]]]=>[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[[],[[]]]]]=>[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[]],[[[[]],[]]]]=>[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[]],[[[[],[]]]]]=>[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[[]]]]]]=>[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[],[],[],[]]]=>[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[]]],[[],[],[[]]]]=>[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[]],[]]]=>[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[]]],[[],[[],[]]]]=>[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[],[[[]]]]]=>[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[]],[],[]]]=>[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[]],[[]]]]=>[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[]],[]]]=>[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]]],[]]]=>[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[]]],[[[],[],[]]]]=>[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[[[],[[]]]]]=>[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]]],[[[[]],[]]]]=>[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]]],[[[[],[]]]]]=>[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[[[[]]]]]]=>[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[],[],[],[]]=>[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[],[],[]]=>[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[],[],[]]=>[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[],[],[]]=>[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[],[[]]]=>[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[],[[]]]=>[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[],[[]]]=>[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[[]]]=>[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[]],[]]=>[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[[]],[]]=>[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[[]],[]]=>[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[]],[]]=>[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[],[]]]=>[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[]]],[],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[],[[[]]]]=>[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[],[[],[]]]=>[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[],[[[]]]]=>[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[],[[],[]]]=>[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[],[[[]]]]=>[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[],[]]]=>[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[],[[[]]]]=>[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]],[],[]]=>[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]],[],[]]=>[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]],[],[]]=>[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[],[]]=>[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]],[],[]]=>[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[]],[[]]]=>[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[]],[[]]]=>[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[]],[[]]]=>[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[[]]]=>[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[]],[[]]]=>[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[],[]],[]]=>[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[]]],[]]=>[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[]],[]]=>[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]]],[]]=>[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[],[]],[]]=>[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[]]],[]]=>[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[],[]],[]]=>[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[]]],[]]=>[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[],[]],[]]=>[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[]]],[]]=>[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[[],[],[]]]=>[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[],[[]]]]=>[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[]],[]]]=>[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[],[]]]]=>[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[[[]]]]]=>[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[],[]]]=>[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[],[[]]]]=>[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]],[]]]=>[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[],[]]]]=>[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[[]]]]]=>[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[],[],[]]]=>[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[],[[]]]]=>[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[]],[]]]=>[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[],[]]]]=>[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[[]]]]]=>[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[],[],[]]]=>[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[],[[]]]]=>[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[]],[]]]=>[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[],[]]]]=>[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[[]]]]]=>[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[],[],[]]]=>[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[],[[]]]]=>[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[]],[]]]=>[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[],[]]]]=>[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[[[]]]]]=>[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[],[]]=>[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[],[],[]]=>[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[],[],[]]=>[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[],[],[]]=>[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[],[],[]]=>[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[],[],[]]=>[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[],[],[]]=>[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[],[],[]]=>[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[],[],[]]=>[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[],[]]=>[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[],[],[]]=>[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[],[],[]]=>[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[],[],[]]=>[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[[]]]=>[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[],[[]]]=>[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[],[[]]]=>[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[],[[]]]=>[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[],[[]]]=>[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[],[[]]]=>[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[],[[]]]=>[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[],[[]]]=>[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[],[[]]]=>[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[[]]]=>[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[],[[]]]=>[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[],[[]]]=>[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[[]]]=>[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[[]],[]]=>[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[[]],[]]=>[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[[]],[]]=>[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[[]],[]]=>[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[[]],[]]=>[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[[]],[]]=>[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[[]],[]]=>[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[[]],[]]=>[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[[]],[]]=>[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[[]],[]]=>[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[[]],[]]=>[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[[]],[]]=>[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[[]],[]]=>[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[]],[[],[]]]=>[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[],[]],[[[]]]]=>[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]],[[],[]]]=>[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[],[[]]],[[[]]]]=>[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[]],[]],[[],[]]]=>[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[]],[]],[[[]]]]=>[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]],[[],[]]]=>[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[],[]]],[[[]]]]=>[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[]]]],[[],[]]]=>[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[],[[[]]]],[[[]]]]=>[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[],[]],[[],[]]]=>[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[],[]],[[[]]]]=>[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[]]],[[],[]]]=>[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[]]],[[[]]]]=>[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]],[[],[]]]=>[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[],[]],[]],[[[]]]]=>[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[]]],[]],[[],[]]]=>[[],[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[]]],[]],[[[]]]]=>[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[],[]]],[[],[]]]=>[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[],[],[]]],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[],[[]]]],[[[]]]]=>[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[]],[]]],[[],[]]]=>[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[]],[]]],[[[]]]]=>[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[],[]]]],[[],[]]]=>[[[]],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[],[]]]],[[[]]]]=>[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]],[[],[]]]=>[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[]]]]],[[[]]]]=>[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]],[],[]]=>[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]],[],[]]=>[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]],[],[]]=>[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]],[],[]]=>[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]],[],[]]=>[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]],[],[]]=>[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]],[],[]]=>[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]],[],[]]=>[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]],[],[]]=>[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]],[],[]]=>[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]],[],[]]=>[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]],[],[]]=>[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[],[]]=>[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]],[],[]]=>[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]],[],[]]=>[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]],[],[]]=>[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]],[],[]]=>[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[],[]]=>[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]],[],[]]=>[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]],[],[]]=>[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[]],[[]]],[],[]]=>[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[]]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]],[],[]]=>[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[]],[],[]]=>[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[]],[],[]]=>[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]],[],[]]=>[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]],[],[]]=>[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]],[],[]]=>[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]],[],[]]=>[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]],[],[]]=>[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]],[],[]]=>[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]],[],[]]=>[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]],[],[]]=>[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]],[],[]]=>[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]],[],[]]=>[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]],[],[]]=>[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]],[],[]]=>[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]]],[],[]]=>[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]],[],[]]=>[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]],[],[]]=>[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[]],[[]]]=>[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]],[[]]]=>[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[],[[]],[]],[[]]]=>[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[],[[],[]]],[[]]]=>[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]]]],[[]]]=>[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[]],[],[]],[[]]]=>[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[]]],[[]]]=>[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[],[]],[]],[[]]]=>[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]],[[]]]=>[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]],[[]]]=>[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]],[[]]]=>[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[]],[]]],[[]]]=>[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[],[]]]],[[]]]=>[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]],[[]]]=>[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]],[[]]]=>[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]],[],[[]]],[[]]]=>[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]],[[]]]=>[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[[]]]=>[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]],[[]]]=>[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[]]],[],[]],[[]]]=>[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[]],[[]]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[]]],[[]]]=>[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[]],[[]]]=>[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[]],[[]]]=>[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[]],[[]]]=>[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[]],[[]]]=>[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[]],[[]]]=>[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]]],[[]]]=>[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]],[[]]]=>[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]]],[[]]]=>[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]],[[]]]=>[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]]],[[]]]=>[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]]],[[]]]=>[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]]],[[]]]=>[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]]],[[]]]=>[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]]],[[]]]=>[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]],[[]]]=>[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]]],[[]]]=>[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]]],[[]]]=>[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]],[[]]]=>[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[],[]],[]]=>[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[],[],[],[],[[]]],[]]=>[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[],[],[],[[]],[]],[]]=>[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[],[],[],[[],[]]],[]]=>[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[],[],[],[[[]]]],[]]=>[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[]],[],[]],[]]=>[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[]]],[]]=>[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[],[]],[]],[]]=>[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[]],[]]=>[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[],[],[]]],[]]=>[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[],[[]]]],[]]=>[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[[]],[]]],[]]=>[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]]],[]]=>[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[]]]]],[]]=>[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[]],[],[],[]],[]]=>[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[]]],[]]=>[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[]],[]],[]]=>[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[],[]]],[]]=>[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[]]]],[]]=>[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[]],[],[]],[]]=>[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[]],[]]=>[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[],[[],[]],[[]]],[]]=>[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[]]],[]]=>[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[],[]],[]],[]]=>[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[]],[]]=>[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[]],[]]=>[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[]],[]]=>[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[]],[]]=>[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[]]],[]]=>[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]]],[]]=>[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[],[[],[[]],[]]],[]]=>[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]]],[]]=>[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[[]]]]],[]]=>[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[]]],[]]=>[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[[]],[[]]]],[]]=>[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]]],[]]=>[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[]]],[]]=>[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]]]],[]]=>[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]]],[]]=>[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]]]],[]]=>[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]]]],[]]=>[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]]],[]]=>[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[]],[]]=>[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]]],[]]=>[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[]],[]]=>[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[],[]]],[]]=>[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[]]]],[]]=>[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[]]],[]]=>[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[],[]],[]],[]]=>[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[]]],[]]=>[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[],[[]]]],[]]=>[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[]]],[]]=>[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]]]],[]]=>[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]]]],[]]=>[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[],[]],[]]=>[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[]],[]]=>[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[[]]],[]]=>[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[]]],[]]=>[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[],[]],[[]],[]],[]]=>[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[]],[]]=>[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[]]],[]]=>[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]]]],[]]=>[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[]]],[]]=>[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]]]],[]]=>[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[],[]],[]]=>[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[]],[]]=>[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[]],[]]=>[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[]],[]]=>[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[]],[]]=>[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[]]],[]]=>[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[]]],[]]=>[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[]]],[]]=>[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[]]],[]]=>[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[]]],[]]=>[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]],[]],[]]=>[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[]],[]]=>[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[]],[]]=>[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[]],[]]=>[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[]],[]]=>[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[]],[]]=>[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[]],[]]=>[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[]],[]]=>[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[]],[]]=>[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]],[]],[]]=>[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]],[]],[]]=>[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[]],[]]=>[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[]],[]]=>[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[]]],[]]=>[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[],[],[],[[]]]],[]]=>[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[],[],[[]],[]]],[]]=>[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]]],[]]=>[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[],[],[[[]]]]],[]]=>[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[]]],[]]=>[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[[]]]],[]]=>[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[]]],[]]=>[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[]]],[]]=>[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]]]],[]]=>[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]]],[]]=>[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]]]],[]]=>[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]]]],[]]=>[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]]],[]]=>[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]]],[]]=>[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[]],[],[[]]]],[]]=>[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[]]],[]]=>[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]]]],[]]=>[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]]]],[]]=>[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[]]],[]]=>[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[]]],[]]=>[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]]]],[]]=>[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[]]]],[]]=>[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[]]],[]]=>[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[]]],[]]=>[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[]]],[]]=>[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[]]],[]]=>[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[]]],[]]=>[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]]]],[]]=>[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]]]],[]]=>[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]]]],[]]=>[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]]]],[]]=>[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]]]],[]]=>[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]]]],[]]=>[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]]]],[]]=>[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]]]],[]]=>[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]]]],[]]=>[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]]]],[]]=>[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[],[[]]]]]],[]]=>[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[]],[]]]]],[]]=>[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[],[]]]]]],[]]=>[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]]]],[]]=>[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[],[],[],[],[],[],[]]]=>[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[],[],[],[],[],[[]]]]=>[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[],[],[],[],[[]],[]]]=>[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[],[],[],[],[[],[]]]]=>[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[],[],[],[],[[[]]]]]=>[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[],[],[[]],[],[]]]=>[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[],[],[[]],[[]]]]=>[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[],[],[],[[],[]],[]]]=>[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[],[],[],[[[]]],[]]]=>[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[],[],[],[[],[],[]]]]=>[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[],[],[],[[],[[]]]]]=>[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[],[],[],[[[]],[]]]]=>[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[],[],[],[[[],[]]]]]=>[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[],[],[],[[[[]]]]]]=>[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[[]],[],[],[]]]=>[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[]],[],[[]]]]=>[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[]],[]]]=>[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[],[],[[]],[[],[]]]]=>[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[[]]]]]=>[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[],[],[[],[]],[],[]]]=>[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[],[]]]=>[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[],[],[[],[]],[[]]]]=>[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[[]]]]=>[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[],[],[[],[],[]],[]]]=>[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[],[],[[],[[]]],[]]]=>[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[],[],[[[]],[]],[]]]=>[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]],[]]]=>[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[]]]],[]]]=>[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[],[],[[],[],[],[]]]]=>[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[],[],[[],[],[[]]]]]=>[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[],[],[[],[[]],[]]]]=>[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[],[],[[],[[],[]]]]]=>[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[],[],[[],[[[]]]]]]=>[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[[]],[],[]]]]=>[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[[]],[[]]]]]=>[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[[],[]],[]]]]=>[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[[]]],[]]]]=>[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[[],[],[]]]]]=>[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[[],[[]]]]]]=>[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[[[]],[]]]]]=>[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[[[],[]]]]]]=>[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[[[[]]]]]]]=>[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[[]],[],[],[],[]]]=>[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[[]],[],[],[[]]]]=>[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[]],[]]]=>[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[],[[]],[],[[],[]]]]=>[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[]],[],[[[]]]]]=>[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[]],[],[]]]=>[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[],[[]],[[]],[[]]]]=>[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[],[]],[]]]=>[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[]]],[]]]=>[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[],[[]],[[],[],[]]]]=>[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[[]],[[],[[]]]]]=>[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[],[[]],[[[]],[]]]]=>[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[[],[]]]]]=>[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[]],[[[[]]]]]]=>[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[]],[],[],[]]]=>[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[],[[],[]],[],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[],[[[]]],[],[[]]]]=>[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[],[[],[]],[[]],[]]]=>[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[]],[]]]=>[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[],[[],[]],[[],[]]]]=>[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[[],[]],[[[]]]]]=>[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[],[]]]]=>[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[],[[[]]],[[[]]]]]=>[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[],[]],[],[]]]=>[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[],[]]]=>[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[],[]]]=>[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[],[]]]=>[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[]],[[]]]]=>[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[[]]]]=>[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[],[[[]],[]],[[]]]]=>[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[],[]]],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[[]]]]=>[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[]],[]]]=>[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]],[]]]=>[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[],[[],[[]],[]],[]]]=>[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]],[]]]=>[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[[]]]],[]]]=>[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[]],[]]]=>[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[[[]],[[]]],[]]]=>[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]],[]]]=>[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[]],[]]]=>[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]]],[]]]=>[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]],[]]]=>[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]]],[]]]=>[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]]],[]]]=>[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]],[]]]=>[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[],[]]]]=>[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[],[[],[],[],[[]]]]]=>[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[],[[],[],[[]],[]]]]=>[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[[],[],[[],[]]]]]=>[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[],[[],[],[[[]]]]]]=>[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[[],[[]],[],[]]]]=>[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[],[[]],[[]]]]]=>[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[[],[[],[]],[]]]]=>[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[],[[],[[[]]],[]]]]=>[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[],[[],[[],[],[]]]]]=>[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[],[[],[[],[[]]]]]]=>[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[],[[],[[[]],[]]]]]=>[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[],[[],[[[],[]]]]]]=>[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[],[[],[[[[]]]]]]]=>[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[],[]]]]=>[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[[]],[],[[]]]]]=>[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[[]],[[]],[]]]]=>[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[[]],[[],[]]]]]=>[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[[]],[[[]]]]]]=>[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[],[]]]]=>[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[[[]]],[],[]]]]=>[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[],[[[],[]],[[]]]]]=>[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[],[[[[]]],[[]]]]]=>[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[[],[],[]],[]]]]=>[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]],[]]]]=>[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[[]],[]],[]]]]=>[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[[],[]]],[]]]]=>[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]],[]]]]=>[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[[],[],[],[]]]]]=>[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[[],[],[[]]]]]]=>[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[],[[[],[[]],[]]]]]=>[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[],[[[],[[],[]]]]]]=>[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[[],[[[]]]]]]]=>[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[[[[]],[],[]]]]]=>[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[[[]],[[]]]]]]=>[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[],[[[[],[]],[]]]]]=>[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[[[[]]],[]]]]]=>[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[],[[[[],[],[]]]]]]=>[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[],[[[[],[[]]]]]]]=>[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[[]],[]]]]]]=>[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[[],[]]]]]]]=>[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[[]]]]]]]]=>[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[],[]]]=>[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[]],[],[],[],[[]]]]=>[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]],[]]]=>[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[]],[],[],[[],[]]]]=>[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[[]]]]]=>[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[],[]]]=>[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[]],[],[[]],[[]]]]=>[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[],[]],[]]]=>[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[]]],[]]]=>[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[]],[],[[],[],[]]]]=>[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[[],[[]]]]]=>[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[[]],[]]]]=>[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[]],[],[[[],[]]]]]=>[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[]],[],[[[[]]]]]]=>[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[]],[],[],[]]]=>[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[]],[[]],[],[[]]]]=>[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[]],[]]]=>[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[]],[[]],[[],[]]]]=>[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[[[]]]]]=>[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[],[]],[],[]]]=>[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[],[]]]=>[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[]],[[]]]]=>[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[[]]]]=>[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[]],[]]]=>[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[],[[]]],[]]]=>[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[]],[]]]=>[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]]],[]]]=>[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]]],[]]]=>[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[],[]]]]=>[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[[],[],[[]]]]]=>[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[],[[]],[]]]]=>[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[[],[[],[]]]]]=>[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[[],[[[]]]]]]=>[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[[]],[],[]]]]=>[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[[]],[[]]]]]=>[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[[],[]],[]]]]=>[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[[]]],[]]]]=>[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[[],[],[]]]]]=>[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[[],[[]]]]]]=>[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[[]],[]]]]]=>[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[[[],[]]]]]]=>[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[[[[]]]]]]]=>[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[],[],[]]]=>[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[],[]]]=>[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[],[]],[],[],[[]]]]=>[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[[]]],[],[],[[]]]]=>[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[[]],[]]]=>[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[]],[]]]=>[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[],[]],[],[[],[]]]]=>[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[],[[[]]]]]=>[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[],[]]]]=>[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[[]]],[],[[[]]]]]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[]],[[]],[],[]]]=>[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[],[]]]=>[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[]],[[]]]]=>[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[[]],[[]]]]=>[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[]],[]]]=>[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]]],[]]]=>[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[]],[]]]=>[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]]],[]]]=>[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[],[]],[[],[],[]]]]=>[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[[],[[]]]]]=>[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]],[]]]]=>[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[[],[]],[[[],[]]]]]=>[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[[]]]]]]=>[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[],[],[]]]]=>[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[[]]],[[],[[]]]]]=>[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]]],[[[]],[]]]]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[]]],[[[],[]]]]]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[[[]]]]]]=>[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[],[],[]]]=>[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[],[]]]=>[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[],[]]]=>[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[],[]]]=>[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[],[]]]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[],[[]]]]=>[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]],[],[[]]]]=>[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]],[],[[]]]]=>[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]],[],[[]]]]=>[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[[]]]],[],[[]]]]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[]],[]]]=>[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[]],[]]]=>[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[]],[]]]=>[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[]],[]]]=>[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[]],[]]]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[]],[[],[]]]]=>[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[],[]],[[[]]]]]=>[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[[],[[]]],[[],[]]]]=>[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[[],[[]]],[[[]]]]]=>[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[]],[[],[]]]]=>[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[[]],[]],[[[]]]]]=>[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[[],[]]],[[],[]]]]=>[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[[],[]]],[[[]]]]]=>[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[]]]],[[],[]]]]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[[]]]],[[[]]]]]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[],[]],[],[]]]=>[[[[[]]]],[[[]]],[]]=>[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[],[]]]=>[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[],[]]]=>[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[],[]]]=>[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[],[]]]=>[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[],[]]]=>[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[],[]]]=>[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[],[]]]=>[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[],[]]]=>[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]],[],[]]]=>[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]],[],[]]]=>[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[],[]]]=>[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[],[]]]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[]],[[]]]]=>[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]],[[]]]]=>[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[[],[[]],[]],[[]]]]=>[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[]]]],[[]]]]=>[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[[]],[],[]],[[]]]]=>[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[[]],[[]]],[[]]]]=>[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]],[[]]]]=>[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[]]],[]],[[]]]]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[[],[],[]]],[[]]]]=>[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]],[[]]]]=>[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[[[]],[]]],[[]]]]=>[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[],[]]]],[[]]]]=>[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]],[[]]]]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[]],[]]]=>[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[],[],[],[[]]],[]]]=>[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[],[],[[]],[]],[]]]=>[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]],[]]]=>[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[],[],[[[]]]],[]]]=>[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[]],[]]]=>[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[[]]],[]]]=>[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[]],[]]]=>[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[]],[]]]=>[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]]],[]]]=>[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]],[]]]=>[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]]],[]]]=>[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]]],[]]]=>[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]],[]]]=>[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]],[]]]=>[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[[]],[],[[]]],[]]]=>[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[]],[]]]=>[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]]],[]]]=>[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]]],[]]]=>[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[]],[]]]=>[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[]],[]]]=>[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]]],[]]]=>[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[]]],[]]]=>[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[]],[]]]=>[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[]],[]]]=>[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[]],[]]]=>[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[]],[]]]=>[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[]],[]]]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]]],[]]]=>[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]]],[]]]=>[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]]],[]]]=>[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]]],[]]]=>[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]]],[]]]=>[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]]],[]]]=>[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]]],[]]]=>[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]]],[]]]=>[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]]],[]]]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]]],[]]]=>[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[],[[]]]]],[]]]=>[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[]],[]]]],[]]]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[],[]]]]],[]]]=>[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]]],[]]]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[],[],[],[],[],[]]]]=>[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[],[],[[]]]]]=>[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[[],[],[],[[]],[]]]]=>[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[],[],[],[[],[]]]]]=>[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[[],[],[],[[[]]]]]]=>[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[],[],[[]],[],[]]]]=>[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[[],[],[[]],[[]]]]]=>[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[],[[],[]],[]]]]=>[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[[],[],[[[]]],[]]]]=>[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[[],[],[[],[],[]]]]]=>[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[[],[],[[],[[]]]]]]=>[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[[],[],[[[]],[]]]]]=>[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[[],[],[[[],[]]]]]]=>[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[[],[],[[[[]]]]]]]=>[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[],[]]]]=>[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[[],[[]],[],[[]]]]]=>[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[[],[[]],[[]],[]]]]=>[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[[],[[]],[[],[]]]]]=>[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[[],[[]],[[[]]]]]]=>[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[[],[]],[],[]]]]=>[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[[],[[[]]],[],[]]]]=>[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[],[]],[[]]]]]=>[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[[]]]]]=>[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]],[]]]]=>[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]],[]]]]=>[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[[],[[[]],[]],[]]]]=>[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[[],[[[],[]]],[]]]]=>[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]],[]]]]=>[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[[],[[],[],[],[]]]]]=>[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[[],[[],[],[[]]]]]]=>[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[[],[[],[[]],[]]]]]=>[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[],[[],[[],[]]]]]]=>[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[],[[],[[[]]]]]]]=>[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[[],[[[]],[],[]]]]]=>[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[[],[[[]],[[]]]]]]=>[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[[[],[]],[]]]]]=>[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[[],[[[[]]],[]]]]]=>[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[[],[[[],[],[]]]]]]=>[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[[],[[[],[[]]]]]]]=>[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[[],[[[[]],[]]]]]]=>[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[[],[[[[],[]]]]]]]=>[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[[],[[[[[]]]]]]]]=>[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[],[]]]]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[[]],[],[],[[]]]]]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[[]],[],[[]],[]]]]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[],[[],[]]]]]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[[]],[],[[[]]]]]]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[],[]]]]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[[]],[[]],[[]]]]]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]],[]]]]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[[]],[[[]]],[]]]]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[[]],[[],[],[]]]]]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[[]],[[],[[]]]]]]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[[]],[[[]],[]]]]]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[[[],[]]]]]]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[[]],[[[[]]]]]]]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[[],[]],[],[],[]]]]=>[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[[[]]],[],[],[]]]]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[[],[]],[],[[]]]]]=>[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[[[]]],[],[[]]]]]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[],[]],[[]],[]]]]=>[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[[[]]],[[]],[]]]]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[[],[]],[[],[]]]]]=>[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[[],[]],[[[]]]]]]=>[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[],[]]]]]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[[]]],[[[]]]]]]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[],[]]]]=>[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[],[]]]]=>[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[],[]]]]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[],[]]]]=>[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[],[]]]]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[],[],[]],[[]]]]]=>[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[[],[[]]],[[]]]]]=>[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[[]],[]],[[]]]]]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[[],[]]],[[]]]]]=>[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[[]]]],[[]]]]]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[],[],[],[]],[]]]]=>[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]],[]]]]=>[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[[],[[]],[]],[]]]]=>[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]],[]]]]=>[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[[],[[[]]]],[]]]]=>[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[[[]],[],[]],[]]]]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[[[]],[[]]],[]]]]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]],[]]]]=>[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[[]]],[]],[]]]]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[[],[],[]]],[]]]]=>[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[[[],[[]]]],[]]]]=>[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[[[]],[]]],[]]]]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[[],[]]]],[]]]]=>[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]],[]]]]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[],[],[],[],[]]]]]=>[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[],[],[],[[]]]]]]=>[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[[],[],[[]],[]]]]]=>[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[[],[],[[],[]]]]]]=>[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[[],[],[[[]]]]]]]=>[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[[],[[]],[],[]]]]]=>[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[[],[[]],[[]]]]]]=>[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[[],[[],[]],[]]]]]=>[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[[],[[[]]],[]]]]]=>[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[[],[[],[],[]]]]]]=>[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[[],[[],[[]]]]]]]=>[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[[],[[[]],[]]]]]]=>[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[[],[[[],[]]]]]]]=>[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[[],[[[[]]]]]]]]=>[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[[]],[],[],[]]]]]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[[]],[],[[]]]]]]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[[]],[[]],[]]]]]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[[]],[[],[]]]]]]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[[]],[[[]]]]]]]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[[],[]],[],[]]]]]=>[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[[[]]],[],[]]]]]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[[],[]],[[]]]]]]=>[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[[]]],[[]]]]]]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[[],[],[]],[]]]]]=>[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[[],[[]]],[]]]]]=>[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[[]],[]],[]]]]]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[[],[]]],[]]]]]=>[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[[]]]],[]]]]]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[],[],[],[]]]]]]=>[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[[],[],[[]]]]]]]=>[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[[],[[]],[]]]]]]=>[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[[],[[],[]]]]]]]=>[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[[],[[[]]]]]]]]=>[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[[]],[],[]]]]]]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[[]],[[]]]]]]]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[[],[]],[]]]]]]=>[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[[]]],[]]]]]]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[[],[],[]]]]]]]=>[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[[],[[]]]]]]]]=>[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[[]],[]]]]]]]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[[],[]]]]]]]]=>[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[[]]]]]]]]]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
DeBruijn-Morselt plane tree automorphism
Description
This automorphism on the set of plane trees with a given number of vertices is the combination of the two "canonical" bijections between plane trees and binary trees, using either the left or right branches. In [3] Shapiro essentially attributes this automorphism to DeBruijn and Morselt [1], hence the name I chose. Shapiro shows in that paper that for a large subset of plane trees (those corresponding to compositions), the sixth power of the automorphism acts as the identity on this subset. However, its behavior in general is quite chaotic. In [2] Donaghey studies this automorphism further and shows that its behavior on all trees can be reduced to its behavior on certain "primitive" trees.
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 to the depth of the tree.
This sends the maximal height of the Dyck path to the depth of the tree.
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