Identifier
Mp00048:
Ordered trees
—left-right symmetry⟶
Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Images
=>
Cc0021;cc-rep-0Cc0021;cc-rep-1Cc0005;cc-rep-2Cc0005;cc-rep-3
[]=>[]=>[]=>[]
[[]]=>[[]]=>[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]=>[1,1,1,0,0,0]
[[],[[]]]=>[[[]],[]]=>[1,1,0,0,1,0]=>[1,1,0,0,1,0]
[[[]],[]]=>[[],[[]]]=>[1,0,1,1,0,0]=>[1,1,0,1,0,0]
[[[],[]]]=>[[[],[]]]=>[1,1,0,1,0,0]=>[1,0,1,1,0,0]
[[[[]]]]=>[[[[]]]]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]
[[],[],[],[]]=>[[],[],[],[]]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]
[[],[],[[]]]=>[[[]],[],[]]=>[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0]
[[],[[]],[]]=>[[],[[]],[]]=>[1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]
[[],[[],[]]]=>[[[],[]],[]]=>[1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]
[[],[[[]]]]=>[[[[]]],[]]=>[1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0]
[[[]],[],[]]=>[[],[],[[]]]=>[1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0]
[[[]],[[]]]=>[[[]],[[]]]=>[1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]
[[[],[]],[]]=>[[],[[],[]]]=>[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0]
[[[[]]],[]]=>[[],[[[]]]]=>[1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0]
[[[],[],[]]]=>[[[],[],[]]]=>[1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0]
[[[],[[]]]]=>[[[[]],[]]]=>[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0]
[[[[]],[]]]=>[[[],[[]]]]=>[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0]
[[[[],[]]]]=>[[[[],[]]]]=>[1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0]
[[[[[]]]]]=>[[[[[]]]]]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]
[[],[],[],[],[]]=>[[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]
[[],[],[],[[]]]=>[[[]],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]
[[],[],[[]],[]]=>[[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]
[[],[],[[],[]]]=>[[[],[]],[],[]]=>[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]
[[],[],[[[]]]]=>[[[[]]],[],[]]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]
[[],[[]],[],[]]=>[[],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]
[[],[[]],[[]]]=>[[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]
[[],[[],[]],[]]=>[[],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]
[[],[[[]]],[]]=>[[],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]
[[],[[],[],[]]]=>[[[],[],[]],[]]=>[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]
[[],[[],[[]]]]=>[[[[]],[]],[]]=>[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]
[[],[[[]],[]]]=>[[[],[[]]],[]]=>[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]
[[],[[[],[]]]]=>[[[[],[]]],[]]=>[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]
[[],[[[[]]]]]=>[[[[[]]]],[]]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]
[[[]],[],[],[]]=>[[],[],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]
[[[]],[],[[]]]=>[[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]
[[[]],[[]],[]]=>[[],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]
[[[]],[[],[]]]=>[[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]
[[[]],[[[]]]]=>[[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]
[[[],[]],[],[]]=>[[],[],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0]
[[[[]]],[],[]]=>[[],[],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]
[[[],[]],[[]]]=>[[[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]
[[[[]]],[[]]]=>[[[]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]
[[[],[],[]],[]]=>[[],[[],[],[]]]=>[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]
[[[],[[]]],[]]=>[[],[[[]],[]]]=>[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]
[[[[]],[]],[]]=>[[],[[],[[]]]]=>[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]
[[[[],[]]],[]]=>[[],[[[],[]]]]=>[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]
[[[[[]]]],[]]=>[[],[[[[]]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]
[[[],[],[],[]]]=>[[[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]
[[[],[],[[]]]]=>[[[[]],[],[]]]=>[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]
[[[],[[]],[]]]=>[[[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]
[[[],[[],[]]]]=>[[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]
[[[],[[[]]]]]=>[[[[[]]],[]]]=>[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]
[[[[]],[],[]]]=>[[[],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]
[[[[]],[[]]]]=>[[[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]
[[[[],[]],[]]]=>[[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]
[[[[[]]],[]]]=>[[[],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]
[[[[],[],[]]]]=>[[[[],[],[]]]]=>[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]
[[[[],[[]]]]]=>[[[[[]],[]]]]=>[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]
[[[[[]],[]]]]=>[[[[],[[]]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]
[[[[[],[]]]]]=>[[[[[],[]]]]]=>[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]
[[[[[[]]]]]]=>[[[[[[]]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[[],[],[],[],[[]]]=>[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[[],[],[],[[],[]]]=>[[[],[]],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[],[],[],[[[]]]]=>[[[[]]],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[],[],[[]],[[]]]=>[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[[],[],[[],[],[]]]=>[[[],[],[]],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[[]]]]=>[[[[]],[]],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[],[],[[[]],[]]]=>[[[],[[]]],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[[],[],[[[],[]]]]=>[[[[],[]]],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[],[],[[[[]]]]]=>[[[[[]]]],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[],[[]],[],[[]]]=>[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[[],[[]],[[]],[]]=>[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[[],[[]],[[],[]]]=>[[[],[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[[],[[]],[[[]]]]=>[[[[]]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[]],[[]]]=>[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[[],[[[]]],[[]]]=>[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[[],[[],[],[],[]]]=>[[[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[],[[],[],[[]]]]=>[[[[]],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[],[[],[[]],[]]]=>[[[],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[[],[[],[[],[]]]]=>[[[[],[]],[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[]]]]]=>[[[[[]]],[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[],[[[]],[],[]]]=>[[[],[],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[[],[[[]],[[]]]]=>[[[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[],[[[],[]],[]]]=>[[[],[[],[]]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[[[]]],[]]]=>[[[],[[[]]]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[[],[[[],[],[]]]]=>[[[[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[],[[[],[[]]]]]=>[[[[[]],[]]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[],[[[[]],[]]]]=>[[[[],[[]]]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[[],[[[[],[]]]]]=>[[[[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[[[]]]]]]=>[[[[[[]]]]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[[]],[],[],[],[]]=>[[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[],[],[[]]]=>[[[]],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[],[[]],[]]=>[[],[[]],[],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[[[]],[],[[],[]]]=>[[[],[]],[],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[[[]],[],[[[]]]]=>[[[[]]],[],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[[]],[[]],[],[]]=>[[],[],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[[[]],[[]],[[]]]=>[[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[],[]],[]]=>[[],[[],[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[[[]],[[[]]],[]]=>[[],[[[]]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[[[]],[[],[],[]]]=>[[[],[],[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[[[]],[[],[[]]]]=>[[[[]],[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[[[]],[[[]],[]]]=>[[[],[[]]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[[],[]]]]=>[[[[],[]]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[[[]],[[[[]]]]]=>[[[[[]]]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[[[],[]],[],[],[]]=>[[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[[[]]],[],[],[]]=>[[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[[],[]],[],[[]]]=>[[[]],[],[[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[[[[]]],[],[[]]]=>[[[]],[],[[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[[[],[]],[[]],[]]=>[[],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[[[[]]],[[]],[]]=>[[],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[[[],[]],[[],[]]]=>[[[],[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[]]]]=>[[[[]]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[[[[]]],[[],[]]]=>[[[],[]],[[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[[[[]]],[[[]]]]=>[[[[]]],[[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[]],[],[]]=>[[],[],[[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[[[],[[]]],[],[]]=>[[],[],[[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[]],[],[]]=>[[],[],[[],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[[[[],[]]],[],[]]=>[[],[],[[[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[[[[[]]]],[],[]]=>[[],[],[[[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[]],[[]]]=>[[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[[[],[[]]],[[]]]=>[[[]],[[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[]],[[]]]=>[[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[[[[],[]]],[[]]]=>[[[]],[[[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[[[[[]]]],[[]]]=>[[[]],[[[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[[[],[],[],[]],[]]=>[[],[[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[[[],[],[[]]],[]]=>[[],[[[]],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[]],[]]=>[[],[[],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[]]],[]]=>[[],[[[],[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[[]]]],[]]=>[[],[[[[]]],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[],[],[[]],[]]]=>[[[],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[]]]]]]]=>[[[[[[[]]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[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]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[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]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[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]
[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[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]
[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[],[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[]],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[[]]]],[[[]]],[]]=>[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[],[],[[]],[[]],[]]]=>[[[],[[]],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[],[],[[],[],[]],[]]]=>[[[],[[],[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[],[[[]],[]],[]]]=>[[[],[[],[[]]],[],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[],[],[[[],[]]],[]]]=>[[[],[[[],[]]],[],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[],[[]],[],[[]],[]]]=>[[[],[[]],[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[],[[]],[[],[]],[]]]=>[[[],[[],[]],[[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]]],[]]]=>[[[],[[[[[]]]]],[]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[[],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[[],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[[],[]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[],[[],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[[[],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[],[]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[[[],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[[[],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[[[[],[]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[],[[],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[[[[],[]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[[],[[],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[[[],[]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[],[[],[[],[[],[[],[[],[]]]]]]]=>[[[[[[[],[]],[]],[]],[]],[]],[]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[],[[],[[[],[]],[]]]]]]=>[[[[[[],[[],[]]],[]],[]],[]],[]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[],[[],[[[],[]],[[],[]]]]]]=>[[[[[[],[]],[[],[]]],[]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[],[[[],[[],[]]],[]]]]]=>[[[[[],[[[],[]],[]]],[]],[]],[]]=>[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[],[[[[],[]],[]],[]]]]]=>[[[[[],[[],[[],[]]]],[]],[]],[]]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[],[]],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[[],[]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[],[[[],[]],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[[],[]]],[]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[[[],[]],[]],[[],[]]]]]=>[[[[[],[]],[[],[[],[]]]],[]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[],[[[],[[],[[],[]]]],[]]]]=>[[[[],[[[[],[]],[]],[]]],[]],[]]=>[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[[],[[[],[]],[]]],[]]]]=>[[[[],[[[],[[],[]]],[]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[[],[]],[[],[]]],[]]]]=>[[[[],[[[],[]],[[],[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[[[],[]],[]],[]],[]]]]=>[[[[],[[],[[],[[],[]]]]],[]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[[],[]],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[[],[]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[[],[]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[],[]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[[],[]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[[],[]],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[[],[]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[[],[]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[],[]]],[]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[],[]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[[],[[],[]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[[[],[]],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[],[[[[],[]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[],[[[],[[],[[],[]]]],[[],[]]]]=>[[[[],[]],[[[[],[]],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[[],[[[],[]],[]]],[[],[]]]]=>[[[[],[]],[[[],[[],[]]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[[[],[]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[],[[[[],[[],[]]],[]],[[],[]]]]=>[[[[],[]],[[],[[[],[]],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[],[[[[[],[]],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[[],[]]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[],[[[],[[],[[],[[],[]]]]],[]]]=>[[[],[[[[[],[]],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[],[[],[[[],[]],[]]]],[]]]=>[[[],[[[[],[[],[]]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[[],[[[],[]],[[],[]]]],[]]]=>[[[],[[[[],[]],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[[],[[[],[[],[]]],[]]],[]]]=>[[[],[[[],[[[],[]],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[],[[[[],[]],[]],[]]],[]]]=>[[[],[[[],[[],[[],[]]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[[[],[]],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[[],[]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[[],[]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[],[[[[],[[],[]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[],[]],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[],[[[[[],[]],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[[],[]]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[],[[[[],[[],[[],[]]]],[]],[]]]=>[[[],[[],[[[[],[]],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[[],[[[],[]],[]]],[]],[]]]=>[[[],[[],[[[],[[],[]]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[],[[[[[],[]],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[],[[[[[],[[],[]]],[]],[]],[]]]=>[[[],[[],[[],[[[],[]],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[[[[],[]],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[[],[]]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[],[]],[[],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[]],[[],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[],[]],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[[],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[],[]],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[]],[[],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[]],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[[],[]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[],[]],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[],[]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[]],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[[],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[]],[[[],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[]]],[[],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[]],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[[],[]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[]],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[[],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[]],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[]],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[[],[]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[],[[],[]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[],[[],[]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[],[[],[]]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[[],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[],[[],[]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[],[]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[],[]],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[],[]],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[],[[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[[],[]],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[[],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[],[[],[[],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[]],[]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[],[[[],[]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[],[]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[],[]],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[],[[],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[]],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[],[[],[]]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[[],[]],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[[],[]],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[[],[]]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]
[[[[[],[]],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[],[[],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[[],[[[],[]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[],[]]],[]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[[[],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[],[[[],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[],[[[[],[]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[],[]]]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[[],[]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[[],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[]],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[[[],[]],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[[],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[[[],[]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[],[]]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[[[],[]],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[[],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[[],[[],[]]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[[],[]],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0]
[[[[[[],[]],[]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[],[[],[]]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]
[[[],[[],[[],[[],[[],[]]]]]],[]]=>[[],[[[[[[],[]],[]],[]],[]],[]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[],[[],[[[],[]],[]]]]],[]]=>[[],[[[[[],[[],[]]],[]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[],[[[],[]],[[],[]]]]],[]]=>[[],[[[[[],[]],[[],[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[[],[[[],[[],[]]],[]]]],[]]=>[[],[[[[],[[[],[]],[]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[[],[[[[],[]],[]],[]]]],[]]=>[[],[[[[],[[],[[],[]]]],[]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[],[[[],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[[],[]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[[],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[[],[[[[],[]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[],[]]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[[],[[[],[[],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[[],[[[],[[[],[]],[]]],[]]],[]]=>[[],[[[],[[[],[[],[]]],[]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[[],[[[[],[]],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[[],[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[[],[[[[],[[],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[]],[]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[[],[[[[[],[]],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[[],[]]]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[],[]],[[],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[]],[[],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[[],[]],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[[],[]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[],[]],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[],[]],[[[],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[]],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[[],[]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[],[[],[]]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[[[],[[],[]]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[[[[],[]],[]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[],[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]
[[[[[],[]],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]
[[[[],[[],[[],[]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[],[]],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[[[],[[[],[]],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[[],[]]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[[],[]],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0]
[[[[[],[[],[]]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[[],[]],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[[[],[]],[]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[],[[],[]]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0]
[[[[],[[],[[],[[],[]]]]],[]],[]]=>[[],[[],[[[[[],[]],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[[],[[[],[]],[]]]],[]],[]]=>[[],[[],[[[[],[[],[]]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[[[],[[[],[]],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[],[[[],[[],[]]],[]]],[]],[]]=>[[],[[],[[[],[[[],[]],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[],[[[[],[]],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[[],[]]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[[],[]],[[],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]
[[[[[],[]],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0]
[[[[[],[[],[]]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[[[],[]],[]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[[],[[],[[],[]]]],[]],[]],[]]=>[[],[[],[[],[[[[],[]],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[[],[[[],[]],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[[],[]]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[],[]],[[],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[]],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]
[[[[[[],[[],[]]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[[],[]],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]
[[[[[[[],[]],[]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[],[[],[]]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path is the depth of the tree.
This sends the maximal height of the Dyck path is the depth of the tree.
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.
searching the database
Sorry, this map was not found in the database.