Identifier
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Images
=>
Cc0021;cc-rep-0Cc0005;cc-rep-1Cc0021;cc-rep-2
[[]]=>[1,0]=>[[]]
[[],[]]=>[1,0,1,0]=>[[],[]]
[[[]]]=>[1,1,0,0]=>[[[]]]
[[],[],[]]=>[1,0,1,0,1,0]=>[[],[],[]]
[[],[[]]]=>[1,0,1,1,0,0]=>[[],[[]]]
[[[]],[]]=>[1,1,0,0,1,0]=>[[[]],[]]
[[[],[]]]=>[1,1,0,1,0,0]=>[[[],[]]]
[[[[]]]]=>[1,1,1,0,0,0]=>[[[[]]]]
[[],[],[],[]]=>[1,0,1,0,1,0,1,0]=>[[],[],[],[]]
[[],[],[[]]]=>[1,0,1,0,1,1,0,0]=>[[],[],[[]]]
[[],[[]],[]]=>[1,0,1,1,0,0,1,0]=>[[],[[]],[]]
[[],[[],[]]]=>[1,0,1,1,0,1,0,0]=>[[],[[],[]]]
[[],[[[]]]]=>[1,0,1,1,1,0,0,0]=>[[],[[[]]]]
[[[]],[],[]]=>[1,1,0,0,1,0,1,0]=>[[[]],[],[]]
[[[]],[[]]]=>[1,1,0,0,1,1,0,0]=>[[[]],[[]]]
[[[],[]],[]]=>[1,1,0,1,0,0,1,0]=>[[[],[]],[]]
[[[[]]],[]]=>[1,1,1,0,0,0,1,0]=>[[[[]]],[]]
[[[],[],[]]]=>[1,1,0,1,0,1,0,0]=>[[[],[],[]]]
[[[],[[]]]]=>[1,1,0,1,1,0,0,0]=>[[[],[[]]]]
[[[[]],[]]]=>[1,1,1,0,0,1,0,0]=>[[[[]],[]]]
[[[[],[]]]]=>[1,1,1,0,1,0,0,0]=>[[[[],[]]]]
[[[[[]]]]]=>[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]=>[[],[],[],[[]]]
[[],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]
[[],[],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0]=>[[],[],[[],[]]]
[[],[],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]
[[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]
[[],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]]]
[[],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]
[[],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]
[[],[[],[],[]]]=>[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]
[[],[[],[[]]]]=>[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]
[[],[[[]],[]]]=>[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]
[[],[[[],[]]]]=>[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]
[[],[[[[]]]]]=>[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]
[[[]],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[],[]]
[[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]]]
[[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[]]
[[[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]
[[[]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]
[[[],[]],[],[]]=>[1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[],[]]
[[[[]]],[],[]]=>[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]
[[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]
[[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]
[[[],[],[]],[]]=>[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]
[[[],[[]]],[]]=>[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]
[[[[]],[]],[]]=>[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]
[[[[],[]]],[]]=>[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]
[[[[[]]]],[]]=>[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]
[[[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]
[[[],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]
[[[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]
[[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]
[[[],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]
[[[[]],[],[]]]=>[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]
[[[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]
[[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]
[[[[[]]],[]]]=>[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]
[[[[],[],[]]]]=>[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]
[[[[],[[]]]]]=>[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]
[[[[[]],[]]]]=>[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]
[[[[[],[]]]]]=>[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]
[[[[[[]]]]]]=>[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]
[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]
[[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[[]]]
[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]
[[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[[],[]]]
[[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[[[]]]]
[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]
[[],[],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[[]],[[]]]
[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]
[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]
[[],[],[[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[[],[],[]]]
[[],[],[[],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[[],[[]]]]
[[],[],[[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[[[]],[]]]
[[],[],[[[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[[[],[]]]]
[[],[],[[[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[[[[]]]]]
[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]
[[],[[]],[],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[[]],[],[[]]]
[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[]]
[[],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[],[]]]
[[],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[[]],[[[]]]]
[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]
[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]
[[],[[],[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[],[]],[[]]]
[[],[[[]]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[[]]],[[]]]
[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[]],[]]
[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[],[[]]],[]]
[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[]],[]]
[[],[[[],[]]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[[],[]]],[]]
[[],[[[[]]]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[[[]]]],[]]
[[],[[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[]]]
[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[[]]]]
[[],[[],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[]]]
[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[],[[],[]]]]
[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[[],[[[]]]]]
[[],[[[]],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[],[]]]
[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]]]]
[[],[[[],[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[]],[]]]
[[],[[[[]]],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[[[]]],[]]]
[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[[],[],[]]]]
[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[[],[[]]]]]
[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[[[]],[]]]]
[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[[[],[]]]]]
[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[[[[]]]]]]
[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[]]
[[[]],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[[]]]
[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[]],[],[[]],[]]
[[[]],[],[[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[]],[],[[],[]]]
[[[]],[],[[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[]],[],[[[]]]]
[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[],[]]
[[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]]]
[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[],[]],[]]
[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[[]]],[]]
[[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[],[],[]]]
[[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[],[[]]]]
[[[]],[[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[]]]
[[[]],[[[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[[],[]]]]
[[[]],[[[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[[[]]]]]
[[[],[]],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[]],[],[],[]]
[[[[]]],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]]],[],[],[]]
[[[],[]],[],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[]],[],[[]]]
[[[[]]],[],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]]],[],[[]]]
[[[],[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[]]
[[[[]]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[]]
[[[],[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[],[]]]
[[[],[]],[[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[[]]]]
[[[[]]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]]],[[],[]]]
[[[[]]],[[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]]],[[[]]]]
[[[],[],[]],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[]],[],[]]
[[[],[[]]],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]]],[],[]]
[[[[]],[]],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[]],[],[]]
[[[[],[]]],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[],[]]],[],[]]
[[[[[]]]],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[]]]],[],[]]
[[[],[],[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[]],[[]]]
[[[],[[]]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]]],[[]]]
[[[[]],[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[]]]
[[[[],[]]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[],[]]],[[]]]
[[[[[]]]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[]]]],[[]]]
[[[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[]],[]]
[[[],[],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[[]]],[]]
[[[],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[]],[]]
[[[],[[],[]]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[[],[]]],[]]
[[[],[[[]]]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[[[]]]],[]]
[[[[]],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[],[]],[]]
[[[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]]],[]]
[[[[],[]],[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[],[]],[]],[]]
[[[[[]]],[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[[]]],[]],[]]
[[[[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[]]],[]]
[[[[],[[]]]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[],[[]]]],[]]
[[[[[]],[]]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[]]],[]]
[[[[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[],[]]]],[]]
[[[[[[]]]]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[]]]]],[]]
[[[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[]]]
[[[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[[]]]]
[[[],[],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[[]],[]]]
[[[],[],[[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[[],[]]]]
[[[],[],[[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[[[]]]]]
[[[],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[],[]]]
[[[],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]]]]
[[[],[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]],[]]]
[[[],[[[]]],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[[[]]],[]]]
[[[],[[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[[],[],[]]]]
[[[],[[],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[[],[[]]]]]
[[[],[[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[[[]],[]]]]
[[[],[[[],[]]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[[[],[]]]]]
[[[],[[[[]]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[[[[]]]]]]
[[[[]],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[]]]
[[[[]],[],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[],[[]]]]
[[[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[]]]
[[[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[[[[]],[[],[]]]]
[[[[]],[[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[[[]]]]]
[[[[],[]],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[],[]],[],[]]]
[[[[[]]],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[]]],[],[]]]
[[[[],[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]]]]
[[[[[]]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[[]]],[[]]]]
[[[[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[]],[]]]
[[[[],[[]]],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[[],[[]]],[]]]
[[[[[]],[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[]]]
[[[[[],[]]],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[],[]]],[]]]
[[[[[[]]]],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[[]]]],[]]]
[[[[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[]]]]
[[[[],[],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[[]]]]]
[[[[],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[]]]]
[[[[],[[],[]]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[[],[[],[]]]]]
[[[[],[[[]]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[[],[[[]]]]]]
[[[[[]],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[],[]]]]
[[[[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]]]]]
[[[[[],[]],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[],[]],[]]]]
[[[[[[]]],[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[[]]],[]]]]
[[[[[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[]]]]]
[[[[[],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]]]]]]
[[[[[[]],[]]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[]]]]]
[[[[[[],[]]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[[],[]]]]]]
[[[[[[[]]]]]]]=>[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]=>[[],[],[],[],[],[],[]]
[[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[],[[]]]
[[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]
[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[[],[]]]
[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[[[]]]]
[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]
[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[],[[]],[[]]]
[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]
[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]
[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[]]]
[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[[],[[]]]]
[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[],[[[]],[]]]
[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[],[[[],[]]]]
[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[],[[[[]]]]]
[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]
[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[],[[]],[],[[]]]
[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]
[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[],[[]],[[],[]]]
[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[],[[]],[[[]]]]
[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]
[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]
[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[]],[[]]]
[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[[[]]],[[]]]
[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]
[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]
[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]
[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]
[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]
[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[]]]
[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[[]]]]
[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[],[[],[[]],[]]]
[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[],[[],[[],[]]]]
[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[],[[],[[[]]]]]
[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[],[[[]],[],[]]]
[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[],[[[]],[[]]]]
[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[[[],[]],[]]]
[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[[[[]]],[]]]
[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[],[[[],[],[]]]]
[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[],[[[],[[]]]]]
[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[[[[]],[]]]]
[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[],[[[[],[]]]]]
[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[],[[[[[]]]]]]
[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]
[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[],[[]],[],[],[[]]]
[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[[]],[]]
[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[],[[]],[],[[],[]]]
[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[]],[],[[[]]]]
[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]
[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]],[[]]]
[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[]],[[],[]],[]]
[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[]],[[[]]],[]]
[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[]]]
[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[]],[[],[[]]]]
[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[[]],[[[]],[]]]
[[],[[]],[[[],[]]]]=>[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]=>[[],[[]],[[[[]]]]]
[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]
[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]
[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[]],[],[[]]]
[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[[]]],[],[[]]]
[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[]],[[]],[]]
[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[[]]],[[]],[]]
[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[[],[]],[[],[]]]
[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[]],[[[]]]]
[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[[]]],[[],[]]]
[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[],[[[]]],[[[]]]]
[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]
[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]
[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]
[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]
[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]
[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[]],[[]]]
[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[[]]],[[]]]
[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[[]],[]],[[]]]
[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[]]],[[]]]
[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[[[]]]],[[]]]
[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[]],[]]
[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[[]]],[]]
[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[[]],[]],[]]
[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[[],[]]],[]]
[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[[[]]]],[]]
[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[]],[]]
[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[[]],[[]]],[]]
[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[]],[]],[]]
[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[[[]]],[]],[]]
[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[]]],[]]
[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[]]]],[]]
[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[[[]],[]]],[]]
[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[]]]],[]]
[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[[[[]]]]],[]]
[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[]]]
[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[[]]]]
[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[[]],[]]]
[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[[],[]]]]
[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[[[]]]]]
[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[[]],[],[]]]
[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[[]],[[]]]]
[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[[],[]],[]]]
[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[[[]]],[]]]
[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[]]]]
[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[[],[[]]]]]
[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[[[]],[]]]]
[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[[[],[]]]]]
[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[],[[],[[[[]]]]]]
[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[],[[[]],[],[],[]]]
[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[[]],[],[[]]]]
[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[],[[[]],[[]],[]]]
[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[],[[[]],[[],[]]]]
[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[],[[[]],[[[]]]]]
[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[]],[],[]]]
[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[[[]]],[],[]]]
[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[]],[[]]]]
[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[[[]]],[[]]]]
[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[]],[]]]
[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[[]]],[]]]
[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[[[]],[]],[]]]
[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[]]],[]]]
[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[[[[]]]],[]]]
[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[]]]]
[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[[]]]]]
[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[[]],[]]]]
[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[[],[]]]]]
[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[],[[[],[[[]]]]]]
[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[],[[[[]],[],[]]]]
[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[[[]],[[]]]]]
[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[]],[]]]]
[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[[[[]]],[]]]]
[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[],[[[[],[],[]]]]]
[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[[]]]]]]
[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[],[[[[[]],[]]]]]
[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[],[[[[[],[]]]]]]
[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[],[[[[[[]]]]]]]
[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[]]
[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[],[[]]]
[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[]],[],[],[[]],[]]
[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[]],[],[],[[],[]]]
[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[]],[],[],[[[]]]]
[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[]],[],[[]],[],[]]
[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[]],[],[[]],[[]]]
[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[]],[],[[],[]],[]]
[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[[[]]],[]]
[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[]]]
[[[]],[],[[],[[]]]]=>[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]=>[[[]],[],[[[]],[]]]
[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[]],[],[[[],[]]]]
[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[]],[],[[[[]]]]]
[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[]],[[]],[],[],[]]
[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[]],[[]],[],[[]]]
[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[[]],[]]
[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[]],[[]],[[],[]]]
[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[]],[[]],[[[]]]]
[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[]],[],[]]
[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[[[]]],[],[]]
[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[]],[[]]]
[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[[[]]],[[]]]
[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[]],[]]
[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[[]]],[]]
[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[[[]],[]],[]]
[[[]],[[[],[]]],[]]=>[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]=>[[[]],[[[[]]]],[]]
[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[]]]
[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[[],[],[[]]]]
[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[]],[[],[[]],[]]]
[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[]],[[],[[],[]]]]
[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[]],[[],[[[]]]]]
[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[]],[[[]],[],[]]]
[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[]],[[[]],[[]]]]
[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[[[],[]],[]]]
[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[[[[]]],[]]]
[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[]],[[[],[],[]]]]
[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[]],[[[],[[]]]]]
[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[]],[[[[]],[]]]]
[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[]],[[[[],[]]]]]
[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[]],[[[[[]]]]]]
[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[]]
[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[]]
[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[[]]]
[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[[]]]
[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[[]],[]]
[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[[]],[]]
[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[],[]],[],[[],[]]]
[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[],[]],[],[[[]]]]
[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[]]],[],[[],[]]]
[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[]]],[],[[[]]]]
[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[]],[[]],[],[]]
[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[]]],[[]],[],[]]
[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[]],[[]],[[]]]
[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[]]],[[]],[[]]]
[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[]],[[],[]],[]]
[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[]],[[[]]],[]]
[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[]]],[[],[]],[]]
[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[]]],[[[]]],[]]
[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[]],[[],[],[]]]
[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[],[]],[[],[[]]]]
[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[]],[[[]],[]]]
[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[],[]],[[[],[]]]]
[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[]],[[[[]]]]]
[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[[]]],[[],[],[]]]
[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[[]]],[[],[[]]]]
[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[[]]],[[[]],[]]]
[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[[]]],[[[],[]]]]
[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[]]],[[[[]]]]]
[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[]]
[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[],[[]]],[],[],[]]
[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[]]
[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[],[]]],[],[],[]]
[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[]]]],[],[],[]]
[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[],[]],[],[[]]]
[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[],[[]]],[],[[]]]
[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[]],[]],[],[[]]]
[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[]]],[],[[]]]
[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[]]]],[],[[]]]
[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[]],[[]],[]]
[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[],[[]]],[[]],[]]
[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[]],[]],[[]],[]]
[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[]]],[[]],[]]
[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[]]]],[[]],[]]
[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[],[]],[[],[]]]
[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[],[]],[[[]]]]
[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[[]]],[[],[]]]
[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[],[[]]],[[[]]]]
[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[]],[]],[[],[]]]
[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[[]],[]],[[[]]]]
[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]]],[[],[]]]
[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[[],[]]],[[[]]]]
[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[[]]]],[[],[]]]
[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[]]]],[[[]]]]
[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[]],[],[]]
[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[[]]],[],[]]
[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[[]],[]],[],[]]
[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[],[[],[]]],[],[]]
[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[],[[[]]]],[],[]]
[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[]],[],[]]
[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[]],[[]]],[],[]]
[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[],[]],[]],[],[]]
[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[]]],[]],[],[]]
[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[]]],[],[]]
[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[[]]]],[],[]]
[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[]],[]]],[],[]]
[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[]]]],[],[]]
[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[[]]]]],[],[]]
[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[]],[[]]]
[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[[]]],[[]]]
[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[[]],[]],[[]]]
[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[],[[],[]]],[[]]]
[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[[[]]]],[[]]]
[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[]],[[]]]
[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[]],[[]]],[[]]]
[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[]],[]],[[]]]
[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[]]],[]],[[]]]
[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[]]],[[]]]
[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[[],[[]]]],[[]]]
[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[]],[]]],[[]]]
[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[],[]]]],[[]]]
[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[[]]]]],[[]]]
[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[]],[]]
[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[],[[]]],[]]
[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[],[[]],[]],[]]
[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[],[[],[]]],[]]
[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[],[[[]]]],[]]
[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[[]],[],[]],[]]
[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[],[[]],[[]]],[]]
[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[[],[]],[]],[]]
[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[[[]]],[]],[]]
[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[[],[],[]]],[]]
[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[[]]]],[]]
[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[[[]],[]]],[]]
[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[[[],[]]]],[]]
[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[[[[]]]]],[]]
[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[]],[]]
[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[],[[]]],[]]
[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[]],[[]],[]],[]]
[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[]],[[],[]]],[]]
[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[[]],[[[]]]],[]]
[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[]],[]]
[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[]]],[],[]],[]]
[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[]],[[]]],[]]
[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[[]]],[[]]],[]]
[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[]],[]],[]]
[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[[]]],[]],[]]
[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[]],[]],[]],[]]
[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[],[]]],[]],[]]
[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[[]]]],[]],[]]
[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[]]],[]]
[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[[]]]],[]]
[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[[]],[]]],[]]
[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[],[[],[]]]],[]]
[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[[],[[[]]]]],[]]
[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[]]],[]]
[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[]],[[]]]],[]]
[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[],[]],[]]],[]]
[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[[]]],[]]],[]]
[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[]]]],[]]
[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[[]]]]],[]]
[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[]],[]]]],[]]
[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[]]]]],[]]
[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[[]]]]]],[]]
[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[]]]
[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[[]]]]
[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[],[[]],[]]]
[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[[],[]]]]
[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[],[[[]]]]]
[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[],[[]],[],[]]]
[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[],[[]],[[]]]]
[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[[],[]],[]]]
[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[[[]]],[]]]
[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[[],[],[]]]]
[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[[],[[]]]]]
[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[],[[[]],[]]]]
[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[],[[[],[]]]]]
[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[],[[[[]]]]]]
[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[[]],[],[],[]]]
[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[],[[]],[],[[]]]]
[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[],[[]],[[]],[]]]
[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[],[[]],[[],[]]]]
[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[],[[]],[[[]]]]]
[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[[],[]],[],[]]]
[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[],[[[]]],[],[]]]
[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[]],[[]]]]
[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[],[[[]]],[[]]]]
[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[[],[],[]],[]]]
[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[],[[],[[]]],[]]]
[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[[[]],[]],[]]]
[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[]]],[]]]
[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[],[[[[]]]],[]]]
[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[]]]]
[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[[]]]]]
[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[[]],[]]]]
[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[[],[]]]]]
[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[],[[],[[[]]]]]]
[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[[[]],[],[]]]]
[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[[[]],[[]]]]]
[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[]],[]]]]
[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[],[[[[]]],[]]]]
[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[]]]]]
[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[[]]]]]]
[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[],[[[[]],[]]]]]
[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[],[[[[],[]]]]]]
[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[],[[[[[]]]]]]]
[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[],[]]]
[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[]],[],[],[[]]]]
[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[]],[],[[]],[]]]
[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[[],[]]]]
[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[[[]]]]]
[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[]],[[]],[],[]]]
[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]],[[]]]]
[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[[],[]],[]]]
[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[[[]]],[]]]
[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[]]]]
[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[]],[[],[[]]]]]
[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[[]],[[[]],[]]]]
[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[[]],[[[],[]]]]]
[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[]],[[[[]]]]]]
[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[]]]
[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[]]]
[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[[]]]]
[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[[]]]]
[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[[],[]],[[]],[]]]
[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[]]],[[]],[]]]
[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[]],[[],[]]]]
[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[]],[[[]]]]]
[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[]]],[[],[]]]]
[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[]]],[[[]]]]]
[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[]],[],[]]]
[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[[]]],[],[]]]
[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[]],[]],[],[]]]
[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[]]],[],[]]]
[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[[]]]],[],[]]]
[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[]],[[]]]]
[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[[]]],[[]]]]
[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[]],[]],[[]]]]
[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[]]],[[]]]]
[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[[]]]],[[]]]]
[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[]],[]]]
[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[[]]],[]]]
[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[[]],[]],[]]]
[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[]]],[]]]
[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[[[]]]],[]]]
[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[]],[]]]
[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[]],[[]]],[]]]
[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[]]]
[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[[]]],[]],[]]]
[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[]]],[]]]
[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[[]]]],[]]]
[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[]]],[]]]
[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[]]]],[]]]
[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[[]]]]],[]]]
[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[]]]]
[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[[]]]]]
[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[[]],[]]]]
[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[],[],[[],[]]]]]
[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[],[],[[[]]]]]]
[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[[]],[],[]]]]
[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[[]],[[]]]]]
[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[]],[]]]]
[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[[[]]],[]]]]
[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[]]]]]
[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[[]]]]]]
[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[],[[[]],[]]]]]
[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[[[],[]]]]]]
[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[[],[[[[]]]]]]]
[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[]]]]
[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[[]]]]]
[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[]],[[]],[]]]]
[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[]],[[],[]]]]]
[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[[]],[[[]]]]]]
[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[]],[],[]]]]
[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[[]]],[],[]]]]
[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[]],[[]]]]]
[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[[]]],[[]]]]]
[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[]],[]]]]
[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[],[[]]],[]]]]
[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[]],[]],[]]]]
[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[]]],[]]]]
[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[[]]]],[]]]]
[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[]]]]]
[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[[]]]]]]
[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[],[[]],[]]]]]
[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[[],[]]]]]]
[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[[[]]]]]]]
[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[]],[],[]]]]]
[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[[]],[[]]]]]]
[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[]],[]]]]]
[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[[]]],[]]]]]
[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[]]]]]]
[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[[]]]]]]]
[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[[[]],[]]]]]]
[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[]]]]]]]
[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[[]]]]]]]]
[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]
[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[],[],[[]]]
[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]
[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[],[[],[]]]
[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[],[[[]]]]
[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]
[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[],[],[[]],[[]]]
[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]
[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]
[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[],[[],[],[]]]
[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[],[[],[[]]]]
[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[],[],[[[]],[]]]
[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[],[],[[[],[]]]]
[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[],[],[[[[]]]]]
[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]
[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[],[],[[]],[],[[]]]
[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]
[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[],[],[[]],[[],[]]]
[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[],[],[[]],[[[]]]]
[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]
[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]
[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[],[[],[]],[[]]]
[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[],[[[]]],[[]]]
[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]
[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]
[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]
[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]
[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]
[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[],[]]]
[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[],[[],[],[[]]]]
[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[],[],[[],[[]],[]]]
[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[],[],[[],[[],[]]]]
[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[],[],[[],[[[]]]]]
[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[],[],[[[]],[],[]]]
[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[],[],[[[]],[[]]]]
[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[],[[[],[]],[]]]
[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[],[[[[]]],[]]]
[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[],[],[[[],[],[]]]]
[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[],[],[[[],[[]]]]]
[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[],[[[[]],[]]]]
[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[],[],[[[[],[]]]]]
[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[],[],[[[[[]]]]]]
[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]
[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[],[],[[]],[],[],[[]]]
[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]
[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[],[],[[]],[],[[],[]]]
[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[],[],[[]],[],[[[]]]]
[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]
[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[],[[]],[[]],[[]]]
[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]
[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]
[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[],[[]],[[],[],[]]]
[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[],[[]],[[],[[]]]]
[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[],[[]],[[[]],[]]]
[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[],[],[[]],[[[],[]]]]
[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[],[],[[]],[[[[]]]]]
[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]
[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]
[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[],[[],[]],[],[[]]]
[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[],[[[]]],[],[[]]]
[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]
[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]
[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[],[[],[]],[[],[]]]
[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[],[[],[]],[[[]]]]
[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[],[],[[[]]],[[],[]]]
[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[],[],[[[]]],[[[]]]]
[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]
[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]
[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]
[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]
[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]
[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[],[]],[[]]]
[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[],[[],[[]]],[[]]]
[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[],[[[]],[]],[[]]]
[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[],[[[],[]]],[[]]]
[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[],[[[[]]]],[[]]]
[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]
[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]
[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]
[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]
[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]
[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]
[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]
[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]
[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]
[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]
[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]
[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]
[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]
[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]
[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[],[]]]
[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[],[[]]]]
[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[],[],[[],[],[[]],[]]]
[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[],[[],[],[[],[]]]]
[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[],[[],[],[[[]]]]]
[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[],[],[[],[[]],[],[]]]
[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[],[],[[],[[]],[[]]]]
[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[],[[],[[],[]],[]]]
[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[],[[],[[[]]],[]]]
[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[],[[],[[],[],[]]]]
[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[],[[],[[],[[]]]]]
[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[],[[],[[[]],[]]]]
[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[],[[],[[[],[]]]]]
[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[],[],[[],[[[[]]]]]]
[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[],[],[[[]],[],[],[]]]
[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[],[],[[[]],[],[[]]]]
[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[],[],[[[]],[[]],[]]]
[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[],[],[[[]],[[],[]]]]
[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[],[],[[[]],[[[]]]]]
[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[],[[[],[]],[],[]]]
[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[],[[[[]]],[],[]]]
[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[],[[[],[]],[[]]]]
[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[],[[[[]]],[[]]]]
[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[],[[[],[],[]],[]]]
[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[],[[[],[[]]],[]]]
[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[],[[[[]],[]],[]]]
[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[],[[[[],[]]],[]]]
[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[],[[[[[]]]],[]]]
[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[],[],[[[],[],[],[]]]]
[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[],[],[[[],[],[[]]]]]
[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[],[[[],[[]],[]]]]
[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[],[[[],[[],[]]]]]
[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[],[],[[[],[[[]]]]]]
[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[],[],[[[[]],[],[]]]]
[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[],[],[[[[]],[[]]]]]
[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[],[[[[],[]],[]]]]
[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[],[[[[[]]],[]]]]
[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[],[],[[[[],[],[]]]]]
[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[],[],[[[[],[[]]]]]]
[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[],[],[[[[[]],[]]]]]
[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[],[],[[[[[],[]]]]]]
[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[],[],[[[[[[]]]]]]]
[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]
[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[],[[]],[],[],[],[[]]]
[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]
[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[],[[]],[],[],[[],[]]]
[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[],[[]],[],[],[[[]]]]
[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]
[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[],[[]],[[]]]
[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[[],[]],[]]
[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]
[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[],[[]],[],[[],[],[]]]
[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[]],[],[[],[[]]]]
[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[],[[]],[],[[[]],[]]]
[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[],[[]],[],[[[],[]]]]
[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[],[[]],[],[[[[]]]]]
[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]
[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[],[[]],[[]],[],[[]]]
[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[[]],[]]
[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[]],[[],[]]]
[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[],[[]],[[]],[[[]]]]
[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]
[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]
[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[]],[[],[]],[[]]]
[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[]],[[[]]],[[]]]
[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[]],[[],[],[]],[]]
[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[]],[[],[[]]],[]]
[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[]],[[[]],[]],[]]
[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[]],[[[],[]]],[]]
[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[]],[[[[]]]],[]]
[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[],[]]]
[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[]],[[],[],[[]]]]
[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[],[[]],[[],[[]],[]]]
[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[]],[[],[[],[]]]]
[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[],[[]],[[],[[[]]]]]
[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[]],[[[]],[],[]]]
[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[]],[[[]],[[]]]]
[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[]],[[[],[]],[]]]
[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[]],[[[[]]],[]]]
[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[]],[[[],[],[]]]]
[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[]],[[[],[[]]]]]
[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[]],[[[[]],[]]]]
[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[]],[[[[],[]]]]]
[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[]],[[[[[]]]]]]
[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]
[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]
[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[],[[],[]],[],[],[[]]]
[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[],[[[]]],[],[],[[]]]
[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]
[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]
[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[],[[],[]],[],[[],[]]]
[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[],[]],[],[[[]]]]
[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[],[[[]]],[],[[],[]]]
[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[],[[[]]],[],[[[]]]]
[[],[[],[]],[[]],[],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]
[[],[[[]]],[[]],[],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]
[[],[[],[]],[[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[],[]],[[]],[[]]]
[[],[[[]]],[[]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[],[[[]]],[[]],[[]]]
[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[[],[]],[]]
[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[[]]],[]]
[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[],[[[]]],[[],[]],[]]
[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[[[]]],[]]
[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[],[[],[]],[[],[],[]]]
[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[],[]],[[],[[]]]]
[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[],[[],[]],[[[]],[]]]
[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[],[[],[]],[[[],[]]]]
[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[],[[],[]],[[[[]]]]]
[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[],[[[]]],[[],[],[]]]
[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[],[[[]]],[[],[[]]]]
[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[],[[[]]],[[[]],[]]]
[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[],[[[]]],[[[],[]]]]
[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[],[[[]]],[[[[]]]]]
[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]
[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]
[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]
[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]
[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]
[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[],[]],[],[[]]]
[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[],[[]]],[],[[]]]
[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[],[[[]],[]],[],[[]]]
[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[],[[[],[]]],[],[[]]]
[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[],[[[[]]]],[],[[]]]
[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[],[]],[[]],[]]
[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[]]],[[]],[]]
[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[[]],[]],[[]],[]]
[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[],[[[],[]]],[[]],[]]
[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[]]]],[[]],[]]
[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[],[[],[],[]],[[],[]]]
[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[],[]],[[[]]]]
[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[],[[]]],[[],[]]]
[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[],[[],[[]]],[[[]]]]
[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[],[[[]],[]],[[],[]]]
[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[],[[[]],[]],[[[]]]]
[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[[],[]]],[[],[]]]
[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[],[[[],[]]],[[[]]]]
[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[[[]]]],[[],[]]]
[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[],[[[[]]]],[[[]]]]
[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]
[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]
[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]
[[],[[],[[],[]]],[],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]
[[],[[],[[[]]]],[],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]
[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]
[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]
[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]
[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]
[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]
[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]
[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]
[[],[[[[],[]]]],[],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]
[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]
[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[],[]],[[]]]
[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[],[[]]],[[]]]
[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[],[[]],[]],[[]]]
[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[],[[],[]]],[[]]]
[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[],[[[]]]],[[]]]
[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[],[[[]],[],[]],[[]]]
[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[],[[[]],[[]]],[[]]]
[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[],[[[],[]],[]],[[]]]
[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[],[[[[]]],[]],[[]]]
[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[],[]]],[[]]]
[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[],[[[],[[]]]],[[]]]
[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[],[[[[]],[]]],[[]]]
[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[],[[[[],[]]]],[[]]]
[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[],[[[[[]]]]],[[]]]
[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[]],[]]
[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[],[[]]],[]]
[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[],[[]],[]],[]]
[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[],[[],[]]],[]]
[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[],[[[]]]],[]]
[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[],[[]],[],[]],[]]
[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[],[[]],[[]]],[]]
[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[],[[],[]],[]],[]]
[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[],[[[]]],[]],[]]
[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[[],[],[]]],[]]
[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[],[[],[[]]]],[]]
[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[]],[]]],[]]
[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[],[[[],[]]]],[]]
[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[],[[[[]]]]],[]]
[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[]],[]]
[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[]],[],[[]]],[]]
[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[[]],[]],[]]
[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[],[[[]],[[],[]]],[]]
[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[],[[[]],[[[]]]],[]]
[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[],[[[],[]],[],[]],[]]
[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[[[]]],[],[]],[]]
[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[],[[[],[]],[[]]],[]]
[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[],[[[[]]],[[]]],[]]
[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[],[]],[]],[]]
[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[[],[[]]],[]],[]]
[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[]],[]],[]],[]]
[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[]]],[]],[]]
[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[[]]]],[]],[]]
[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[],[]]],[]]
[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[],[[]]]],[]]
[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[]],[]]],[]]
[[],[[[],[[],[]]]],[]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[]]]],[]]
[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[],[[[],[[[]]]]],[]]
[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[],[[[[]],[],[]]],[]]
[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[[[[]],[[]]]],[]]
[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[],[[[[],[]],[]]],[]]
[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[[[[]]],[]]],[]]
[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[],[]]]],[]]
[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[[[],[[]]]]],[]]
[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[[[[]],[]]]],[]]
[[],[[[[[],[]]]]],[]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[[[],[]]]]],[]]
[[],[[[[[[]]]]]],[]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[],[[[[[[]]]]]],[]]
[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[],[]]]
[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[],[[]]]]
[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[],[[]],[]]]
[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[],[[],[]]]]
[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[],[[[]]]]]
[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[],[[]],[],[]]]
[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[],[[]],[[]]]]
[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[],[[],[]],[]]]
[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[],[[[]]],[]]]
[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[],[[],[],[]]]]
[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[],[[],[[]]]]]
[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[],[[[]],[]]]]
[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[],[[[],[]]]]]
[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[],[[],[],[[[[]]]]]]
[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[],[[],[[]],[],[],[]]]
[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[],[[]],[],[[]]]]
[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[[]],[]]]
[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[],[[],[[]],[[],[]]]]
[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[],[[],[[]],[[[]]]]]
[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[],[[],[]],[],[]]]
[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[],[[[]]],[],[]]]
[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[],[[],[]],[[]]]]
[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[],[[[]]],[[]]]]
[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[],[[],[],[]],[]]]
[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[],[[],[[]]],[]]]
[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[],[[[]],[]],[]]]
[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[],[[[],[]]],[]]]
[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[],[[[[]]]],[]]]
[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[],[]]]]
[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[],[[],[[],[],[[]]]]]
[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[],[[],[[]],[]]]]
[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[],[[],[[],[]]]]]
[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[],[[],[[],[[[]]]]]]
[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[],[[],[[[]],[],[]]]]
[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[],[[[]],[[]]]]]
[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[],[[[],[]],[]]]]
[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[],[[[[]]],[]]]]
[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[],[[],[[[],[],[]]]]]
[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[],[[],[[[],[[]]]]]]
[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[],[[],[[[[]],[]]]]]
[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[],[[],[[[[],[]]]]]]
[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[],[[],[[[[[]]]]]]]
[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[],[[[]],[],[],[],[]]]
[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[],[[[]],[],[],[[]]]]
[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[],[[[]],[],[[]],[]]]
[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[],[[[]],[],[[],[]]]]
[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[],[[[]],[],[[[]]]]]
[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[[]],[],[]]]
[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]],[[]]]]
[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[],[[[]],[[],[]],[]]]
[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[],[[[]],[[[]]],[]]]
[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[],[[[]],[[],[],[]]]]
[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[],[[[]],[[],[[]]]]]
[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[],[[[]],[[[]],[]]]]
[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[],[[[]],[[[],[]]]]]
[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[],[[[]],[[[[]]]]]]
[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[],[[[],[]],[],[],[]]]
[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[],[[[[]]],[],[],[]]]
[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[],[[[],[]],[],[[]]]]
[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[],[[[[]]],[],[[]]]]
[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[],[[[],[]],[[]],[]]]
[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[],[[[[]]],[[]],[]]]
[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[],[]],[[],[]]]]
[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[],[[[],[]],[[[]]]]]
[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[[]]],[[],[]]]]
[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[],[[[[]]],[[[]]]]]
[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[],[]],[],[]]]
[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[],[[[],[[]]],[],[]]]
[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[],[[[[]],[]],[],[]]]
[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[],[[[[],[]]],[],[]]]
[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[],[[[[[]]]],[],[]]]
[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[],[]],[[]]]]
[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[],[[[],[[]]],[[]]]]
[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[],[[[[]],[]],[[]]]]
[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[],[]]],[[]]]]
[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[],[[[[[]]]],[[]]]]
[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[],[]],[]]]
[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[],[[]]],[]]]
[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[],[[[],[[]],[]],[]]]
[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[],[[],[]]],[]]]
[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[],[[[],[[[]]]],[]]]
[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[],[[[[]],[],[]],[]]]
[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[],[[[[]],[[]]],[]]]
[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[],[]],[]],[]]]
[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[[]]],[]],[]]]
[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[],[]]],[]]]
[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[],[[[[],[[]]]],[]]]
[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[],[[[[[]],[]]],[]]]
[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[[[],[]]]],[]]]
[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[],[[[[[[]]]]],[]]]
[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[],[]]]]
[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[],[[]]]]]
[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[],[[]],[]]]]
[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[],[[],[]]]]]
[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[],[[[],[],[[[]]]]]]
[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[],[[[],[[]],[],[]]]]
[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[],[[[],[[]],[[]]]]]
[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[],[[[],[[],[]],[]]]]
[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[],[[[],[[[]]],[]]]]
[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[],[[[],[[],[],[]]]]]
[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[],[[[],[[],[[]]]]]]
[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[],[[[],[[[]],[]]]]]
[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[],[[[],[[[],[]]]]]]
[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[],[[[],[[[[]]]]]]]
[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[],[[[[]],[],[],[]]]]
[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[[[]],[],[[]]]]]
[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[],[[[[]],[[]],[]]]]
[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[[[]],[[],[]]]]]
[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[],[[[[]],[[[]]]]]]
[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[],[[[[],[]],[],[]]]]
[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[],[[[[[]]],[],[]]]]
[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[],[[[[],[]],[[]]]]]
[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[],[[[[[]]],[[]]]]]
[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[],[]],[]]]]
[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[[[[],[[]]],[]]]]
[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[],[[[[[]],[]],[]]]]
[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[[[[],[]]],[]]]]
[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[],[[[[[[]]]],[]]]]
[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[],[[[[],[],[],[]]]]]
[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[],[[]]]]]]
[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[[[[],[[]],[]]]]]
[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[[[],[[],[]]]]]]
[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[],[[[[],[[[]]]]]]]
[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[],[[[[[]],[],[]]]]]
[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[],[[[[[]],[[]]]]]]
[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[],[[[[[],[]],[]]]]]
[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[],[[[[[[]]],[]]]]]
[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[],[],[]]]]]]
[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[[[[],[[]]]]]]]
[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[],[[[[[[]],[]]]]]]
[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[[[[[[],[]]]]]]]
[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[[[[[[]]]]]]]]
[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[],[]]
[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[],[],[[]]]
[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[]],[],[],[],[[]],[]]
[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[]],[],[],[],[[],[]]]
[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[]],[],[],[],[[[]]]]
[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[]],[],[],[[]],[],[]]
[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[]],[],[],[[]],[[]]]
[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[]],[],[],[[],[]],[]]
[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[],[[[]]],[]]
[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[],[[],[],[]]]
[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[]],[],[],[[],[[]]]]
[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[]],[],[],[[[]],[]]]
[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[]],[],[],[[[],[]]]]
[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[]],[],[],[[[[]]]]]
[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[[]],[],[],[]]
[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]],[],[[]]]
[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[]],[],[[]],[[]],[]]
[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[]],[],[[]],[[],[]]]
[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[]],[],[[]],[[[]]]]
[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[]],[],[[],[]],[],[]]
[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[],[[[]]],[],[]]
[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[],[[],[]],[[]]]
[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[],[[[]]],[[]]]
[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[],[[],[],[]],[]]
[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[],[[],[[]]],[]]
[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[],[[[]],[]],[]]
[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[]],[],[[[],[]]],[]]
[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[],[[[[]]]],[]]
[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[],[]]]
[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[],[[],[],[[]]]]
[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[]],[],[[],[[]],[]]]
[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[]],[],[[],[[],[]]]]
[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[]],[],[[],[[[]]]]]
[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[]],[],[[[]],[],[]]]
[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[]],[],[[[]],[[]]]]
[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[],[[[],[]],[]]]
[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[],[[[[]]],[]]]
[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[]],[],[[[],[],[]]]]
[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[]],[],[[[],[[]]]]]
[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[]],[],[[[[]],[]]]]
[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[]],[],[[[[],[]]]]]
[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[]],[],[[[[[]]]]]]
[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[[]],[],[],[],[]]
[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[]],[[]],[],[],[[]]]
[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[]],[[]],[],[[]],[]]
[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[]],[[]],[],[[],[]]]
[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[]],[[]],[],[[[]]]]
[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[[]],[],[]]
[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]],[[]]]
[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[]],[[],[]],[]]
[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[]],[[[]]],[]]
[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[]],[[],[],[]]]
[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[]],[[],[[]]]]
[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[]],[[[]],[]]]
[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[]],[[[],[]]]]
[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[]],[[[[]]]]]
[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[]],[[],[]],[],[],[]]
[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[]],[[[]]],[],[],[]]
[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[]],[[],[]],[],[[]]]
[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[]],[[[]]],[],[[]]]
[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[]],[[],[]],[[]],[]]
[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[]],[[[]]],[[]],[]]
[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]],[[],[]]]
[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[]],[[],[]],[[[]]]]
[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[]],[[[]]],[[],[]]]
[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[]],[[[]]],[[[]]]]
[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[],[]],[],[]]
[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[]],[[],[[]]],[],[]]
[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[]],[[[]],[]],[],[]]
[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[]],[[[],[]]],[],[]]
[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[]],[[[[]]]],[],[]]
[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[],[]],[[]]]
[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[]],[[],[[]]],[[]]]
[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[]],[[]]]
[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[]],[[[],[]]],[[]]]
[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[]],[[[[]]]],[[]]]
[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[],[]],[]]
[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[],[[]]],[]]
[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[]],[[],[[]],[]],[]]
[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[]],[[],[[],[]]],[]]
[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[]],[[],[[[]]]],[]]
[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[]],[[[]],[],[]],[]]
[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[]],[[[]],[[]]],[]]
[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[]],[[[],[]],[]],[]]
[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[]],[[[[]]],[]],[]]
[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[]],[[[],[],[]]],[]]
[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[]],[[[],[[]]]],[]]
[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[]],[[[[]],[]]],[]]
[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[]],[[[[],[]]]],[]]
[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[]],[[[[[]]]]],[]]
[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[],[]]]
[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[]],[[],[],[],[[]]]]
[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[]],[[],[],[[]],[]]]
[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[]],[[],[],[[],[]]]]
[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[]],[[],[],[[[]]]]]
[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[[]],[[],[[]],[],[]]]
[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[],[[]],[[]]]]
[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[[]],[[],[[],[]],[]]]
[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[]],[[],[[[]]],[]]]
[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[]],[[],[[],[],[]]]]
[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[]],[[],[[],[[]]]]]
[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[]],[[],[[[]],[]]]]
[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[]],[[],[[[],[]]]]]
[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[]],[[],[[[[]]]]]]
[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[]],[[[]],[],[],[]]]
[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[]],[[[]],[],[[]]]]
[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[]],[[]],[]]]
[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[]],[[[]],[[],[]]]]
[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[[]],[[[]],[[[]]]]]
[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[]],[[[],[]],[],[]]]
[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[]],[[[[]]],[],[]]]
[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[]],[[[],[]],[[]]]]
[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[]],[[[[]]],[[]]]]
[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[]],[[[],[],[]],[]]]
[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[]],[[[],[[]]],[]]]
[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[]]]
[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[]],[[[[],[]]],[]]]
[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[[]],[[[[[]]]],[]]]
[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[]],[[[],[],[],[]]]]
[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[]],[[[],[],[[]]]]]
[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[]],[[[],[[]],[]]]]
[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[]],[[[],[[],[]]]]]
[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[]],[[[],[[[]]]]]]
[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[]],[[[[]],[],[]]]]
[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[]],[[[[]],[[]]]]]
[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[]],[[[[],[]],[]]]]
[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[]],[[[[[]]],[]]]]
[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[[]],[[[[],[],[]]]]]
[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[]],[[[[],[[]]]]]]
[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[[]],[[[[[]],[]]]]]
[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[]],[[[[[],[]]]]]]
[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[]],[[[[[[]]]]]]]
[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[],[]]
[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[],[]]
[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[],[[]]]
[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[],[[]]]
[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[],[[]],[]]
[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[],[[]],[]]
[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[],[]],[],[],[[],[]]]
[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[],[]],[],[],[[[]]]]
[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[]]],[],[],[[],[]]]
[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[]]],[],[],[[[]]]]
[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[],[]],[],[[]],[],[]]
[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[]]],[],[[]],[],[]]
[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[],[]],[],[[]],[[]]]
[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[]]],[],[[]],[[]]]
[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[],[]],[],[[],[]],[]]
[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[],[]],[],[[[]]],[]]
[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[]]],[],[[],[]],[]]
[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[]]],[],[[[]]],[]]
[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[],[]],[],[[],[],[]]]
[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[],[]],[],[[],[[]]]]
[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[],[]],[],[[[]],[]]]
[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[],[]],[],[[[],[]]]]
[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[],[]],[],[[[[]]]]]
[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[]]],[],[[],[],[]]]
[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[]]],[],[[],[[]]]]
[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[]]],[],[[[]],[]]]
[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[]]],[],[[[],[]]]]
[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[]]],[],[[[[]]]]]
[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[],[]],[[]],[],[],[]]
[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[]]],[[]],[],[],[]]
[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[],[]],[[]],[],[[]]]
[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[]]],[[]],[],[[]]]
[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[[]],[]]
[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[[]],[]]
[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[]],[[],[]]]
[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[]],[[[]]]]
[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[]]],[[]],[[],[]]]
[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[]]],[[]],[[[]]]]
[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[[],[]],[],[]]
[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[],[]],[[[]]],[],[]]
[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[]]],[[],[]],[],[]]
[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[[[]]],[],[]]
[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[],[]],[[]]]
[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[],[]],[[[]]],[[]]]
[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[]]],[[],[]],[[]]]
[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[[]]],[[]]]
[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[],[]],[[],[],[]],[]]
[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[],[]],[[],[[]]],[]]
[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[],[]],[[[]],[]],[]]
[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[],[]],[[[],[]]],[]]
[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[],[]],[[[[]]]],[]]
[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[]]],[[],[],[]],[]]
[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[]]],[[],[[]]],[]]
[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[]]],[[[]],[]],[]]
[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[]]],[[[],[]]],[]]
[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[]]],[[[[]]]],[]]
[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[],[]],[[],[],[],[]]]
[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[],[]],[[],[],[[]]]]
[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[],[]],[[],[[]],[]]]
[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[]],[[],[[],[]]]]
[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[],[]],[[],[[[]]]]]
[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[],[]],[[[]],[],[]]]
[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[],[]],[[[]],[[]]]]
[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[]],[[[],[]],[]]]
[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[],[]],[[[[]]],[]]]
[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[],[]],[[[],[],[]]]]
[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[],[]],[[[],[[]]]]]
[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[],[]],[[[[]],[]]]]
[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[],[]],[[[[],[]]]]]
[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[],[]],[[[[[]]]]]]
[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[[]]],[[],[],[],[]]]
[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[[]]],[[],[],[[]]]]
[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[[]]],[[],[[]],[]]]
[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[]]],[[],[[],[]]]]
[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[]]],[[],[[[]]]]]
[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[[]]],[[[]],[],[]]]
[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[[]]],[[[]],[[]]]]
[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[]]],[[[],[]],[]]]
[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[[]]],[[[[]]],[]]]
[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[[]]],[[[],[],[]]]]
[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[[]]],[[[],[[]]]]]
[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[]]],[[[[]],[]]]]
[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[[]]],[[[[],[]]]]]
[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[]]],[[[[[]]]]]]
[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[],[]]
[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[],[[]]],[],[],[],[]]
[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[],[]]
[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[],[]]],[],[],[],[]]
[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[]]]],[],[],[],[]]
[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[],[]],[],[],[[]]]
[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[],[[]]],[],[],[[]]]
[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[]],[]],[],[],[[]]]
[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[],[]]],[],[],[[]]]
[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[]]]],[],[],[[]]]
[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[],[]],[],[[]],[]]
[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[],[[]]],[],[[]],[]]
[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[]],[]],[],[[]],[]]
[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[],[]]],[],[[]],[]]
[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[]]]],[],[[]],[]]
[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[],[],[]],[],[[],[]]]
[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[],[],[]],[],[[[]]]]
[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[],[[]]],[],[[],[]]]
[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[],[[]]],[],[[[]]]]
[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[]],[]],[],[[],[]]]
[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[]],[]],[],[[[]]]]
[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[],[]]],[],[[],[]]]
[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[],[]]],[],[[[]]]]
[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[]]]],[],[[],[]]]
[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[[]]]],[],[[[]]]]
[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[],[]],[[]],[],[]]
[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[[]]],[[]],[],[]]
[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[]],[]],[[]],[],[]]
[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[],[]]],[[]],[],[]]
[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[]]]],[[]],[],[]]
[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[],[]],[[]],[[]]]
[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[],[[]]],[[]],[[]]]
[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[]],[[]],[[]]]
[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[],[]]],[[]],[[]]]
[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[]]]],[[]],[[]]]
[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[],[]],[[],[]],[]]
[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[],[]],[[[]]],[]]
[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[],[[]]],[[],[]],[]]
[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[],[[]]],[[[]]],[]]
[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[]],[]],[[],[]],[]]
[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[]],[]],[[[]]],[]]
[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[],[]]],[[],[]],[]]
[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[],[]]],[[[]]],[]]
[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[[]]]],[[],[]],[]]
[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[]]]],[[[]]],[]]
[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[],[]],[[],[],[]]]
[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[],[],[]],[[],[[]]]]
[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[],[]],[[[]],[]]]
[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[],[],[]],[[[],[]]]]
[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[],[]],[[[[]]]]]
[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[],[[]]],[[],[],[]]]
[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[],[[]]],[[],[[]]]]
[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[],[[]]],[[[]],[]]]
[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[],[[]]],[[[],[]]]]
[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[],[[]]],[[[[]]]]]
[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[[]],[]],[[],[],[]]]
[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[[]],[]],[[],[[]]]]
[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[]],[[[]],[]]]
[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[[]],[]],[[[],[]]]]
[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[[]],[]],[[[[]]]]]
[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[[],[]]],[[],[],[]]]
[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[[],[]]],[[],[[]]]]
[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[[],[]]],[[[]],[]]]
[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[[],[]]],[[[],[]]]]
[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[],[]]],[[[[]]]]]
[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[[[]]]],[[],[],[]]]
[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[[[]]]],[[],[[]]]]
[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[[[[]]]],[[[]],[]]]
[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[[[]]]],[[[],[]]]]
[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[[]]]],[[[[]]]]]
[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[],[]],[],[],[]]
[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[],[],[[]]],[],[],[]]
[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[],[[]],[]],[],[],[]]
[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[],[[],[]]],[],[],[]]
[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[],[[[]]]],[],[],[]]
[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[]],[],[]],[],[],[]]
[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]],[[]]],[],[],[]]
[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[],[]],[]],[],[],[]]
[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[]]],[]],[],[],[]]
[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[],[],[]]],[],[],[]]
[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[],[[]]]],[],[],[]]
[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[]],[]]],[],[],[]]
[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[],[]]]],[],[],[]]
[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[]]]]],[],[],[]]
[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[],[],[]],[],[[]]]
[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[],[],[[]]],[],[[]]]
[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[],[[]],[]],[],[[]]]
[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[],[[],[]]],[],[[]]]
[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[],[[[]]]],[],[[]]]
[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[]],[],[]],[],[[]]]
[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]],[[]]],[],[[]]]
[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[],[]],[]],[],[[]]]
[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[[[]]],[]],[],[[]]]
[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[],[]]],[],[[]]]
[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[],[[]]]],[],[[]]]
[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[]],[]]],[],[[]]]
[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[],[]]]],[],[[]]]
[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[[]]]]],[],[[]]]
[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[],[]],[[]],[]]
[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[],[],[[]]],[[]],[]]
[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[],[[]],[]],[[]],[]]
[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[],[[],[]]],[[]],[]]
[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[],[[[]]]],[[]],[]]
[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[]],[],[]],[[]],[]]
[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]],[[]]],[[]],[]]
[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[],[]],[]],[[]],[]]
[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[]]],[]],[[]],[]]
[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[],[]]],[[]],[]]
[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[],[[]]]],[[]],[]]
[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[]],[]]],[[]],[]]
[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[],[]]]],[[]],[]]
[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[]]]]],[[]],[]]
[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[],[],[]],[[],[]]]
[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[],[],[]],[[[]]]]
[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[],[[]]],[[],[]]]
[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[],[],[[]]],[[[]]]]
[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[],[[]],[]],[[],[]]]
[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[],[[]],[]],[[[]]]]
[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[],[]]]
[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[],[[],[]]],[[[]]]]
[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[[]]]],[[],[]]]
[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[],[[[]]]],[[[]]]]
[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[]],[],[]],[[],[]]]
[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[[]],[],[]],[[[]]]]
[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]],[[]]],[[],[]]]
[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]],[[]]],[[[]]]]
[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[]],[]],[[],[]]]
[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[[],[]],[]],[[[]]]]
[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[]]],[]],[[],[]]]
[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[[[[]]],[]],[[[]]]]
[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[],[]]],[[],[]]]
[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[[],[],[]]],[[[]]]]
[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[],[[]]]],[[],[]]]
[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[],[[]]]],[[[]]]]
[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[]],[]]],[[],[]]]
[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[[[[]],[]]],[[[]]]]
[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[[],[]]]],[[],[]]]
[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[],[]]]],[[[]]]]
[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[[[[]]]]],[[],[]]]
[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[[]]]]],[[[]]]]
[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[],[]],[],[]]
[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[],[[]]],[],[]]
[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[],[[]],[]],[],[]]
[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[],[],[[],[]]],[],[]]
[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[],[],[[[]]]],[],[]]
[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[],[[]],[],[]],[],[]]
[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]],[[]]],[],[]]
[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[],[[],[]],[]],[],[]]
[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[],[[[]]],[]],[],[]]
[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[],[[],[],[]]],[],[]]
[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[],[[],[[]]]],[],[]]
[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[],[[[]],[]]],[],[]]
[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[],[[[],[]]]],[],[]]
[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[],[[[[]]]]],[],[]]
[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[],[]],[],[]]
[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[]],[],[[]]],[],[]]
[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[[]],[]],[],[]]
[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[]],[[],[]]],[],[]]
[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[]],[[[]]]],[],[]]
[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[],[]],[],[]],[],[]]
[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[[[]]],[],[]],[],[]]
[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[],[]],[[]]],[],[]]
[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[[]]],[[]]],[],[]]
[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[],[],[]],[]],[],[]]
[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[],[[]]],[]],[],[]]
[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[]],[]],[]],[],[]]
[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[],[]]],[]],[],[]]
[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[[]]]],[]],[],[]]
[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[],[]]],[],[]]
[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[],[[]]]],[],[]]
[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[],[[]],[]]],[],[]]
[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[],[[],[]]]],[],[]]
[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[],[[[]]]]],[],[]]
[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[[]],[],[]]],[],[]]
[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[[]],[[]]]],[],[]]
[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[],[]],[]]],[],[]]
[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[[]]],[]]],[],[]]
[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[],[]]]],[],[]]
[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[],[[]]]]],[],[]]
[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[[]],[]]]],[],[]]
[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[[],[]]]]],[],[]]
[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[]]]]]],[],[]]
[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[],[]],[[]]]
[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[],[[]]],[[]]]
[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[],[[]],[]],[[]]]
[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[],[],[[],[]]],[[]]]
[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[],[[[]]]],[[]]]
[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[],[[]],[],[]],[[]]]
[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]],[[]]],[[]]]
[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[],[[],[]],[]],[[]]]
[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[],[[[]]],[]],[[]]]
[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[],[[],[],[]]],[[]]]
[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[],[[],[[]]]],[[]]]
[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[],[[[]],[]]],[[]]]
[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[],[[[],[]]]],[[]]]
[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[],[[[[]]]]],[[]]]
[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[],[]],[[]]]
[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[[]],[],[[]]],[[]]]
[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[]],[]],[[]]]
[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[[]],[[],[]]],[[]]]
[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[[]],[[[]]]],[[]]]
[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[],[]],[],[]],[[]]]
[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[[[]]],[],[]],[[]]]
[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[],[]],[[]]],[[]]]
[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[[[]]],[[]]],[[]]]
[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[],[]],[]],[[]]]
[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[],[[]]],[]],[[]]]
[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[]],[]],[[]]]
[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[],[]]],[]],[[]]]
[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[[]]]],[]],[[]]]
[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[],[]]],[[]]]
[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[[],[],[[]]]],[[]]]
[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[],[[]],[]]],[[]]]
[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[],[[],[]]]],[[]]]
[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[],[[[]]]]],[[]]]
[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[[]],[],[]]],[[]]]
[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[[[]],[[]]]],[[]]]
[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[],[]],[]]],[[]]]
[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[[]]],[]]],[[]]]
[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[],[],[]]]],[[]]]
[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[],[[]]]]],[[]]]
[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[[]],[]]]],[[]]]
[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[[],[]]]]],[[]]]
[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[]]]]]],[[]]]
[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[],[]],[]]
[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[],[],[[]]],[]]
[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[],[],[[]],[]],[]]
[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[],[],[[],[]]],[]]
[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[],[],[[[]]]],[]]
[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[],[[]],[],[]],[]]
[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[],[],[[]],[[]]],[]]
[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[],[[],[]],[]],[]]
[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[],[[[]]],[]],[]]
[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[],[[],[],[]]],[]]
[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[],[[],[[]]]],[]]
[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[],[[[]],[]]],[]]
[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[],[[[],[]]]],[]]
[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[],[[[[]]]]],[]]
[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[],[[]],[],[],[]],[]]
[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[],[[]],[],[[]]],[]]
[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[[]],[]],[]]
[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[],[[]],[[],[]]],[]]
[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[],[[]],[[[]]]],[]]
[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[],[[],[]],[],[]],[]]
[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[],[[[]]],[],[]],[]]
[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[],[[],[]],[[]]],[]]
[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[],[[[]]],[[]]],[]]
[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[],[[],[],[]],[]],[]]
[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[],[[],[[]]],[]],[]]
[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[],[[[]],[]],[]],[]]
[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[],[[[],[]]],[]],[]]
[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[],[[[[]]]],[]],[]]
[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[],[[],[],[],[]]],[]]
[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[],[[]]]],[]]
[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[],[[],[[]],[]]],[]]
[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[],[[],[[],[]]]],[]]
[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[],[[],[[[]]]]],[]]
[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[],[[[]],[],[]]],[]]
[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[],[[[]],[[]]]],[]]
[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[],[[[],[]],[]]],[]]
[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[],[[[[]]],[]]],[]]
[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[],[[[],[],[]]]],[]]
[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[],[[[],[[]]]]],[]]
[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[],[[[[]],[]]]],[]]
[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[],[[[[],[]]]]],[]]
[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[],[[[[[]]]]]],[]]
[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[],[]],[]]
[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[],[],[[]]],[]]
[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[]],[],[[]],[]],[]]
[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[]],[],[[],[]]],[]]
[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[[]],[],[[[]]]],[]]
[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[[]],[],[]],[]]
[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]],[[]]],[]]
[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[[]],[[],[]],[]],[]]
[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[[]],[[[]]],[]],[]]
[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[[]],[[],[],[]]],[]]
[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[[]],[[],[[]]]],[]]
[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[[]],[[[]],[]]],[]]
[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[[]],[[[],[]]]],[]]
[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[[]],[[[[]]]]],[]]
[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[],[]],[]]
[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[[[]]],[],[],[]],[]]
[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[],[]],[],[[]]],[]]
[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[[[]]],[],[[]]],[]]
[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[],[]],[[]],[]],[]]
[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[[[]]],[[]],[]],[]]
[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[],[]],[[],[]]],[]]
[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[[],[]],[[[]]]],[]]
[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[[]]],[[],[]]],[]]
[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[[[]]],[[[]]]],[]]
[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[],[]],[],[]],[]]
[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[],[[]]],[],[]],[]]
[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[[]],[]],[],[]],[]]
[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[],[]]],[],[]],[]]
[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[[]]]],[],[]],[]]
[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[],[]],[[]]],[]]
[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[],[[]]],[[]]],[]]
[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[[]],[]],[[]]],[]]
[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[[],[]]],[[]]],[]]
[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[[]]]],[[]]],[]]
[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[],[]],[]],[]]
[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[],[[]]],[]],[]]
[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[],[[]],[]],[]],[]]
[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[],[[],[]]],[]],[]]
[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[],[[[]]]],[]],[]]
[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[[]],[],[]],[]],[]]
[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[[[]],[[]]],[]],[]]
[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[],[]],[]],[]],[]]
[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[[]]],[]],[]],[]]
[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[],[],[]]],[]],[]]
[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[],[[]]]],[]],[]]
[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[[]],[]]],[]],[]]
[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[[],[]]]],[]],[]]
[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[[]]]]],[]],[]]
[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[],[]]],[]]
[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[],[[]]]],[]]
[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[],[[]],[]]],[]]
[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[],[],[[],[]]]],[]]
[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[[],[],[[[]]]]],[]]
[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[],[[]],[],[]]],[]]
[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[],[[]],[[]]]],[]]
[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[],[[],[]],[]]],[]]
[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[],[[[]]],[]]],[]]
[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[],[[],[],[]]]],[]]
[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[],[[],[[]]]]],[]]
[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[],[[[]],[]]]],[]]
[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[],[[[],[]]]]],[]]
[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[],[[[[]]]]]],[]]
[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[],[]]],[]]
[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[[]],[],[[]]]],[]]
[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[[]],[]]],[]]
[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[]],[[],[]]]],[]]
[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[[]],[[[]]]]],[]]
[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[],[]],[],[]]],[]]
[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[[]]],[],[]]],[]]
[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[]],[[]]]],[]]
[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[[]]],[[]]]],[]]
[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[],[],[]],[]]],[]]
[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[],[[]]],[]]],[]]
[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[[]],[]],[]]],[]]
[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[[],[]]],[]]],[]]
[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[]]]],[]]],[]]
[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[],[]]]],[]]
[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[],[[]]]]],[]]
[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[],[[]],[]]]],[]]
[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[],[[],[]]]]],[]]
[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[],[[[]]]]]],[]]
[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[],[]]]],[]]
[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[[]],[[]]]]],[]]
[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[[],[]],[]]]],[]]
[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[]]],[]]]],[]]
[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[],[]]]]],[]]
[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[[]]]]]],[]]
[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[]],[]]]]],[]]
[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[]]]]]],[]]
[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[]]]]]]],[]]
[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[],[]]]
[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[],[[]]]]
[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[],[],[[]],[]]]
[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[],[[],[]]]]
[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[],[],[[[]]]]]
[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[],[],[[]],[],[]]]
[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[],[],[[]],[[]]]]
[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[],[[],[]],[]]]
[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[],[[[]]],[]]]
[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[],[[],[],[]]]]
[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[],[[],[[]]]]]
[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[],[],[[[]],[]]]]
[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[],[],[[[],[]]]]]
[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[],[],[[[[]]]]]]
[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[],[[]],[],[],[]]]
[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[],[],[[]],[],[[]]]]
[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[],[],[[]],[[]],[]]]
[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[],[],[[]],[[],[]]]]
[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[],[],[[]],[[[]]]]]
[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[],[[],[]],[],[]]]
[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[],[],[[[]]],[],[]]]
[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[],[],[[],[]],[[]]]]
[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[],[],[[[]]],[[]]]]
[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[],[[],[],[]],[]]]
[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[],[],[[],[[]]],[]]]
[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[],[[[]],[]],[]]]
[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[],[[[],[]]],[]]]
[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[],[],[[[[]]]],[]]]
[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[[],[],[],[]]]]
[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[],[[],[],[[]]]]]
[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[],[[],[[]],[]]]]
[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[],[[],[[],[]]]]]
[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[],[],[[],[[[]]]]]]
[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[],[[[]],[],[]]]]
[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[],[[[]],[[]]]]]
[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[],[[[],[]],[]]]]
[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[],[],[[[[]]],[]]]]
[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[],[],[[[],[],[]]]]]
[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[],[],[[[],[[]]]]]]
[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[],[],[[[[]],[]]]]]
[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[],[],[[[[],[]]]]]]
[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[],[],[[[[[]]]]]]]
[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[[]],[],[],[],[]]]
[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[],[[]],[],[],[[]]]]
[[[],[[]],[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[],[[]],[]]]
[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[],[[]],[],[[],[]]]]
[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[],[[]],[],[[[]]]]]
[[[],[[]],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[[]],[],[]]]
[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]],[[]]]]
[[[],[[]],[[],[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[],[[]],[[],[]],[]]]
[[[],[[]],[[[]]],[]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[],[[]],[[[]]],[]]]
[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[],[[]],[[],[],[]]]]
[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[],[[]],[[],[[]]]]]
[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[],[[]],[[[]],[]]]]
[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[],[[]],[[[],[]]]]]
[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[],[[]],[[[[]]]]]]
[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[],[[],[]],[],[],[]]]
[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[],[[[]]],[],[],[]]]
[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[],[[],[]],[],[[]]]]
[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[],[[[]]],[],[[]]]]
[[[],[[],[]],[[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[],[[],[]],[[]],[]]]
[[[],[[[]]],[[]],[]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[],[[[]]],[[]],[]]]
[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[[],[]],[[],[]]]]
[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[],[[],[]],[[[]]]]]
[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[],[[[]]],[[],[]]]]
[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[],[[[]]],[[[]]]]]
[[[],[[],[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[],[[],[],[]],[],[]]]
[[[],[[],[[]]],[],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[],[[],[[]]],[],[]]]
[[[],[[[]],[]],[],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[],[[[]],[]],[],[]]]
[[[],[[[],[]]],[],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[],[[[],[]]],[],[]]]
[[[],[[[[]]]],[],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[],[[[[]]]],[],[]]]
[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[],[]],[[]]]]
[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[],[[],[[]]],[[]]]]
[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[],[[[]],[]],[[]]]]
[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[],[[[],[]]],[[]]]]
[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[],[[[[]]]],[[]]]]
[[[],[[],[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[],[[],[],[],[]],[]]]
[[[],[[],[],[[]]],[]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[],[[],[],[[]]],[]]]
[[[],[[],[[]],[]],[]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[],[[],[[]],[]],[]]]
[[[],[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[],[[],[]]],[]]]
[[[],[[],[[[]]]],[]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[],[[],[[[]]]],[]]]
[[[],[[[]],[],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[],[[[]],[],[]],[]]]
[[[],[[[]],[[]]],[]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[],[[[]],[[]]],[]]]
[[[],[[[],[]],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[],[]],[]],[]]]
[[[],[[[[]]],[]],[]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[[]]],[]],[]]]
[[[],[[[],[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[],[]]],[]]]
[[[],[[[],[[]]]],[]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[],[[[],[[]]]],[]]]
[[[],[[[[]],[]]],[]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[],[[[[]],[]]],[]]]
[[[],[[[[],[]]]],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[[[[],[]]]],[]]]
[[[],[[[[[]]]]],[]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[],[[[[[]]]]],[]]]
[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[],[]]]]
[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[],[[]]]]]
[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[],[[]],[]]]]
[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[],[[],[]]]]]
[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[],[[],[],[[[]]]]]]
[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[],[[],[[]],[],[]]]]
[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[],[[],[[]],[[]]]]]
[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[],[[],[[],[]],[]]]]
[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[],[[],[[[]]],[]]]]
[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[],[[],[[],[],[]]]]]
[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[],[[],[[],[[]]]]]]
[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[],[[],[[[]],[]]]]]
[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[],[[],[[[],[]]]]]]
[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[],[[],[[[[]]]]]]]
[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[],[[[]],[],[],[]]]]
[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[],[[[]],[],[[]]]]]
[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[],[[[]],[[]],[]]]]
[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[],[[[]],[[],[]]]]]
[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[],[[[]],[[[]]]]]]
[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[],[[[],[]],[],[]]]]
[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[],[[[[]]],[],[]]]]
[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[],[[[],[]],[[]]]]]
[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[],[[[[]]],[[]]]]]
[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[],[]],[]]]]
[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[[[],[[]]],[]]]]
[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[],[[[[]],[]],[]]]]
[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[],[[[[],[]]],[]]]]
[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[],[[[[[]]]],[]]]]
[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[],[]]]]]
[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[],[[]]]]]]
[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[],[[[],[[]],[]]]]]
[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[],[[[],[[],[]]]]]]
[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[],[[[],[[[]]]]]]]
[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[],[[[[]],[],[]]]]]
[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[],[[[[]],[[]]]]]]
[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[],[[[[],[]],[]]]]]
[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[],[[[[[]]],[]]]]]
[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[],[[[[],[],[]]]]]]
[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[],[[[[],[[]]]]]]]
[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[],[[[[[]],[]]]]]]
[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[],[[[[[],[]]]]]]]
[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[],[[[[[[]]]]]]]]
[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[],[],[]]]
[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[]],[],[],[],[[]]]]
[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[]],[],[],[[]],[]]]
[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[],[[],[]]]]
[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[],[[[]]]]]
[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[[]],[],[]]]
[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[]],[],[[]],[[]]]]
[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[],[[],[]],[]]]
[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[],[[[]]],[]]]
[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[],[[],[],[]]]]
[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[]],[],[[],[[]]]]]
[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[]],[],[[[]],[]]]]
[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[[]],[],[[[],[]]]]]
[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[[]],[],[[[[]]]]]]
[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[[]],[],[],[]]]
[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[[]],[],[[]]]]
[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[[]],[]]]
[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[[]],[[]],[[],[]]]]
[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[[]],[[[]]]]]
[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[]],[[],[]],[],[]]]
[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[[]],[[[]]],[],[]]]
[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[[]],[[],[]],[[]]]]
[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[[]],[[[]]],[[]]]]
[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[[]],[[],[],[]],[]]]
[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[[]],[[],[[]]],[]]]
[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[]],[]],[]]]
[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[]],[[[],[]]],[]]]
[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[[]],[[[[]]]],[]]]
[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[],[]]]]
[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[[]],[[],[],[[]]]]]
[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[]],[[],[[]],[]]]]
[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[]],[[],[[],[]]]]]
[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[[]],[[],[[[]]]]]]
[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[]],[[[]],[],[]]]]
[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[[]],[[[]],[[]]]]]
[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[]],[[[],[]],[]]]]
[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[[]],[[[[]]],[]]]]
[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[[]],[[[],[],[]]]]]
[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[[]],[[[],[[]]]]]]
[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[[]],[[[[]],[]]]]]
[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[]],[[[[],[]]]]]]
[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[]],[[[[[]]]]]]]
[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[],[]]]
[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[],[]]]
[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[],[[]]]]
[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[],[[]]]]
[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[],[]],[],[[]],[]]]
[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[[]]],[],[[]],[]]]
[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[],[[],[]]]]
[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[],[]],[],[[[]]]]]
[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[[]]],[],[[],[]]]]
[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[[]]],[],[[[]]]]]
[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[],[]],[[]],[],[]]]
[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[[]]],[[]],[],[]]]
[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]],[[]]]]
[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[[]]],[[]],[[]]]]
[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[[],[]],[]]]
[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[]],[[[]]],[]]]
[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[]]],[[],[]],[]]]
[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[[[]]],[]]]
[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[],[]],[[],[],[]]]]
[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[],[]],[[],[[]]]]]
[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[[],[]],[[[]],[]]]]
[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[[],[]],[[[],[]]]]]
[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[],[]],[[[[]]]]]]
[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[[[]]],[[],[],[]]]]
[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[]]],[[],[[]]]]]
[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[[]]],[[[]],[]]]]
[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[[]]],[[[],[]]]]]
[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[]]],[[[[]]]]]]
[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[],[]],[],[],[]]]
[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[],[[]]],[],[],[]]]
[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[[]],[]],[],[],[]]]
[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[],[]]],[],[],[]]]
[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[]]]],[],[],[]]]
[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[],[]],[],[[]]]]
[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[]]],[],[[]]]]
[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[]],[]],[],[[]]]]
[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[],[]]],[],[[]]]]
[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[[]]]],[],[[]]]]
[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[[],[],[]],[[]],[]]]
[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[],[[]]],[[]],[]]]
[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[]],[[]],[]]]
[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[],[]]],[[]],[]]]
[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[[]]]],[[]],[]]]
[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[],[]],[[],[]]]]
[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[],[]],[[[]]]]]
[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[],[[]]],[[],[]]]]
[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[],[[]]],[[[]]]]]
[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[[]],[]],[[],[]]]]
[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[[]],[]],[[[]]]]]
[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[]]],[[],[]]]]
[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[],[]]],[[[]]]]]
[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[[]]]],[[],[]]]]
[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[]]]],[[[]]]]]
[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[],[]],[],[]]]
[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[],[[]]],[],[]]]
[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[],[[]],[]],[],[]]]
[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[],[[],[]]],[],[]]]
[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[],[[[]]]],[],[]]]
[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[[]],[],[]],[],[]]]
[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[[]],[[]]],[],[]]]
[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[],[]],[]],[],[]]]
[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[[]]],[]],[],[]]]
[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[],[]]],[],[]]]
[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[],[[]]]],[],[]]]
[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[[]],[]]],[],[]]]
[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[[],[]]]],[],[]]]
[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[]]]]],[],[]]]
[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[],[]],[[]]]]
[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[],[[]]],[[]]]]
[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[],[[]],[]],[[]]]]
[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[],[[],[]]],[[]]]]
[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[],[[[]]]],[[]]]]
[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[[]],[],[]],[[]]]]
[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[[]],[[]]],[[]]]]
[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[],[]],[]],[[]]]]
[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[[]]],[]],[[]]]]
[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[],[]]],[[]]]]
[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[],[[]]]],[[]]]]
[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[[]],[]]],[[]]]]
[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[[],[]]]],[[]]]]
[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[]]]]],[[]]]]
[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[],[]],[]]]
[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[],[[]]],[]]]
[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[],[[]],[]],[]]]
[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[],[[],[]]],[]]]
[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[],[[[]]]],[]]]
[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[],[[]],[],[]],[]]]
[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[],[[]],[[]]],[]]]
[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[[],[]],[]],[]]]
[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[],[[[]]],[]],[]]]
[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[],[]]],[]]]
[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[],[[],[[]]]],[]]]
[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[],[[[]],[]]],[]]]
[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[],[[[],[]]]],[]]]
[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[[[]]]]],[]]]
[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[],[]],[]]]
[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[[]],[],[[]]],[]]]
[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[]],[]],[]]]
[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[]],[[],[]]],[]]]
[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[]],[[[]]]],[]]]
[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[],[]],[],[]],[]]]
[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[[]]],[],[]],[]]]
[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[],[]],[[]]],[]]]
[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[[]]],[[]]],[]]]
[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[],[]],[]],[]]]
[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[],[[]]],[]],[]]]
[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[]],[]],[]]]
[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[[],[]]],[]],[]]]
[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[[]]]],[]],[]]]
[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[],[]]],[]]]
[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[],[[]]]],[]]]
[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[],[[]],[]]],[]]]
[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[[],[]]]],[]]]
[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[],[[[]]]]],[]]]
[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[[]],[],[]]],[]]]
[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[[]],[[]]]],[]]]
[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[],[]],[]]],[]]]
[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[[]]],[]]],[]]]
[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[],[]]]],[]]]
[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[[],[[]]]]],[]]]
[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[[]],[]]]],[]]]
[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[],[]]]]],[]]]
[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[]]]]]],[]]]
[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[],[]]]]
[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[],[[]]]]]
[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[],[[]],[]]]]
[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[],[],[],[[],[]]]]]
[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[],[],[],[[[]]]]]]
[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[],[[]],[],[]]]]
[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[],[[]],[[]]]]]
[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[],[[],[]],[]]]]
[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[],[[[]]],[]]]]
[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[],[],[[],[],[]]]]]
[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[],[[],[[]]]]]]
[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[],[],[[[]],[]]]]]
[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[],[[[],[]]]]]]
[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[[],[],[[[[]]]]]]]
[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[],[[]],[],[],[]]]]
[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[],[[]],[],[[]]]]]
[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[[]],[]]]]
[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[],[[]],[[],[]]]]]
[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[],[[]],[[[]]]]]]
[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[],[[],[]],[],[]]]]
[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[],[[[]]],[],[]]]]
[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[],[[],[]],[[]]]]]
[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[],[[[]]],[[]]]]]
[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[],[]],[]]]]
[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[],[[],[[]]],[]]]]
[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[],[[[]],[]],[]]]]
[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[],[[[],[]]],[]]]]
[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[],[[[[]]]],[]]]]
[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[],[]]]]]
[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[],[[]]]]]]
[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[],[[],[[]],[]]]]]
[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[],[[],[[],[]]]]]]
[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[],[[],[[[]]]]]]]
[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[],[[[]],[],[]]]]]
[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[],[[[]],[[]]]]]]
[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[],[[[],[]],[]]]]]
[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[],[[[[]]],[]]]]]
[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[[[],[],[]]]]]]
[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[[],[[]]]]]]]
[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[],[[[[]],[]]]]]]
[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[],[[[[],[]]]]]]]
[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[],[[[[[]]]]]]]]
[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[],[]]]]
[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[],[[]]]]]
[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[[]],[],[[]],[]]]]
[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[[[]],[],[[],[]]]]]
[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[[[]],[],[[[]]]]]]
[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[[]],[],[]]]]
[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]],[[]]]]]
[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[[]],[[],[]],[]]]]
[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[[]],[[[]]],[]]]]
[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[[]],[[],[],[]]]]]
[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[[]],[[],[[]]]]]]
[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[[[[]],[[[]],[]]]]]
[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[[[]],[[[],[]]]]]]
[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[[]],[[[[]]]]]]]
[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[],[]],[],[],[]]]]
[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[[]]],[],[],[]]]]
[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[],[]],[],[[]]]]]
[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[[]]],[],[[]]]]]
[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[],[]],[[]],[]]]]
[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[[]]],[[]],[]]]]
[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[],[]],[[],[]]]]]
[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[[],[]],[[[]]]]]]
[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[[]]],[[],[]]]]]
[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[[[[]]],[[[]]]]]]
[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[],[]],[],[]]]]
[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[],[[]]],[],[]]]]
[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[[]],[]],[],[]]]]
[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[[],[]]],[],[]]]]
[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[[]]]],[],[]]]]
[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[],[]],[[]]]]]
[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[],[[]]],[[]]]]]
[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[[]],[]],[[]]]]]
[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[[[],[]]],[[]]]]]
[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[[]]]],[[]]]]]
[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[],[]],[]]]]
[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[],[],[[]]],[]]]]
[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[],[[]],[]],[]]]]
[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[],[[],[]]],[]]]]
[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[],[[[]]]],[]]]]
[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[[]],[],[]],[]]]]
[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[[]],[[]]],[]]]]
[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[[],[]],[]],[]]]]
[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[[]]],[]],[]]]]
[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[],[]]],[]]]]
[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[[],[[]]]],[]]]]
[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[[]],[]]],[]]]]
[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[[],[]]]],[]]]]
[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[[]]]]],[]]]]
[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[],[]]]]]
[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[],[[]]]]]]
[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[],[],[[]],[]]]]]
[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[],[[],[]]]]]]
[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[],[[[]]]]]]]
[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[],[[]],[],[]]]]]
[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[],[[]],[[]]]]]]
[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[],[[],[]],[]]]]]
[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[],[[[]]],[]]]]]
[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[],[[],[],[]]]]]]
[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[],[[],[[]]]]]]]
[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[],[[[]],[]]]]]]
[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[],[[[],[]]]]]]]
[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[],[[[[]]]]]]]]
[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[]],[],[],[]]]]]
[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[[]],[],[[]]]]]]
[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[[]],[]]]]]
[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[[]],[[],[]]]]]]
[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[[]],[[[]]]]]]]
[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[],[]],[],[]]]]]
[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[[]]],[],[]]]]]
[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[],[]],[[]]]]]]
[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[]]],[[]]]]]]
[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[],[]],[]]]]]
[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[[],[[]]],[]]]]]
[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[[]],[]],[]]]]]
[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[[],[]]],[]]]]]
[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[[]]]],[]]]]]
[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[],[]]]]]]
[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[],[[]]]]]]]
[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[[],[[]],[]]]]]]
[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[[],[[],[]]]]]]]
[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[],[[[]]]]]]]]
[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[]],[],[]]]]]]
[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[[]],[[]]]]]]]
[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[],[]],[]]]]]]
[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[[]]],[]]]]]]
[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[],[]]]]]]]
[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[[]]]]]]]]
[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[[]],[]]]]]]]
[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[],[]]]]]]]]
[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[]]]]]]]]]
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path is the depth of the tree.
This sends the maximal height of the Dyck path is the depth of the tree.
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
searching the database
Sorry, this map was not found in the database.