Identifier
Mp00026:
Dyck paths
—to ordered tree⟶
Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00328: Ordered trees —DeBruijn-Morselt plane tree automorphism⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00328: Ordered trees —DeBruijn-Morselt plane tree automorphism⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0021;cc-rep-1Cc0021;cc-rep-2Cc0021;cc-rep-3
[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]=>[[[],[]],[]]=>[[],[[],[]]]=>[[[[]],[]]]
[1,1,0,1,0,1,0,0]=>[[[],[],[]]]=>[[[],[],[]]]=>[[[[]]],[]]
[1,1,0,1,1,0,0,0]=>[[[],[[]]]]=>[[[[]],[]]]=>[[],[[]],[]]
[1,1,1,0,0,0,1,0]=>[[[[]]],[]]=>[[],[[[]]]]=>[[[],[],[]]]
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[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]=>[[],[[],[]],[]]=>[[],[[],[]],[]]=>[[[[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]=>[[[],[],[]],[]]=>[[[[]]],[[]]]
[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]=>[[[[]],[]],[]]=>[[],[[]],[[]]]
[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]=>[[],[[[]]],[]]=>[[[],[],[[]]]]
[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]=>[[[],[]],[],[]]=>[[],[],[[],[]]]=>[[[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]=>[[[]],[[],[]]]=>[[],[[[]],[]]]
[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]=>[[],[[],[],[]]]=>[[[[[]]],[]]]
[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]=>[[[],[],[],[]]]=>[[[[[]]]],[]]
[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]=>[[[[]],[],[]]]=>[[],[[[]]],[]]
[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]=>[[],[[[]],[]]]=>[[[],[[]],[]]]
[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]=>[[[],[[[]]]]]=>[[[[[]]],[]]]=>[[],[],[[]],[]]
[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]=>[[],[],[[[]]]]=>[[[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]=>[[[]],[[[]]]]=>[[],[[],[],[]]]
[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]=>[[],[[],[[]]]]=>[[[[],[]],[]]]
[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]=>[[[],[],[[]]]]=>[[[[],[]]],[]]
[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]=>[[[[]],[[]]]]=>[[],[[],[]],[]]
[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]=>[[],[[[],[]]]]=>[[[[]],[],[]]]
[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]=>[[[],[[],[]]]]=>[[[[]],[]],[]]
[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]=>[[[[],[],[]]]]=>[[[[]]],[],[]]
[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]=>[[[[[]],[]]]]=>[[],[[]],[],[]]
[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]=>[[],[[[[]]]]]=>[[[],[],[],[]]]
[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]=>[[[],[[[]]]]]=>[[[],[],[]],[]]
[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]=>[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]=>[[[[]],[[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[[],[],[]]]=>[[[],[],[]],[],[]]=>[[[[]]],[[[]]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[[],[[]]]]=>[[[[]],[]],[],[]]=>[[],[[]],[[[]]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]=>[[[],[],[[[]]]]]
[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]=>[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]=>[[[[[]],[[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[],[]],[[]]]=>[[[]],[[],[]],[]]=>[[],[[[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]=>[[[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[]]]=>[[[],[],[],[]],[]]=>[[[[[]]]],[[]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[[]]]]=>[[[[]],[],[]],[]]=>[[],[[[]]],[[]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]=>[[[],[[]],[[]]]]
[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]=>[[],[[],[[[]]]]]=>[[[[[]]],[]],[]]=>[[],[],[[]],[[]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]=>[[[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[[]]],[[]]]=>[[[]],[[[]]],[]]=>[[],[[],[],[[]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]=>[[[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[],[]]]=>[[[],[],[[]]],[]]=>[[[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]]]]=>[[[[]],[[]]],[]]=>[[],[[],[]],[[]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]=>[[[[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[]],[]]]=>[[[],[[],[]]],[]]=>[[[[]],[]],[[]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[[],[],[]]]]=>[[[[],[],[]]],[]]=>[[[[]]],[],[[]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[[],[[]]]]]=>[[[[[]],[]]],[]]=>[[],[[]],[],[[]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]=>[[[],[],[],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[[[]]],[]]]=>[[[],[[[]]]],[]]=>[[[],[],[]],[[]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[[[]],[]]]]=>[[[[],[[]]]],[]]=>[[[],[]],[],[[]]]
[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]=>[[[]],[[],[]],[]]=>[[],[[],[]],[[]]]=>[[[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[],[],[]]]=>[[[],[],[]],[[]]]=>[[[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[],[[]]]]=>[[[[]],[]],[[]]]=>[[],[[]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[[]]],[]]=>[[],[[[]]],[[]]]=>[[[],[],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[]]]=>[[[],[[]]],[[]]]=>[[[],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[[],[]]]]=>[[[[],[]]],[[]]]=>[[[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[[[]]]]]=>[[[[[]]]],[[]]]=>[[],[],[],[[],[]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[]],[],[],[]]=>[[],[],[],[[],[]]]=>[[[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[]],[],[[]]]=>[[[]],[],[[],[]]]=>[[],[[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[]]=>[[],[[]],[[],[]]]=>[[[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[],[]]]=>[[[],[]],[[],[]]]=>[[[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[[]]]]=>[[[[]]],[[],[]]]=>[[],[],[[[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[]],[],[]]=>[[],[],[[],[],[]]]=>[[[[[[]]],[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[]],[[]]]=>[[[]],[[],[],[]]]=>[[],[[[[]]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[]],[]]=>[[],[[],[],[],[]]]=>[[[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[[[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[[],[[[[]]]],[]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[[]]],[]]=>[[],[[[]],[],[]]]=>[[[],[[[]]],[]]]
[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]=>[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[[],[],[[[]]],[]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]]],[],[]]=>[[],[],[[[]],[]]]=>[[[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]]],[[]]]=>[[[]],[[[]],[]]]=>[[],[[],[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[]],[]]=>[[],[[],[[]],[]]]=>[[[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[[[[],[[]]]],[]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[[],[[],[[]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[[],[]]],[]]=>[[],[[[],[]],[]]]=>[[[[]],[[]],[]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[[[[]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[[[[]]],[[]],[]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[[],[[]],[[]],[]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[[[]]]],[]]=>[[],[[[[]]],[]]]=>[[[],[],[[]],[]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[[[],[],[[]]],[]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[[[],[]],[[]],[]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[[[]],[],[[]],[]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[[],[],[],[[]],[]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]]],[],[],[]]=>[[],[],[],[[[]]]]=>[[[[[],[],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]]],[],[[]]]=>[[[]],[],[[[]]]]=>[[],[[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[]]=>[[],[[]],[[[]]]]=>[[[],[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]]],[[],[]]]=>[[[],[]],[[[]]]]=>[[[]],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]]],[[[]]]]=>[[[[]]],[[[]]]]=>[[],[],[[],[],[]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[]],[],[]]=>[[],[],[[],[[]]]]=>[[[[[],[]],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[]]]=>[[[]],[[],[[]]]]=>[[],[[[],[]],[]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[[[[[],[]]],[]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[[[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[[],[[[],[]]],[]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[[[],[[],[]],[]]]
[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]=>[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[[],[],[[],[]],[]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[],[]]],[],[]]=>[[],[],[[[],[]]]]=>[[[[[]],[],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[],[]]],[[]]]=>[[[]],[[[],[]]]]=>[[],[[[]],[],[]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[[[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[[[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[[],[[[]],[]],[]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[[[[[]]],[],[]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[[[[[]]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[[[[[]]]],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[[],[[[]]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[[[],[[]],[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[[[],[[]],[]],[]]
[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]=>[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[[],[],[[]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[]]]],[],[]]=>[[],[],[[[[]]]]]=>[[[[],[],[],[]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[]]]],[[]]]=>[[[]],[[[[]]]]]=>[[],[[],[],[],[]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[[[[],[],[]],[]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[[[[],[],[]]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[[],[[],[],[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[[[[],[]],[],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[[[[],[]],[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[[[[],[]]],[],[]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[[],[[],[]],[],[]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[[[[]],[],[],[]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[[[[]],[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[[[[]],[]],[],[]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[[[[]]],[],[],[]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[[],[[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[[[],[],[],[],[]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[[[],[],[],[]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[[[],[],[]],[],[]]
[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]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[[[[]],[[[[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[[[[]]],[[[[]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[[],[[]],[[[[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[[[],[],[[[[]]]]]]
[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]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[[[[[]],[[[]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[[],[[[]],[[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[[[[[]]],[[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[[[[[]]]],[[[]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[[],[[[]]],[[[]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[[[],[[]],[[[]]]]]
[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]=>[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[[],[],[[]],[[[]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[[[[],[],[[[]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[[],[[],[],[[[]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[[[[],[]],[[[]]]]]
[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]=>[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[[],[[],[]],[[[]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[[[[]],[],[[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[[[[]],[]],[[[]]]]
[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]=>[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[[],[[]],[],[[[]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[[[],[],[],[[[]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[[[],[],[]],[[[]]]]
[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]=>[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[[[[]],[[],[[]]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[[[[]]],[[],[[]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[[[],[],[[],[[]]]]]
[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]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[[[[[[]],[[]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[[],[[[[]],[[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[[[],[[[]],[[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[[[]],[[[]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[[],[],[[[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[[[[[[]]],[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[[],[[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[[[[[[]]]],[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[[[[[[]]]]],[[]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[[],[[[[]]]],[[]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[[[],[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[[[],[[[]]]],[[]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[[[]],[[[]]],[[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[[],[],[[[]]],[[]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[[[[],[[]],[[]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[[],[[],[[]],[[]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[[[[],[[]]],[[]]]]
[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]=>[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[[],[[],[[]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[[[[]],[[]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[[[[]],[[]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[[[[]]],[[]],[[]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[[],[[]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[[[],[],[[]],[[]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[[[],[],[[]]],[[]]]
[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]=>[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[[],[],[],[[]],[[]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[[[[[],[],[[]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[[],[[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[[[],[[],[],[[]]]]]
[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]=>[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[[],[],[[],[],[[]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[[[[[],[]],[[]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[[],[[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[[[[[],[]]],[[]]]]
[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]=>[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[[],[[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[[[],[[],[]],[[]]]]
[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]=>[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[[],[],[[],[]],[[]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[[[[[]],[],[[]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[[],[[[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[[[[[]],[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[[[[[]],[]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[[],[[[]],[]],[[]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[[[[[]]],[],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[[[[[]]],[]],[[]]]
[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]=>[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[[],[[[]]],[],[[]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[[[],[[]],[],[[]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[[[],[[]],[]],[[]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[[[],[[]]],[],[[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[[[]],[[]],[],[[]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[[],[],[[]],[],[[]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[[[[],[],[],[[]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[[],[[],[],[],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[[[[],[],[]],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[[[[],[],[]]],[[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[[],[[],[],[]],[[]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[[[[],[]],[],[[]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[[[[],[]],[]],[[]]]
[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]=>[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[[],[[],[]],[],[[]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[[[[]],[],[],[[]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[[[[]],[],[]],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[[[[]],[]],[],[[]]]
[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]=>[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[[],[[]],[],[],[[]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[[[],[],[],[],[[]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[[[],[],[],[]],[[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[[[],[],[]],[],[[]]]
[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]=>[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[[[[]],[[[],[]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[[[[]]],[[[],[]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[[],[[]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[[[],[],[[[],[]]]]]
[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]=>[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[[[[[]],[[],[]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[[],[[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[[[[[]]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[[[[[]]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[[],[[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[[[],[[]],[[],[]]]]
[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]=>[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[[],[],[[]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[[[[],[],[[],[]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[[],[[],[],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[[[[],[]],[[],[]]]]
[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]=>[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[[],[[],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[[[[]],[],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[[[[]],[]],[[],[]]]
[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]=>[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[[],[[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[[[],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[[[],[],[]],[[],[]]]
[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]=>[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[[[[[[[]],[]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[[],[[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[[[],[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[[[]],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[[],[],[[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[[[[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[[],[[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[[[[]],[[[]],[]]]]
[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]=>[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[[],[[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[[[],[],[[[]],[]]]]
[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]=>[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[[],[],[],[[[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[[[[[[[]]],[]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[[],[[[[[]]],[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[[[],[[[[]]],[]]]]
[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]=>[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[[],[],[[[[]]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[[[[[[[]]]],[]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[[],[[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[[[[[[[]]]]],[]]]
[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]=>[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[[],[[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[[[],[[[[]]]],[]]]
[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]=>[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[[],[],[[[[]]]],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[[[[],[[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[[],[[],[[[]]],[]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[[[[],[[[]]]],[]]]
[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]=>[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[[],[[],[[[]]]],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[[[[]],[[[]]],[]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[[[[]],[[[]]]],[]]
[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]=>[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[[],[[]],[[[]]],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]
[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]=>[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[[],[],[],[[[]]],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[[[[[],[[]],[]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[[],[[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[[[],[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[[[]],[[],[[]],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[[],[],[[],[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[[[[[],[[]]],[]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[[],[[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[[[[[],[[]]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[[[[[],[[]]]]],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[[],[[[],[[]]]],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[[[],[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[[[],[[],[[]]]],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[[[]],[[],[[]]],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[[],[],[[],[[]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[[[[[]],[[]],[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[[],[[[]],[[]],[]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[[[[[]],[[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[[[[[]],[[]]]],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[[],[[[]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[[[[[]]],[[]],[]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[[[[[]]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[[[[[]]]],[[]],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[[],[[[]]],[[]],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[[[],[[]],[[]],[]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[[[],[[]],[[]]],[]]
[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]=>[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[[],[],[[]],[[]],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[[[[],[],[[]],[]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[[],[[],[],[[]],[]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[[[[],[],[[]]],[]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[[[[],[],[[]]]],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[[],[[],[],[[]]],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[[[[],[]],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[[[[],[]],[[]]],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[[[[],[]]],[[]],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[[],[[],[]],[[]],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[[[[]],[],[[]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[[[[]],[],[[]]],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[[[[]],[]],[[]],[]]
[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]=>[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[[],[[]],[],[[]],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[[[],[],[],[[]],[]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[[[],[],[],[[]]],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[[[],[],[]],[[]],[]]
[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]=>[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[[],[],[],[],[[]],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[[[[[[],[],[]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[[],[[[[],[],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[[[],[[[],[],[]]]]]
[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]=>[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[[],[],[[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[[[[],[[],[],[]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[[],[[],[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[[[[]],[[],[],[]]]]
[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]=>[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[[],[[]],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[[[],[],[[],[],[]]]]
[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]=>[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[[],[],[],[[],[],[]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[[[[[[],[]],[]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[[],[[[[],[]],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[[[],[[[],[]],[]]]]
[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]=>[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[[],[],[[[],[]],[]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[[[[[[],[]]],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[[],[[[[],[]]],[]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[[[[[[],[]]]],[]]]
[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]=>[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[[],[[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[[[],[[[],[]]],[]]]
[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]=>[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[[],[],[[[],[]]],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[[[[],[[],[]],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[[],[[],[[],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[[[[],[[],[]]],[]]]
[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]=>[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[[],[[],[[],[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]
[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]=>[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[[],[[]],[[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[[[],[],[[],[]],[]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[[[],[],[[],[]]],[]]
[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]=>[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[[],[],[],[[],[]],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[[[[[[]],[],[]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[[],[[[[]],[],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[[[],[[[]],[],[]]]]
[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]=>[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[[],[],[[[]],[],[]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[[[[[[]],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[[],[[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[[[[[[]],[]]],[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[[[[[[]],[]]]],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[[],[[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[[[],[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[[[],[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[[[]],[[[]],[]],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[[],[],[[[]],[]],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[[[[[[]]],[],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[[],[[[[]]],[],[]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[[[[[[]]],[]],[]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[[[[[[]]],[]]],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[[],[[[[]]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[[[[[[]]]],[],[]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[[[[[[]]]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[[[[[[]]]]],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[[],[[[[]]]],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[[[],[[[]]],[],[]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[[[],[[[]]],[]],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[[[],[[[]]]],[],[]]
[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]=>[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[[],[],[[[]]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[[[[],[[]],[],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[[],[[],[[]],[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[[[[],[[]],[]],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[[[[],[[]],[]]],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[[],[[],[[]],[]],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[[[[],[[]]],[],[]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[[[[],[[]]],[]],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[[[[],[[]]]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[[],[[],[[]]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[[[[]],[[]],[],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[[[[]],[[]],[]],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[[[[]],[[]]],[],[]]
[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]=>[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[[],[[]],[[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[[[],[],[[]],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[[[],[],[[]],[]],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[[[],[],[[]]],[],[]]
[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]=>[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[[],[],[],[[]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[[[[[],[],[],[]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[[],[[[],[],[],[]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[[[],[[],[],[],[]]]]
[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]=>[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[[],[],[[],[],[],[]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[[[[[],[],[]],[]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[[],[[[],[],[]],[]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[[[[[],[],[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[[[[[],[],[]]]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[[],[[[],[],[]]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[[[],[[],[],[]],[]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[[[],[[],[],[]]],[]]
[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]=>[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[[[[[],[]],[],[]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[[],[[[],[]],[],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[[[[[],[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[[[[[],[]],[]]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[[],[[[],[]],[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[[[[[],[]]],[],[]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[[[[[],[]]],[]],[]]
[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]=>[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[[],[[[],[]]],[],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[[[],[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[[[],[[],[]],[]],[]]
[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]=>[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[[],[],[[],[]],[],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[[[[[]],[],[],[]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[[],[[[]],[],[],[]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[[[[[]],[],[]],[]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[[[[[]],[],[]]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[[[[[]],[]],[],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[[[[[]],[]],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[[[[[]],[]]],[],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[[],[[[]],[]],[],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[[[[[]]],[],[],[]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[[[[[]]],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[[[[[]]],[]],[],[]]
[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]=>[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[[],[[[]]],[],[],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[[[],[[]],[],[],[]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[[[],[[]],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[[[],[[]],[]],[],[]]
[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]=>[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[[],[],[[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[[[[],[],[],[],[]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[[],[[],[],[],[],[]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[[[[],[],[],[]],[]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[[[[],[],[],[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[[],[[],[],[],[]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[[[[],[],[]],[],[]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[[[[],[],[]],[]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[[[[],[],[]]],[],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[[],[[],[],[]],[],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[[[[],[]],[],[],[]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[[[[],[]],[],[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[[[[],[]],[]],[],[]]
[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]=>[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[[],[[],[]],[],[],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[[[[]],[],[],[],[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[[[[]],[],[],[]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[[[[]],[],[]],[],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[[[[]],[]],[],[],[]]
[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]=>[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[[],[[]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[[[],[],[],[],[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[[[],[],[],[],[]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[[[],[],[],[]],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[[[],[],[]],[],[],[]]
[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]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[[[[]],[[[[[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[[[[]]],[[[[[]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[[],[[]],[[[[[]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]=>[[[],[],[[[[[]]]]]]]
[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]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[[[[[]],[[[[]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[[],[[[]],[[[[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[[[[[]]],[[[[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[[[[[]]]],[[[[]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[[],[[[]]],[[[[]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[[[],[[]],[[[[]]]]]]
[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]=>[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[[],[],[[]],[[[[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[[[[],[],[[[[]]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[[],[[],[],[[[[]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[[[[],[]],[[[[]]]]]]
[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]=>[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[[],[[],[]],[[[[]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[[[[]],[],[[[[]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[[[[]],[]],[[[[]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[[[[]]],[],[[[[]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[[],[[]],[],[[[[]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[[[],[],[],[[[[]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[[[],[],[]],[[[[]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[[[],[]],[],[[[[]]]]]
[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]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[[[[]],[[],[[[]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[[[[]]],[[],[[[]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[[],[[]],[[],[[[]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]=>[[[],[],[[],[[[]]]]]]
[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]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[[[[[[]],[[[]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[[],[[[[]],[[[]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[[[],[[[]],[[[]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[[[]],[[[]],[[[]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[[],[],[[[]],[[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[[[[[[]]],[[[]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[[],[[[[]]],[[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[[[[[[]]]],[[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[[[[[[]]]]],[[[]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[[],[[[[]]]],[[[]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[[[],[[[]]],[[[]]]]]
[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]=>[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[[],[],[[[]]],[[[]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[[[[],[[]],[[[]]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[[],[[],[[]],[[[]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[[[[],[[]]],[[[]]]]]
[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]=>[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[[],[[],[[]]],[[[]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[[[[]],[[]],[[[]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[[[[]],[[]]],[[[]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[[[[]]],[[]],[[[]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[[],[[]],[[]],[[[]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[[[],[],[[]],[[[]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[[[],[],[[]]],[[[]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[[[],[]],[[]],[[[]]]]
[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]=>[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[[],[],[],[[]],[[[]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[[[[[],[],[[[]]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[[],[[[],[],[[[]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[[[],[[],[],[[[]]]]]]
[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]=>[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[[],[],[[],[],[[[]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[[[[[],[]],[[[]]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[[],[[[],[]],[[[]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[[[[[],[]]],[[[]]]]]
[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]=>[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[[],[[[],[]]],[[[]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[[[],[[],[]],[[[]]]]]
[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]=>[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[[],[],[[],[]],[[[]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[[[[[]],[],[[[]]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[[],[[[]],[],[[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[[[[[]],[]],[[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[[[[[]],[]]],[[[]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[[],[[[]],[]],[[[]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[[[[[]]],[],[[[]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[[[[[]]],[]],[[[]]]]
[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]=>[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[[],[[[]]],[],[[[]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[[[],[[]],[],[[[]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[[[],[[]],[]],[[[]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[[[],[[]]],[],[[[]]]]
[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]=>[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[[],[],[[]],[],[[[]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[[[[],[],[],[[[]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[[],[[],[],[],[[[]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]=>[[[[],[],[]],[[[]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[[[[],[],[]]],[[[]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[[],[[],[],[]],[[[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[[[[],[]],[],[[[]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[[[[],[]],[]],[[[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[[[[],[]]],[],[[[]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[[],[[],[]],[],[[[]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[[[[]],[],[],[[[]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[[[[]],[],[]],[[[]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[[[[]],[]],[],[[[]]]]
[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]=>[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[[],[[]],[],[],[[[]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[[[],[],[],[],[[[]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[[[],[],[],[]],[[[]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[[[],[],[]],[],[[[]]]]
[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]=>[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[[[[]],[[[],[[]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[[[[]]],[[[],[[]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[[],[[]],[[[],[[]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[[[],[],[[[],[[]]]]]]
[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]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[[[[[]],[[],[[]]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[[],[[[]],[[],[[]]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[[[[[]]],[[],[[]]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[[[[[]]]],[[],[[]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[[],[[[]]],[[],[[]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[[[],[[]],[[],[[]]]]]
[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]=>[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[[],[],[[]],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[[[[],[],[[],[[]]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[[],[[],[],[[],[[]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[[[[],[]],[[],[[]]]]]
[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]=>[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[[],[[],[]],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[[[[]],[],[[],[[]]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[[[[]],[]],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[[[[]]],[],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[[],[[]],[],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[[[],[],[],[[],[[]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[[[],[],[]],[[],[[]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[[[],[]],[],[[],[[]]]]
[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]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[[[[[[[]],[[]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[[],[[[[[]],[[]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[[[],[[[[]],[[]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[[[]],[[[[]],[[]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[[],[],[[[[]],[[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[[[[],[[[]],[[]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[[],[[],[[[]],[[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[[[[]],[[[]],[[]]]]]
[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]=>[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[[],[[]],[[[]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[[[],[],[[[]],[[]]]]]
[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]=>[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[[],[],[],[[[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[[[[[[[]]],[[]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[[],[[[[[]]],[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[[[],[[[[]]],[[]]]]]
[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]=>[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[[],[],[[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[[[[[[[]]]],[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[[],[[[[[]]]],[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[[[[[[[]]]]],[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[[[[[[[]]]]]],[[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[[],[[[[[]]]]],[[]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[[[],[[[[]]]],[[]]]]
[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]=>[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[[],[],[[[[]]]],[[]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[[[[],[[[]]],[[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[[],[[],[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[[[[],[[[]]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[[[[],[[[]]]]],[[]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[[],[[],[[[]]]],[[]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[[[[]],[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[[[[]],[[[]]]],[[]]]
[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]=>[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[[],[[]],[[[]]],[[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[[[],[],[[[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[[[],[],[[[]]]],[[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[[[],[]],[[[]]],[[]]]
[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]=>[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[[],[],[],[[[]]],[[]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[[[[[],[[]],[[]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[[],[[[],[[]],[[]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[[[],[[],[[]],[[]]]]]
[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]=>[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[[],[],[[],[[]],[[]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[[[[[],[[]]],[[]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[[],[[[],[[]]],[[]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[[[[[],[[]]]],[[]]]]
[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]=>[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[[],[[[],[[]]]],[[]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[[[],[[],[[]]],[[]]]]
[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]=>[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[[],[],[[],[[]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[[[[[]],[[]],[[]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[[],[[[]],[[]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[[[[[]],[[]]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[[[[[]],[[]]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[[],[[[]],[[]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[[[[[]]],[[]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[[[[[]]],[[]]],[[]]]
[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]=>[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[[],[[[]]],[[]],[[]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[[[],[[]],[[]],[[]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[[[],[[]],[[]]],[[]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[[[],[[]]],[[]],[[]]]
[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]=>[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[[],[],[[]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[[[[],[],[[]],[[]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[[],[[],[],[[]],[[]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[[[[],[],[[]]],[[]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[[[[],[],[[]]]],[[]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[[],[[],[],[[]]],[[]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[[[[],[]],[[]],[[]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[[[[],[]],[[]]],[[]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[[[[],[]]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[[],[[],[]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[[[[]],[],[[]],[[]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[[[[]],[],[[]]],[[]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[[[[]],[]],[[]],[[]]]
[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]=>[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[[],[[]],[],[[]],[[]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[[[],[],[],[[]],[[]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[[[],[],[],[[]]],[[]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[[[],[],[]],[[]],[[]]]
[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]=>[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[[],[],[],[],[[]],[[]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[[[[[[],[],[[]]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[[],[[[[],[],[[]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[[[],[[[],[],[[]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[[[]],[[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[[],[],[[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[[[[],[[],[],[[]]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[[],[[],[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[[[[]],[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[[[[]]],[[],[],[[]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[[],[[]],[[],[],[[]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[[[],[],[[],[],[[]]]]]
[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]=>[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[[],[],[],[[],[],[[]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[[[[[[],[]],[[]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[[],[[[[],[]],[[]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[[[],[[[],[]],[[]]]]]
[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]=>[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[[],[],[[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[[[[[[],[]]],[[]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[[],[[[[],[]]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[[[[[[],[]]]],[[]]]]
[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]=>[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[[],[[[[],[]]]],[[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[[[],[[[],[]]],[[]]]]
[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]=>[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[[],[],[[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[[[[],[[],[]],[[]]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[[],[[],[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[[[[],[[],[]]],[[]]]]
[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]=>[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[[],[[],[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[[[[]],[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[[[[]],[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[[[[]]],[[],[]],[[]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[[],[[]],[[],[]],[[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[[[],[],[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[[[],[],[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[[[],[]],[[],[]],[[]]]
[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]=>[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[[],[],[],[[],[]],[[]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[[[[[[]],[],[[]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[[],[[[[]],[],[[]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[[[],[[[]],[],[[]]]]]
[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]=>[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[[],[],[[[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[[[[[[]],[]],[[]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[[],[[[[]],[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[[[[[[]],[]]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[[[[[[]],[]]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[[],[[[[]],[]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[[[],[[[]],[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[[[],[[[]],[]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[[[]],[[[]],[]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[[],[],[[[]],[]],[[]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[[[[[[]]],[],[[]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[[],[[[[]]],[],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[[[[[[]]],[]],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[[[[[[]]],[]]],[[]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[[],[[[[]]],[]],[[]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[[[[[[]]]],[],[[]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[[[[[[]]]],[]],[[]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[[[[[[]]]]],[],[[]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[[],[[[[]]]],[],[[]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[[[],[[[]]],[],[[]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[[[],[[[]]],[]],[[]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[[[],[[[]]]],[],[[]]]
[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]=>[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[[],[],[[[]]],[],[[]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[[[[],[[]],[],[[]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[[],[[],[[]],[],[[]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[[[[],[[]],[]],[[]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[[[[],[[]],[]]],[[]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[[],[[],[[]],[]],[[]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[[[[],[[]]],[],[[]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[[[[],[[]]],[]],[[]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[[[[],[[]]]],[],[[]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[[],[[],[[]]],[],[[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[[[[]],[[]],[],[[]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[[[[]],[[]],[]],[[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[[[[]],[[]]],[],[[]]]
[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]=>[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[[],[[]],[[]],[],[[]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[[[],[],[[]],[],[[]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[[[],[],[[]],[]],[[]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[[[],[],[[]]],[],[[]]]
[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]=>[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[[],[],[],[[]],[],[[]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[[[[[],[],[],[[]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[[],[[[],[],[],[[]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[[[],[[],[],[],[[]]]]]
[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]=>[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[[],[],[[],[],[],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[[[[[],[],[]],[[]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[[],[[[],[],[]],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[[[[[],[],[]]],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[[[[[],[],[]]]],[[]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[[],[[[],[],[]]],[[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[[[],[[],[],[]],[[]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[[[],[[],[],[]]],[[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[[[]],[[],[],[]],[[]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[[],[],[[],[],[]],[[]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[[[[[],[]],[],[[]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[[],[[[],[]],[],[[]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[[[[[],[]],[]],[[]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[[[[[],[]],[]]],[[]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[[],[[[],[]],[]],[[]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[[[[[],[]]],[],[[]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[[[[[],[]]],[]],[[]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[[[[[],[]]]],[],[[]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[[],[[[],[]]],[],[[]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[[[],[[],[]],[],[[]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[[[],[[],[]],[]],[[]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[[[],[[],[]]],[],[[]]]
[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]=>[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[[],[],[[],[]],[],[[]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[[[[[]],[],[],[[]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[[],[[[]],[],[],[[]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[[[[[]],[],[]],[[]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[[[[[]],[],[]]],[[]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[[],[[[]],[],[]],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[[[[[]],[]],[],[[]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[[[[[]],[]],[]],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[[[[[]],[]]],[],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[[],[[[]],[]],[],[[]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[[[[[]]],[],[],[[]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[[[[[]]],[],[]],[[]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[[[[[]]],[]],[],[[]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[[[[[]]]],[],[],[[]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[[],[[[]]],[],[],[[]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[[[],[[]],[],[],[[]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[[[],[[]],[],[]],[[]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[[[],[[]],[]],[],[[]]]
[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]=>[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[[],[],[[]],[],[],[[]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[[[[],[],[],[],[[]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[[],[[],[],[],[],[[]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[[[[],[],[],[]],[[]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[[[[],[],[],[]]],[[]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[[],[[],[],[],[]],[[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[[[[],[],[]],[],[[]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[[[[],[],[]],[]],[[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[[[[],[],[]]],[],[[]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[[],[[],[],[]],[],[[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[[[[],[]],[],[],[[]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[[[[],[]],[],[]],[[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[[[[],[]],[]],[],[[]]]
[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]=>[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[[],[[],[]],[],[],[[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[[[[]],[],[],[],[[]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[[[[]],[],[],[]],[[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[[[[]],[],[]],[],[[]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[[[[]],[]],[],[],[[]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[[[[]]],[],[],[],[[]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[[],[[]],[],[],[],[[]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]=>[[[],[],[],[],[],[[]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[[[],[],[],[],[]],[[]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[[[],[],[],[]],[],[[]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[[[],[],[]],[],[],[[]]]
[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]=>[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[[[[]],[[[[],[]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[[[[]]],[[[[],[]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[[],[[]],[[[[],[]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[[[],[],[[[[],[]]]]]]
[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]=>[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[[[[[]],[[[],[]]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[[],[[[]],[[[],[]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[[[[[]]],[[[],[]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[[[[[]]]],[[[],[]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[[],[[[]]],[[[],[]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[[[],[[]],[[[],[]]]]]
[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]=>[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[[],[],[[]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[[[[],[],[[[],[]]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[[],[[],[],[[[],[]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[[[[],[]],[[[],[]]]]]
[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]=>[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[[],[[],[]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[[[[]],[],[[[],[]]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[[[[]],[]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[[[[]]],[],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[[],[[]],[],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[[[],[],[],[[[],[]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[[[],[],[]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[[[],[]],[],[[[],[]]]]
[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]=>[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[[[[]],[[],[[],[]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[[[[]]],[[],[[],[]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[[],[[]],[[],[[],[]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]=>[[[],[],[[],[[],[]]]]]
[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]=>[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[[[[[[]],[[],[]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[[],[[[[]],[[],[]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[[[],[[[]],[[],[]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[[[]],[[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[[],[],[[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[[[[[[]]],[[],[]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[[],[[[[]]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[[[[[[]]]],[[],[]]]]
[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]=>[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[[],[[[[]]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[[[],[[[]]],[[],[]]]]
[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]=>[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[[],[],[[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[[[[],[[]],[[],[]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[[],[[],[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[[[[],[[]]],[[],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[[[[],[[]]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[[],[[],[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[[[[]],[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[[[[]],[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[[[[]]],[[]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[[],[[]],[[]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[[[],[],[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[[[],[],[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[[[],[]],[[]],[[],[]]]
[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]=>[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[[],[],[],[[]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[[[[[],[],[[],[]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[[],[[[],[],[[],[]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[[[],[[],[],[[],[]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[[[]],[[],[],[[],[]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[[],[],[[],[],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[[[[[],[]],[[],[]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[[],[[[],[]],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[[[[[],[]]],[[],[]]]]
[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]=>[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[[],[[[],[]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[[[],[[],[]],[[],[]]]]
[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]=>[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[[],[],[[],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[[[[[]],[],[[],[]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[[],[[[]],[],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[[[[[]],[]],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[[[[[]],[]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[[],[[[]],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[[[[[]]],[],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[[[[[]]],[]],[[],[]]]
[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]=>[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[[],[[[]]],[],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[[[],[[]],[],[[],[]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[[[],[[]],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[[[],[[]]],[],[[],[]]]
[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]=>[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[[],[],[[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[[[[],[],[],[[],[]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[[],[[],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[[[[],[],[]],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[[[[],[],[]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[[],[[],[],[]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[[[[],[]],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[[[[],[]],[]],[[],[]]]
[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]=>[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[[],[[],[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[[[[]],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[[[[]],[],[]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[[[[]],[]],[],[[],[]]]
[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]=>[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[[],[[]],[],[],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[[[],[],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[[[],[],[],[]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[[[],[],[]],[],[[],[]]]
[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]=>[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[[[[[[[[]],[]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[[],[[[[[[]],[]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[[[],[[[[[]],[]]]]]]
[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]=>[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[[],[],[[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[[[[],[[[[]],[]]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[[],[[],[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[[[[]],[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[[[[]]],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[[],[[]],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[[[],[],[[[[]],[]]]]]
[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]=>[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[[],[],[],[[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[[[[[],[[[]],[]]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[[],[[[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[[[],[[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[[[]],[[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[[],[],[[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[[[[[]],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[[],[[[]],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[[[[[]]],[[[]],[]]]]
[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]=>[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[[],[[[]]],[[[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[[[],[[]],[[[]],[]]]]
[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]=>[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[[],[],[[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[[[[],[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[[],[[],[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[[[[],[]],[[[]],[]]]]
[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]=>[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[[],[[],[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[[[[]],[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[[[[]],[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[[[[]]],[],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[[],[[]],[],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[[[],[],[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[[[],[],[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[[[],[]],[],[[[]],[]]]
[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]=>[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[[],[],[],[],[[[]],[]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[[[[[[[[]]],[]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[[],[[[[[[]]],[]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[[[],[[[[[]]],[]]]]]
[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]=>[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[[],[],[[[[[]]],[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[[[[],[[[[]]],[]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[[],[[],[[[[]]],[]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[[[[]],[[[[]]],[]]]]
[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]=>[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[[],[[]],[[[[]]],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]=>[[[],[],[[[[]]],[]]]]
[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]=>[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[[],[],[],[[[[]]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[[[[[[[[]]]],[]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[[],[[[[[[]]]],[]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[[[],[[[[[]]]],[]]]]
[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]=>[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[[],[],[[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[[[[[[[[]]]]],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[[],[[[[[[]]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[[[[[[[[]]]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[[[[[[[[]]]]]]],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[[],[[[[[[]]]]]],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[[[],[[[[[]]]]],[]]]
[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]=>[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[[],[],[[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[[[[],[[[[]]]],[]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[[],[[],[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[[[[],[[[[]]]]],[]]]
[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]=>[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[[],[[],[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[[[[]],[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[[[[]],[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[[[[]]],[[[[]]]],[]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[[],[[]],[[[[]]]],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[[[],[],[[[[]]]],[]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[[[],[],[[[[]]]]],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[[[],[]],[[[[]]]],[]]
[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]=>[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[[],[],[],[[[[]]]],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[[[[[],[[[]]],[]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[[],[[[],[[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[[[],[[],[[[]]],[]]]]
[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]=>[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[[],[],[[],[[[]]],[]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[[[[[],[[[]]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[[],[[[],[[[]]]],[]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[[[[[],[[[]]]]],[]]]
[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]=>[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[[],[[[],[[[]]]]],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[[[],[[],[[[]]]],[]]]
[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]=>[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[[],[],[[],[[[]]]],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[[[[[]],[[[]]],[]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[[],[[[]],[[[]]],[]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[[[[[]],[[[]]]],[]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[[[[[]],[[[]]]]],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]=>[[],[[[]],[[[]]]],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[[[[[]]],[[[]]],[]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[],[[],[],[]],[]]]=>[[[],[[],[],[]],[],[]]]=>[[[[[]]],[[[]]]],[]]
[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]=>[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[[],[[[]]],[[[]]],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[[[],[[]],[[[]]],[]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]=>[[[],[[]],[[[]]]],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[[[],[[]]],[[[]]],[]]
[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]=>[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[[],[],[[]],[[[]]],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[[[[],[],[[[]]],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[[],[[],[],[[[]]],[]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[[[[],[],[[[]]]],[]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[[[[],[],[[[]]]]],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[[],[[],[],[[[]]]],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[[[[],[]],[[[]]],[]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[],[[[]],[]],[]]]=>[[[],[[],[[]]],[],[]]]=>[[[[],[]],[[[]]]],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[[[[],[]]],[[[]]],[]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[[],[[],[]],[[[]]],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[[[[]],[],[[[]]],[]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[],[[[],[]]],[]]]=>[[[],[[[],[]]],[],[]]]=>[[[[]],[],[[[]]]],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[[[[]],[]],[[[]]],[]]
[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]=>[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[[],[[]],[],[[[]]],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[[[],[],[],[[[]]],[]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]=>[[[],[],[],[[[]]]],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[[[],[],[]],[[[]]],[]]
[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]=>[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[[],[],[],[],[[[]]],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[[[[[[],[[]],[]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[[],[[[[],[[]],[]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[[[],[[[],[[]],[]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[[[]],[[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[[],[],[[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[[[[],[[],[[]],[]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[[],[[],[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[[[[]],[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[[[[]]],[[],[[]],[]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[[],[[]],[[],[[]],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[[[],[],[[],[[]],[]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[[[],[]],[[],[[]],[]]]
[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]=>[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[[],[],[],[[],[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[[[[[[],[[]]],[]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[[],[[[[],[[]]],[]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[[[],[[[],[[]]],[]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[[[]],[[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[[],[],[[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[[[[[[],[[]]]],[]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[[],[[[[],[[]]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[[[[[[],[[]]]]],[]]]
[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]=>[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[[],[[[[],[[]]]]],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[[[],[[[],[[]]]],[]]]
[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]=>[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[[],[],[[[],[[]]]],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[[[[],[[],[[]]],[]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[[],[[],[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[[[[],[[],[[]]]],[]]]
[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]=>[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[[],[[],[[],[[]]]],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[[[[]],[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[],[[]],[[],[]],[]]]=>[[[],[[],[]],[[]],[]]]=>[[[[]],[[],[[]]]],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[[[[]]],[[],[[]]],[]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[[],[[]],[[],[[]]],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[[[],[],[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]=>[[[],[],[[],[[]]]],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[[[],[]],[[],[[]]],[]]
[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]=>[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[[],[],[],[[],[[]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[[[[[[]],[[]],[]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[[],[[[[]],[[]],[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[[[],[[[]],[[]],[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[[[]],[[[]],[[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[[],[],[[[]],[[]],[]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[[[[[[]],[[]]],[]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[[],[[[[]],[[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[[[[[[]],[[]]]],[]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[[[[[[]],[[]]]]],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[[],[[[[]],[[]]]],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[[[],[[[]],[[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]=>[[[],[[[]],[[]]]],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[[[]],[[[]],[[]]],[]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[[],[],[[[]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[[[[[[]]],[[]],[]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[[],[[[[]]],[[]],[]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[[[[[[]]],[[]]],[]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[[[[[[]]],[[]]]],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[[],[[[[]]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[[[[[[]]]],[[]],[]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]=>[[[[[[]]]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[[[[[[]]]]],[[]],[]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[[],[[[[]]]],[[]],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[[[],[[[]]],[[]],[]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]=>[[[],[[[]]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[[[],[[[]]]],[[]],[]]
[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]=>[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[[],[],[[[]]],[[]],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[[[[],[[]],[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[[],[[],[[]],[[]],[]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[[[[],[[]],[[]]],[]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[[[[],[[]],[[]]]],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[[],[[],[[]],[[]]],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[[[[],[[]]],[[]],[]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]=>[[[[],[[]]],[[]]],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[[[[],[[]]]],[[]],[]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[[],[[],[[]]],[[]],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[[[[]],[[]],[[]],[]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]=>[[[[]],[[]],[[]]],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[[[[]],[[]]],[[]],[]]
[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]=>[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[[],[[]],[[]],[[]],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[[[],[],[[]],[[]],[]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]=>[[[],[],[[]],[[]]],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[[[],[],[[]]],[[]],[]]
[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]=>[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[[],[],[],[[]],[[]],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[[[[[],[],[[]],[]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[[],[[[],[],[[]],[]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[[[],[[],[],[[]],[]]]]
[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]=>[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[[],[],[[],[],[[]],[]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[[[[[],[],[[]]],[]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[[],[[[],[],[[]]],[]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[[[[[],[],[[]]]],[]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[[[[[],[],[[]]]]],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[[],[[[],[],[[]]]],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[[[],[[],[],[[]]],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]=>[[[],[[],[],[[]]]],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[[[]],[[],[],[[]]],[]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[[],[],[[],[],[[]]],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[[[[[],[]],[[]],[]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[[],[[[],[]],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[[[[[],[]],[[]]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[[[[[],[]],[[]]]],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[[],[[[],[]],[[]]],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[[[[[],[]]],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]=>[[[[[],[]]],[[]]],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[[[[[],[]]]],[[]],[]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[[],[[[],[]]],[[]],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[[[],[[],[]],[[]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]=>[[[],[[],[]],[[]]],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[[[],[[],[]]],[[]],[]]
[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]=>[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[[],[],[[],[]],[[]],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[[[[[]],[],[[]],[]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[[],[[[]],[],[[]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[[[[[]],[],[[]]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[[[[[]],[],[[]]]],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[[],[[[]],[],[[]]],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[[[[[]],[]],[[]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]=>[[[[[]],[]],[[]]],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[[[[[]],[]]],[[]],[]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[[],[[[]],[]],[[]],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[[[[[]]],[],[[]],[]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]=>[[[[[]]],[],[[]]],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[[[[[]]],[]],[[]],[]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[[[[[]]]],[],[[]],[]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[[],[[[]]],[],[[]],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[[[],[[]],[],[[]],[]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]=>[[[],[[]],[],[[]]],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[[[],[[]],[]],[[]],[]]
[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]=>[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[[],[],[[]],[],[[]],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[[[[],[],[],[[]],[]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[[],[[],[],[],[[]],[]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[[[[],[],[],[[]]],[]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[[[[],[],[],[[]]]],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[[],[[],[],[],[[]]],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[[[[],[],[]],[[]],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]=>[[[[],[],[]],[[]]],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[[[[],[],[]]],[[]],[]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[[],[[],[],[]],[[]],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[[[[],[]],[],[[]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]=>[[[[],[]],[],[[]]],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[[[[],[]],[]],[[]],[]]
[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]=>[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[[],[[],[]],[],[[]],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[[[[]],[],[],[[]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]=>[[[[]],[],[],[[]]],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[[[[]],[],[]],[[]],[]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[[[[]],[]],[],[[]],[]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[[[[]]],[],[],[[]],[]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[[],[[]],[],[],[[]],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[[[],[],[],[],[[]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[],[[[[[]]]]],[]]]=>[[[],[[[[[]]]]],[]]]=>[[[],[],[],[],[[]]],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[[[],[],[],[]],[[]],[]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[[[],[],[]],[],[[]],[]]
[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]=>[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[[[[[[[],[],[]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[[],[[[[[],[],[]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[[[],[[[[],[],[]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[[[]],[[[[],[],[]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[[],[],[[[[],[],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[[[[],[[[],[],[]]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[[],[[],[[[],[],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[[[[]],[[[],[],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[[[[]]],[[[],[],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[[],[[]],[[[],[],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]=>[[[],[],[[[],[],[]]]]]
[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]=>[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[[],[],[],[[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[[[[[],[[],[],[]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[[],[[[],[[],[],[]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[[[],[[],[[],[],[]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[[[]],[[],[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[[],[],[[],[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[[[[[]],[[],[],[]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[[],[[[]],[[],[],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[[[[[]]],[[],[],[]]]]
[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]=>[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[[],[[[]]],[[],[],[]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[[[],[[]],[[],[],[]]]]
[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]=>[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[[],[],[[]],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[[[[],[],[[],[],[]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[[],[[],[],[[],[],[]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[[[[],[]],[[],[],[]]]]
[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]=>[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[[],[[],[]],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[[[[]],[],[[],[],[]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[[[[]],[]],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[[[[]]],[],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[[],[[]],[],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[[[],[],[],[[],[],[]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[[[],[],[]],[[],[],[]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[[[],[]],[],[[],[],[]]]
[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]=>[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[[],[],[],[],[[],[],[]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[[[[[[[],[]],[]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[[],[[[[[],[]],[]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[[[],[[[[],[]],[]]]]]
[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]=>[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[[],[],[[[[],[]],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[[[[],[[[],[]],[]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[[],[[],[[[],[]],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[[[[]],[[[],[]],[]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[[[[]]],[[[],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[[],[[]],[[[],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]=>[[[],[],[[[],[]],[]]]]
[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]=>[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[[],[],[],[[[],[]],[]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[[[[[[[],[]]],[]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[[],[[[[[],[]]],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[[[],[[[[],[]]],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[[[]],[[[[],[]]],[]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[[],[],[[[[],[]]],[]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[[[[[[[],[]]]],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[[],[[[[[],[]]]],[]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]=>[[[[[[[],[]]]]],[]]]
[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]=>[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[[],[[[[[],[]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[[[],[[[[],[]]]],[]]]
[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]=>[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[[],[],[[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[[[[],[[[],[]]],[]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[[],[[],[[[],[]]],[]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]=>[[[[],[[[],[]]]],[]]]
[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]=>[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[[],[[],[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[[[[]],[[[],[]]],[]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[[[[]],[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[[[[]]],[[[],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[[],[[]],[[[],[]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[[[],[],[[[],[]]],[]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[[[],[],[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[[[],[]],[[[],[]]],[]]
[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]=>[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[[[[[],[[],[]],[]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[[],[[[],[[],[]],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[[[],[[],[[],[]],[]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[[[]],[[],[[],[]],[]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[[],[],[[],[[],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[[[[[],[[],[]]],[]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[[],[[[],[[],[]]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[[[[[],[[],[]]]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[[[[[],[[],[]]]]],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[[],[[[],[[],[]]]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[[[],[[],[[],[]]],[]]]
[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]=>[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[[],[],[[],[[],[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[[[[[]],[[],[]],[]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[[],[[[]],[[],[]],[]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[[[[[]],[[],[]]],[]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[[[[[]],[[],[]]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[[],[[[]],[[],[]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[[[[[]]],[[],[]],[]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[[[[[]]],[[],[]]],[]]
[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]=>[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[[],[[[]]],[[],[]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[[[],[[]],[[],[]],[]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[[[],[[]],[[],[]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[[[],[[]]],[[],[]],[]]
[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]=>[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[[],[],[[]],[[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[[[[],[],[[],[]],[]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[[],[[],[],[[],[]],[]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[[[[],[],[[],[]]],[]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[[[[],[],[[],[]]]],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[[],[[],[],[[],[]]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[[[[],[]],[[],[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[[[[],[]],[[],[]]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[[[[],[]]],[[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[[],[[],[]],[[],[]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[[[[]],[],[[],[]],[]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[[[[]],[],[[],[]]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[[[[]],[]],[[],[]],[]]
[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]=>[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[[],[[]],[],[[],[]],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[[[],[],[],[[],[]],[]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[[[],[],[],[[],[]]],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[[[],[],[]],[[],[]],[]]
[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]=>[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[[[[[[[]],[],[]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[[],[[[[[]],[],[]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[[[],[[[[]],[],[]]]]]
[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]=>[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[[],[],[[[[]],[],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[[[[],[[[]],[],[]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[[],[[],[[[]],[],[]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[[[[]],[[[]],[],[]]]]
[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]=>[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[[],[[]],[[[]],[],[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]=>[[[],[],[[[]],[],[]]]]
[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]=>[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[[],[],[],[[[]],[],[]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[[[[[[[]],[]],[]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[[],[[[[[]],[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[[[],[[[[]],[]],[]]]]
[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]=>[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[[],[],[[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[[[[[[[]],[]]],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[[],[[[[[]],[]]],[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]=>[[[[[[[]],[]]]],[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[[[[[[[]],[]]]]],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[[],[[[[[]],[]]]],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[[[],[[[[]],[]]],[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[[[],[[[[]],[]]]],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[[[]],[[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[[],[],[[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[[[[],[[[]],[]],[]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[[],[[],[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[[[[],[[[]],[]]],[]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[[[[],[[[]],[]]]],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[[],[[],[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[[[[]],[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[[[[]],[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[[[[]]],[[[]],[]],[]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[[],[[]],[[[]],[]],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[[[],[],[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[[[],[],[[[]],[]]],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[[[],[]],[[[]],[]],[]]
[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]=>[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[[[[[[[]]],[],[]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[[],[[[[[]]],[],[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[[[],[[[[]]],[],[]]]]
[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]=>[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[[],[],[[[[]]],[],[]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[[[[[[[]]],[]],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[[],[[[[[]]],[]],[]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]=>[[[[[[[]]],[]]],[]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[[[[[[[]]],[]]]],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[[],[[[[[]]],[]]],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[[[],[[[[]]],[]],[]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[[[],[[[[]]],[]]],[]]
[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]=>[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[[],[],[[[[]]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[[[[[[[]]]],[],[]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[[],[[[[[]]]],[],[]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[[[[[[[]]]],[]],[]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[[[[[[[]]]],[]]],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[[],[[[[[]]]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[[[[[[[]]]]],[],[]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[[[[[[[]]]]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[[[[[[[]]]]]],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[[],[[[[[]]]]],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[[[],[[[[]]]],[],[]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[[[],[[[[]]]],[]],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[[[],[[[[]]]]],[],[]]
[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]=>[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[[],[],[[[[]]]],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[[[[],[[[]]],[],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[[],[[],[[[]]],[],[]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[[[[],[[[]]],[]],[]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[[[[],[[[]]],[]]],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[[],[[],[[[]]],[]],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[[[[],[[[]]]],[],[]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[[[[],[[[]]]],[]],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[[[[],[[[]]]]],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[[],[[],[[[]]]],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[[[[]],[[[]]],[],[]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[[[[]],[[[]]],[]],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[[[[]],[[[]]]],[],[]]
[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]=>[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[[],[[]],[[[]]],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[[[],[],[[[]]],[],[]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[[[],[],[[[]]],[]],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[[[],[],[[[]]]],[],[]]
[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]=>[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[[[[[],[[]],[],[]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[[],[[[],[[]],[],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[[[],[[],[[]],[],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[[[]],[[],[[]],[],[]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[[],[],[[],[[]],[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[[[[[],[[]],[]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[[],[[[],[[]],[]],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[[[[[],[[]],[]]],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[[[[[],[[]],[]]]],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[[],[[[],[[]],[]]],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[[[],[[],[[]],[]],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[[[],[[],[[]],[]]],[]]
[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]=>[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[[],[],[[],[[]],[]],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[[[[[],[[]]],[],[]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[[],[[[],[[]]],[],[]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[[[[[],[[]]],[]],[]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[[[[[],[[]]],[]]],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[[],[[[],[[]]],[]],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[[[[[],[[]]]],[],[]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[[[[[],[[]]]],[]],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[[[[[],[[]]]]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[[],[[[],[[]]]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[[[],[[],[[]]],[],[]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[[[],[[],[[]]],[]],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[[[],[[],[[]]]],[],[]]
[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]=>[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[[],[],[[],[[]]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[[[[[]],[[]],[],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[[],[[[]],[[]],[],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[[[[[]],[[]],[]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[[[[[]],[[]],[]]],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[[],[[[]],[[]],[]],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[[[[[]],[[]]],[],[]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[[[[[]],[[]]],[]],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[[[[[]],[[]]]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[[],[[[]],[[]]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[[[[[]]],[[]],[],[]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[[[[[]]],[[]],[]],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[[[[[]]],[[]]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[[[[[]]]],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[[],[[[]]],[[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[[[],[[]],[[]],[],[]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[[[],[[]],[[]],[]],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[[[],[[]],[[]]],[],[]]
[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]=>[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[[],[],[[]],[[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[[[[],[],[[]],[],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[[],[[],[],[[]],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[[[[],[],[[]],[]],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[[[[],[],[[]],[]]],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[[],[[],[],[[]],[]],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[[[[],[],[[]]],[],[]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[[[[],[],[[]]],[]],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[[[[],[],[[]]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[[],[[],[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[[[[],[]],[[]],[],[]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[[[[],[]],[[]],[]],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[[[[],[]],[[]]],[],[]]
[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]=>[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[[],[[],[]],[[]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[[[[]],[],[[]],[],[]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[[[[]],[],[[]],[]],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[[[[]],[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[[[[]],[]],[[]],[],[]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[[[[]]],[],[[]],[],[]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[[],[[]],[],[[]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[[[],[],[],[[]],[],[]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[[[],[],[],[[]],[]],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[[[],[],[],[[]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[[[],[],[]],[[]],[],[]]
[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]=>[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[[[[[[],[],[],[]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[[],[[[[],[],[],[]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[[[],[[[],[],[],[]]]]]
[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]=>[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[[],[],[[[],[],[],[]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[[[[],[[],[],[],[]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[[],[[],[[],[],[],[]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[[[[]],[[],[],[],[]]]]
[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]=>[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[[],[[]],[[],[],[],[]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[]]]],[[[]]],[]]=>[[],[[[]]],[[[[]]]]]=>[[[],[],[[],[],[],[]]]]
[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]=>[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[[],[],[],[[],[],[],[]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[[[[[[],[],[]],[]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[[],[[[[],[],[]],[]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[[[],[[[],[],[]],[]]]]
[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]=>[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[[],[],[[[],[],[]],[]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[[[[[[],[],[]]],[]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[[],[[[[],[],[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]=>[[[[[[],[],[]]]],[]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[[[[[[],[],[]]]]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[[],[[[[],[],[]]]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[[[],[[[],[],[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[[[],[[[],[],[]]]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[[[]],[[[],[],[]]],[]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[[[[],[[],[],[]],[]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[[],[[],[[],[],[]],[]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[[[[],[[],[],[]]],[]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[[[[],[[],[],[]]]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[[],[[],[[],[],[]]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[[[[]],[[],[],[]],[]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[[[[]],[[],[],[]]],[]]
[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]=>[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[[],[[]],[[],[],[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[[[],[],[[],[],[]],[]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[[[],[],[[],[],[]]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[[[],[]],[[],[],[]],[]]
[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]=>[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[[[[[[],[]],[],[]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[[],[[[[],[]],[],[]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[[[],[[[],[]],[],[]]]]
[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]=>[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[[],[],[[[],[]],[],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[[[[[[],[]],[]],[]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[[],[[[[],[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[[[[[[],[]],[]]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[[[[[[],[]],[]]]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[[],[[[[],[]],[]]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[[[],[[[],[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[[[],[[[],[]],[]]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[[[]],[[[],[]],[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[[[[[[],[]]],[],[]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[[],[[[[],[]]],[],[]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[[[[[[],[]]],[]],[]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[[[[[[],[]]],[]]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[[],[[[[],[]]],[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[[[[[[],[]]]],[],[]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[[[[[[],[]]]],[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[[[[[[],[]]]]],[],[]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[[],[[[[],[]]]],[],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[[[],[[[],[]]],[],[]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[[[],[[[],[]]],[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[[[],[[[],[]]]],[],[]]
[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]=>[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[[],[],[[[],[]]],[],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[[[[],[[],[]],[],[]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[[],[[],[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[[[[],[[],[]],[]],[]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[[[[],[[],[]],[]]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[[],[[],[[],[]],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[[[[],[[],[]]],[],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[[[[],[[],[]]],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[[[[],[[],[]]]],[],[]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[[],[[],[[],[]]],[],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[[[[]],[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[[[[]],[[],[]],[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[[[[]],[[],[]]],[],[]]
[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]=>[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[[],[[]],[[],[]],[],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[[[],[],[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[[[],[],[[],[]],[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[[[],[],[[],[]]],[],[]]
[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]=>[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[[[[[[]],[],[],[]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[[],[[[[]],[],[],[]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[[[],[[[]],[],[],[]]]]
[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]=>[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[[],[],[[[]],[],[],[]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[[[[[[]],[],[]],[]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[[],[[[[]],[],[]],[]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[[[[[[]],[],[]]],[]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[[[[[[]],[],[]]]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[[],[[[[]],[],[]]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[[[],[[[]],[],[]],[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[[[],[[[]],[],[]]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[[[]],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[[[[[[]],[]],[],[]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[[],[[[[]],[]],[],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[[[[[[]],[]],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[[[[[[]],[]],[]]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[[],[[[[]],[]],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[[[[[[]],[]]],[],[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[[[[[[]],[]]],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[[[[[[]],[]]]],[],[]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[[],[[[[]],[]]],[],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[[[],[[[]],[]],[],[]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[[[],[[[]],[]],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[[[],[[[]],[]]],[],[]]
[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]=>[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[[],[],[[[]],[]],[],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[[[[[[]]],[],[],[]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[[],[[[[]]],[],[],[]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[[[[[[]]],[],[]],[]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[[[[[[]]],[],[]]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[[],[[[[]]],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[[[[[[]]],[]],[],[]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[[[[[[]]],[]],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[[[[[[]]],[]]],[],[]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[[],[[[[]]],[]],[],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[[[[[[]]]],[],[],[]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[[[[[[]]]],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[[[[[[]]]],[]],[],[]]
[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]=>[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[[],[[[[]]]],[],[],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[[[],[[[]]],[],[],[]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[[[],[[[]]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[[[],[[[]]],[]],[],[]]
[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]=>[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[[[[],[[]],[],[],[]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[[],[[],[[]],[],[],[]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]=>[[[[],[[]],[],[]],[]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[[[[],[[]],[],[]]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[[],[[],[[]],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[[[[],[[]],[]],[],[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[[[[],[[]],[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[[[[],[[]],[]]],[],[]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[[],[[],[[]],[]],[],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[[[[],[[]]],[],[],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[[[[],[[]]],[],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[[[[],[[]]],[]],[],[]]
[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]=>[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[[],[[],[[]]],[],[],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[[[[]],[[]],[],[],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[[[[]],[[]],[],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[[[[]],[[]],[]],[],[]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[[[[]],[[]]],[],[],[]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[[[[]]],[[]],[],[],[]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[[],[[]],[[]],[],[],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[[[],[],[[]],[],[],[]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[[[],[],[[]],[],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[[[],[],[[]],[]],[],[]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[[[],[],[[]]],[],[],[]]
[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]=>[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[[[[[],[],[],[],[]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[[],[[[],[],[],[],[]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[[[],[[],[],[],[],[]]]]
[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]=>[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[[],[],[[],[],[],[],[]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[[[[[],[],[],[]],[]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[[],[[[],[],[],[]],[]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[[[[[],[],[],[]]],[]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[[[[[],[],[],[]]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[[],[[[],[],[],[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[[[],[[],[],[],[]],[]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[[[],[[],[],[],[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[[[]],[[],[],[],[]],[]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[[[[[],[],[]],[],[]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[[],[[[],[],[]],[],[]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[[[[[],[],[]],[]],[]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[[[[[],[],[]],[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[[],[[[],[],[]],[]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[[[[[],[],[]]],[],[]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[[[[[],[],[]]],[]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[[[[[],[],[]]]],[],[]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[[],[[[],[],[]]],[],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[[[],[[],[],[]],[],[]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[[[],[[],[],[]],[]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[[[],[[],[],[]]],[],[]]
[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]=>[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[[],[],[[],[],[]],[],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[[[[[],[]],[],[],[]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[[],[[[],[]],[],[],[]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[[[[[],[]],[],[]],[]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[[[[[],[]],[],[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[[],[[[],[]],[],[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[[[[[],[]],[]],[],[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[[[[[],[]],[]],[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[[[[[],[]],[]]],[],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[[],[[[],[]],[]],[],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[[[[[],[]]],[],[],[]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[[[[[],[]]],[],[]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[[[[[],[]]],[]],[],[]]
[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]=>[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[[],[[[],[]]],[],[],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[[[],[[],[]],[],[],[]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[[[],[[],[]],[],[]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[[[],[[],[]],[]],[],[]]
[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]=>[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[[[[[]],[],[],[],[]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[[],[[[]],[],[],[],[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[[[[[]],[],[],[]],[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[[[[[]],[],[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[[],[[[]],[],[],[]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[[[[[]],[],[]],[],[]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[[[[[]],[],[]],[]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[[[[[]],[],[]]],[],[]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[[],[[[]],[],[]],[],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[[[[[]],[]],[],[],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[[[[[]],[]],[],[]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[[[[[]],[]],[]],[],[]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[[[[[]],[]]],[],[],[]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[[],[[[]],[]],[],[],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[[[[[]]],[],[],[],[]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[[[[[]]],[],[],[]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[[[[[]]],[],[]],[],[]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[[[[[]]],[]],[],[],[]]
[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]=>[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[[],[[[]]],[],[],[],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[[[],[[]],[],[],[],[]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]=>[[[],[[]],[],[],[]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[[[],[[]],[],[]],[],[]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[[[],[[]],[]],[],[],[]]
[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]=>[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[[[[],[],[],[],[],[]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[[],[[],[],[],[],[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]=>[[[[],[],[],[],[]],[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[[[[],[],[],[],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[[],[[],[],[],[],[]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[[[[],[],[],[]],[],[]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[[[[],[],[],[]],[]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[[[[],[],[],[]]],[],[]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[[],[[],[],[],[]],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[[[[],[],[]],[],[],[]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]=>[[[[],[],[]],[],[]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[[[[],[],[]],[]],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[[[[],[],[]]],[],[],[]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[[],[[],[],[]],[],[],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[[[[],[]],[],[],[],[]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[[[[],[]],[],[],[]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[[[[],[]],[],[]],[],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[[[[],[]],[]],[],[],[]]
[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]=>[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[[],[[],[]],[],[],[],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[[[[]],[],[],[],[],[]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[[[[]],[],[],[],[]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[[[[]],[],[],[]],[],[]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[[[[]],[],[]],[],[],[]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[[[[]],[]],[],[],[],[]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[[[[]]],[],[],[],[],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[[[],[],[],[],[],[],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]=>[[[],[],[],[],[],[]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[[[],[],[],[],[]],[],[]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[[[],[],[],[]],[],[],[]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[[[],[],[]],[],[],[],[]]
[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 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.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
Map
DeBruijn-Morselt plane tree automorphism
Description
This automorphism on the set of plane trees with a given number of vertices is the combination of the two "canonical" bijections between plane trees and binary trees, using either the left or right branches. In [3] Shapiro essentially attributes this automorphism to DeBruijn and Morselt [1], hence the name I chose. Shapiro shows in that paper that for a large subset of plane trees (those corresponding to compositions), the sixth power of the automorphism acts as the identity on this subset. However, its behavior in general is quite chaotic. In [2] Donaghey studies this automorphism further and shows that its behavior on all trees can be reduced to its behavior on certain "primitive" trees.
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