Identifier
Mp00026:
Dyck paths
—to ordered tree⟶
Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Images
=>
Cc0005;cc-rep-0Cc0021;cc-rep-1Cc0005;cc-rep-2
[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]=>[[],[],[]]=>[1,0,1,0,1,0]
[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]=>[[[],[]]]=>[1,1,0,1,0,0]
[1,1,1,0,0,0]=>[[[[]]]]=>[1,1,1,0,0,0]
[1,0,1,0,1,0,1,0]=>[[],[],[],[]]=>[1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0]=>[[],[],[[]]]=>[1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0]=>[[],[[]],[]]=>[1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0]=>[[],[[],[]]]=>[1,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0]=>[[],[[[]]]]=>[1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0]=>[[[]],[],[]]=>[1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0]=>[[[]],[[]]]=>[1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0]=>[[[],[]],[]]=>[1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,0]=>[[[],[],[]]]=>[1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0]=>[[[],[[]]]]=>[1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,0]=>[[[[]]],[]]=>[1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0]=>[[[[]],[]]]=>[1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0]=>[[[[],[]]]]=>[1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0]=>[[[[[]]]]]=>[1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0]=>[[],[],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0]=>[[],[],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[]]]=>[1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]]]=>[1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0]=>[[],[[[]],[]]]=>[1,0,1,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]]]]=>[1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,0]=>[[],[[[[]]]]]=>[1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0]=>[[[]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[],[]]=>[1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[]]=>[1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0]=>[[[],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[]]=>[1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,0]=>[[[],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[],[]]=>[1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[]]=>[1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[]]]=>[1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[]]=>[1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]]]=>[1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]]]]=>[1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]]]]=>[1,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[]]=>[1,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[]]]=>[1,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]]]]=>[1,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]]]]=>[1,1,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]]]=>[1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[[],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[[[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[[[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[[]],[],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[],[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[[]]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[[],[]]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[[[]]]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[[[]]],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[[[]],[],[[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[[[]],[],[[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[]],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[]],[],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[]],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]]],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[[],[]]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[[],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[[[]]]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[[[]]],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[[[],[]]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[[[[]]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]]],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]]],[],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]]],[[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[]],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[[[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[],[]]],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[],[]]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[[[[],[]],[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[],[]],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[[[[],[[]]]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[[[[],[[]]],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[[[[],[[],[]]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[[[[],[[[]]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[]]]],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[]]]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[[]]],[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[]]],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[[]]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[]]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[],[]]],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[],[]],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[]]]]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[[]]]],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[[]]],[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[]]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[[],[]]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[[]]]]]]]=>[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]=>[[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[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]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[[]]]]=>[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]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[],[[[[]]]]]]=>[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]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[],[[[[[]]]]]]]=>[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]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[]],[[[[]]]]]]=>[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]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[[],[[[[]]]]]]]=>[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]=>[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[],[]],[[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[],[[[]]],[[]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[]]]],[]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[[[],[]]]]],[]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[],[[[[[[]]]]]],[]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[],[[]],[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[],[[]],[[],[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[],[[]],[[[]]],[]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[],[[],[]],[[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[],[[],[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[],[[],[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[],[[],[],[[]]],[]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[],[[],[[]]],[],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[],[[],[[]],[]],[]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[],[[],[[[]]]],[]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[],[[[]]],[[]],[]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[],[[[]],[]],[],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[],[[[]],[],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[],[[[]],[[]]],[]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[],[[[],[]]],[],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[],[]],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[],[[[],[[]]]],[]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[],[[[[]]]],[],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[[]]],[]],[]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[],[[[[]],[]]],[]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[[[[],[]]]],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[],[[[[[]]]]],[]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[]]]]]]]]]=>[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
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path is the depth of the tree.
This sends the maximal height of the Dyck path is the depth of the tree.
searching the database
Sorry, this map was not found in the database.