Identifier
Mp00103:
Dyck paths
—peeling map⟶
Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0021;cc-rep-2Cc0021;cc-rep-3
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[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[]]=>[[],[[]],[[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[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]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]
[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]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[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]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]
Map
peeling map
Description
Send a Dyck path to its peeled Dyck path.
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
searching the database
Sorry, this map was not found in the database.