- FindStat

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Identifier

Mp00026: Dyck paths —to ordered tree⟶ Ordered trees

Images

=>
            
              Cc0005;cc-rep-0Cc0021;cc-rep-1
            

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[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[],[]]],[]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[],[]],[]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[],[]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[],[[]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[[]]]]]],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[[],[[]]]]],[]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[[],[[]]]],[]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[[],[[]]],[]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[[],[[]],[]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[[],[[],[]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[],[[[]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[]]]]]],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[]]]]]],[[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[[]]]]],[]],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[]]]]],[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[]]]]],[[]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[]]]],[]]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[[]]]],[]],[]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[[]]]],[],[]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[[]]]],[[]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[]]],[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[[]]],[]]],[]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[[]]],[]],[]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[[]]],[],[]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[]]],[[]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[]],[]]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[[]],[]]]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[[]],[]]],[]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[[]],[]],[]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[]],[],[]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[[]],[[]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[]]]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[],[]]]]],[]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[[],[]]]],[]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[[],[]]],[]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[],[]],[]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[],[]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[]]]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[]]]]]],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[[]]]]],[]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[[]]]],[]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[[]]],[]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[[]],[]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[],[]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[],[]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[],[[[[[[[],[]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[[]],[]]]]]],[]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[],[[]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[],[[[[[[[]],[]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[],[[[[[[],[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[[]]],[]]]]],[]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[],[]]]]]],[]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[],[[[]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[],[[[[[[[]]],[]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[],[[[[[[],[],[]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[],[[[[[],[[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[[]]]],[]]]],[]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[],[]],[]]]]],[]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[[]],[[]]]]]],[]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[],[[],[]]]]]],[]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[],[[[[]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[],[[[[[[[]]]],[]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[],[[[[[[],[]],[]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[],[[[[[[]],[[]]]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[],[[[[[],[[],[]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[[[],[[[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[[]]]]],[]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[],[]]],[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[[]],[],[]]]]],[]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[],[[]],[]]]]],[]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[],[[]]]]]],[]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[],[[[],[]]]]]],[]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[],[[[[[]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[],[[[[[[[]]]]],[]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[],[[[[[[],[]]],[]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[],[[[[[[]],[],[]]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[],[[[[[],[[]],[]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[],[[[[[],[],[[]]]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[],[[[[],[[[],[]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[[],[[[[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[[[[[[[[]]]]]],[]],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[[[]],[]],[]]]],[]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[[[]]],[[]]]]],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[],[],[]]]]],[]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[],[[],[[]]]]]],[]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[],[[[[[[]]]]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[[]]]]]]],[[]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[],[[[[[[[]]]]]],[]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[],[[[[[[]],[]],[]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[],[[[[[[]]],[[]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[],[],[],[]]]]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[[[],[[],[[]]]]]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[[[],[[[[],[]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[]],[[[[[[[]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[],[[[[[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[[]]]]]]],[],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[[],[]]]]],[]],[]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[[],[],[]],[]]]],[]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[],[[[]]],[]]]],[]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[[],[]],[[]]]]],[]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[[]],[[],[]]]]],[]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[],[[],[],[]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[],[[[[[[[]]]]]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[],[]]]]]],[[]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[],[[[[[[],[]]]]],[]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[],[[[[[[]],[]]],[]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[],[[[[[[]]],[],[]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[],[[[[[],[],[]],[]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[],[[[[],[[[]]],[]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[],[[[[[],[]],[[]]]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[],[[[[[]],[[],[]]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[],[[],[],[]]]]]]
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[],[[[[],[],[[[]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[]],[[[[[[],[]]]]]]]
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[[],[[[[[],[]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[],[[[[[[[]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[],[]]]]]],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[[[]]],[]],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[[],[],[]]],[]]],[]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[],[[[],[],[]]]]],[]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[],[[[[],[[]]]]]],[]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[],[[[[[[],[]]]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[[[]],[]]]]],[[]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[],[[]]]]]],[[]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[],[[[[[],[],[]]],[]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[],[[[[],[[]],[[]]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[],[[[],[[[],[],[]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[]],[[[[[[]],[]]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[],[[],[[[[[]],[]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[]],[[[[[],[[]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[],[[[[[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[[[]],[]]]]],[],[]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[],[[]]]]]],[],[]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[[],[],[]]]],[]],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[[[]]]],[],[]]],[]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[],[[[[]]]],[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[],[],[]]]],[]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[[[]]],[[[]]]]],[]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[],[],[[]]]]],[]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[],[[[[[[]],[]]]]],[]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[],[[[[[],[[]]]]]],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[[[]]],[]]]],[[]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[[],[],[]]]]],[[]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[],[[[]]]]]],[[]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[],[[[[[[]]]],[],[]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[[[],[[],[]]],[]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[],[[[],[[[[]]]],[]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[],[[[[[]],[],[],[]]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[],[[[[],[[]],[],[]]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[],[[[[[]]],[[[]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[],[],[[]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[]],[[[[[],[],[]]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[],[[],[[[[],[],[]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[],[],[[[[[[]],[]]]]]]
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[],[[[],[],[[[[]]]]]]]
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[]],[[[[],[[[]]]]]]]
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[],[],[[[[[],[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[],[],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[],[],[[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[],[],[],[[]],[]]]
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[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[]],[],[[[[],[]]]]]]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[]],[],[[[[[]]]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[[]],[],[],[],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[]],[[]],[[]],[],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[]],[[]],[[]],[[]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[]],[[]],[[],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[]],[[]],[[],[[]]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[]],[[],[]],[],[],[]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[]],[[],[]],[[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[],[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[]],[[],[],[],[[]]]]]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[]],[[],[],[[[]]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[]],[[],[[],[[]]]]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[[]],[[],[[[[]]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[]],[[[]]],[],[],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[]],[[[]],[],[],[]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[]],[[[],[],[],[]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[]],[[[[]]]],[],[]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[]],[[[[],[],[]]]]]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[]],[[[[],[[]]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[]],[[[[[]]]]],[]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[]],[[[[[]]]],[]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[]],[[[[[],[]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[]],[[[[[[]]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[],[],[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[],[],[[]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[],[],[[],[]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[],[]],[],[[],[],[]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[[],[]],[],[[[[]]]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[],[]],[[]],[],[],[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[],[]],[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[],[]],[[[[],[]]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[],[]],[[[[[]]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[],[],[]],[],[],[],[]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[],[],[]],[],[],[[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[],[],[]],[],[[],[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[],[],[]],[],[[[]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[],[],[]],[[],[],[]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[],[],[]],[[[[]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[],[],[]],[],[],[]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[],[],[]],[],[[]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[],[],[]],[[[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[],[],[]],[],[]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[],[],[]],[[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[],[],[]],[]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[],[],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[],[],[[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[[],[],[],[],[[]]],[]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[],[],[[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[],[],[],[],[[],[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[],[],[],[],[[[]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[],[],[],[[]]],[],[]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[],[],[[]],[],[]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[],[],[[],[]]],[]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[],[],[],[[],[],[]]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[],[],[[],[[]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[],[],[[[]]]],[]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[],[],[[[],[]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[[],[],[],[[[[]]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[],[],[[]]],[],[],[]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[],[],[[]],[],[],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[],[],[[],[]]],[],[]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[],[],[[],[],[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[],[],[[],[],[],[]]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[],[],[[],[[],[]]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[],[],[[[]]]],[],[]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[],[],[[[]]],[],[]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[],[],[[[],[]]],[]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[],[[[],[],[]]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[],[[[[]]]]],[]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[],[],[[[[]]]],[]]]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[],[],[[[[[]]]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[],[[]]],[],[],[],[]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[[]],[],[],[],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[[]],[],[[]],[]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[],[[]],[[]],[]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[[]],[[]],[[]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[[]],[[],[[]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[],[[],[]]],[],[],[]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[],[[],[]],[],[],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[],[[],[],[]]],[],[]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[],[[],[],[]],[],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[],[[],[],[]],[[]]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[],[],[]]],[]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[],[[],[],[],[]],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[],[],[]]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[],[],[[]]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[],[[],[[]],[]]],[]]]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[[],[[],[],[]]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[],[[[]]]]],[]]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[],[[],[[[[]]]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[],[[[]]]],[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[[]]]],[],[[]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[],[[[]]],[],[],[]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[],[[[]]],[[],[]]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[[],[[[]]],[[[]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[],[[[]],[]]],[[]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[],[[[],[]]],[],[]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[],[[[],[]],[]],[]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[],[[[],[],[]]],[]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[],[[[],[],[]],[]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[],[[[],[],[],[]]]]]]
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[[],[],[[]]]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[[],[[]]]]],[]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[],[[[],[[]]],[]]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[],[[[],[[[]]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[],[[[[]]]]],[[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[],[[[[]]]],[],[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[],[[[[]]]],[[]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[],[[[[]]],[],[]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[],[[[[]]],[[]]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[],[[[[]],[],[]]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[],[[[[],[]]]],[]]]]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[],[[[[],[],[]]]]]]]
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[],[[[[],[[]]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[],[[[[[]]]]]],[]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[],[[[[[]]]]],[]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[],[[[[[]]]],[]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[],[[[[[]]],[]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[],[[[[[]],[]]]]]]]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[],[[[[[],[]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[],[[[[[[]]]]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[],[],[]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[]]],[],[],[],[[]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[[]]],[],[],[[],[]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[]]],[],[],[[[]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[[[]]],[],[[],[],[]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[]]],[],[[[]],[]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[[[]]],[],[[[],[]]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[[[]]],[],[[[[]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[[[]]],[[]],[],[],[]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[[[]]],[[]],[[[]]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[[[]]],[[],[[[]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[[[]]],[[[]]],[[]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[]]],[[[],[],[]]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[[[]]],[[[],[[]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[]]],[[[[]]]],[]]]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[]]],[[[[],[]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[]]],[[[[[]]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[]],[]],[],[],[],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[[[]],[]],[[]],[[]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[]],[]],[[[[]]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[[]],[],[]],[],[],[]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[[]],[],[],[]],[],[]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[[]],[],[],[]],[[]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[],[],[]],[]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[],[],[]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[],[],[[]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[[]],[],[],[[],[]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[[]],[],[],[[[]]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[],[[]],[[]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[[]],[],[[],[]],[]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[[]],[],[[],[[]]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[[]],[],[[[]]],[]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[]],[[]],[],[],[]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[]],[[],[],[],[]]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[]],[[[],[],[]]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[]],[[[[]]]],[]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[]],[[[[]],[]]]]]]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[]],[[[[],[]]]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[]],[[[[[]]]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[],[]]],[],[],[],[]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[[],[]]],[[[],[]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[],[]]],[[[[]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[],[]],[]],[[]],[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[[],[]],[],[],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[],[]],[],[],[],[]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[[[],[]],[],[[],[]]]]]
[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[[],[]],[[[[]]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[],[],[]]],[],[],[]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[],[],[]]],[],[[]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[],[]]],[[],[]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[],[],[]]],[[[]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[],[],[]],[]],[],[]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[],[],[]],[]],[[]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[[],[],[]],[],[]],[]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[],[],[]],[],[],[]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[[],[],[]],[[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[],[],[]]],[],[]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[],[],[]]],[[]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[],[],[]],[]],[]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[],[],[]],[],[]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[],[],[]],[[]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[[],[],[],[],[]]],[]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[],[],[]],[]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[],[],[]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[],[],[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[],[],[[]]]],[]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[],[],[],[[]],[]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[],[],[[],[]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[],[],[[[]]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[],[],[[]]]],[],[]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[],[],[[]]]],[[]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[],[],[[]],[],[]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[],[[],[]]]],[]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[],[],[[],[]],[]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[],[],[[],[],[]]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[],[],[[[]]]]],[]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[],[],[[[],[]]]]]]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[],[],[[[[]]]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[],[[]]]],[],[],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[[]],[]],[]],[]]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]],[],[[]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[],[[],[]],[],[]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[],[[],[],[]]],[]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[],[[],[],[],[]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[],[[],[],[[]]]]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[],[[],[[],[]]]]]]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[],[[],[[[]]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[],[[[]]]]],[],[]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[],[[[]]]]],[[]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[],[[[]]]],[],[]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[],[[[]]],[]]],[]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[],[[[]]],[],[]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[],[[[]]],[[]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[],[[[]],[]]],[]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[],[[[]],[],[]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[],[[[]],[[]]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[],[[[],[]]]]],[]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[],[[[],[]]],[]]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[],[[[],[],[]]]]]]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[],[[[],[[]]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[],[[[[]]]]]],[]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[],[[[[]]]]],[]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[],[[[[]]]],[]]]]]
[1,1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[],[[[[]],[]]]]]]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[],[[[[],[]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[],[[[[[]]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[[]]]],[],[],[],[]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[[[]]]],[],[[],[]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[[[]]]],[],[[[]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[[[]]]],[[[],[]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]],[[[[]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[[[]]],[]],[],[],[]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[[[]]],[],[]],[],[]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[[[]]],[],[],[]],[]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[[]]],[],[],[],[]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[[[]]],[],[],[[]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[[[]]],[],[[]],[]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[[[[]]],[],[[[]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[[]]],[[]],[[]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[[[[]]],[[[],[]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[[[]],[]]],[],[],[]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[[]],[]]],[[[]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[[]],[]],[]],[],[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[[]],[]],[],[],[]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[[]],[],[],[]],[]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[]],[],[],[],[]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[]],[],[],[[]]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[[]],[],[[]]],[]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[[]],[[]],[[]]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[[]],[[],[],[]]]]]]
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[[]],[[],[[]]]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[]],[[[]]],[]]]]]
[1,1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[]],[[[],[]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[],[]]]],[],[],[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[[],[]]]],[],[[]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[],[]]]],[[[]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[[],[]]],[],[],[]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[],[]],[]],[]],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[[],[]],[]],[],[]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[],[]],[],[],[]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[[],[]],[[]]],[]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[[],[]],[[],[]]]]]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[[],[]],[[[]]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[[],[],[]]],[]],[]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[[],[],[]]],[],[]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[],[],[]],[],[]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[],[],[]],[[]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[],[],[]]],[]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[],[],[]],[]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[],[],[]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[],[],[[]]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[[],[],[[]],[]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[[],[],[[],[]]]]]]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[],[],[[[]]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[],[[]]]]],[],[]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[],[[]]]],[],[]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[],[[]],[],[]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[],[[]],[[]]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[],[[],[]],[]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[],[[],[],[]]]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[],[[],[[]]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[],[[[]]]]]],[]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[],[[[]]]]],[]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[[[[],[[[]]]],[]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[],[[[]]],[]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[],[[[]],[]]]]]]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[],[[[],[]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[],[[[[]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[[]]]]],[],[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[[[]]]]],[],[[]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[[[]]]]],[[],[]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[[]]]]],[[[]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[[[]]]],[]],[],[]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[[[]]]],[],[]],[]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[[[]]]],[[],[]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[[[[[[[]]]],[[[]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[[[]]],[]]],[],[]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[]]],[]],[]],[]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[]]],[],[],[]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[[[]]],[],[[]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[[[]]],[[]]],[]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[[[]]],[[],[]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[[[]]],[[[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[[[]],[]]]],[[]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[[[]],[]],[]],[]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[[]],[]],[],[]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[[]],[]],[[]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[[]],[],[]],[]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[[]],[],[],[]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[[[]],[],[[]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[[[]],[[]]]]],[]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[[[]],[[]],[]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[[[]],[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[]],[[[]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[],[]]]]],[],[]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[],[]]]]],[[]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[[],[]]]],[],[]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[[],[]]],[],[]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[],[]]],[[]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[[],[]],[]]],[]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[[],[]],[]],[]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[],[]],[],[]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[[],[]],[[]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[],[],[]]]]],[]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[[],[],[]]]],[]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[[],[],[]]],[]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[],[],[]],[]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[],[],[]]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[],[[]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[],[[]]]]]],[]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[],[[]]]]],[]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[],[[]]],[]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[],[[]],[]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[],[[],[]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[],[[[]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[[]]]]]],[],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[[]]]]]],[[]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[[[[[[]]]]],[]],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[[[[[[[[]]]]],[],[]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[[[[[[[[]]]]],[[]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[[[[[[[[]]]],[]]],[]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[[]]]],[[]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[[[[[[[[]]],[]]]],[]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[[[[[[[[]]],[]]],[]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[[]]],[],[]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[[[[[[[[]]],[[]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[[]],[]]]]],[]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[[[[[[[[]],[]]]],[]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[[[[[[[[]],[]]],[]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[[]],[]],[]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[[]],[],[]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[[]],[[]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[],[]]]]]],[]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[[],[]]]]],[]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[[[[[[[[],[]]]],[]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[[[[[[[[],[]]],[]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[[],[]],[]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[],[],[]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[],[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[]]]]]]],[]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[]]]]]],[]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[[[[[[[[]]]]],[]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[[[[[[[[]]]],[]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[[[[[[[[]]],[]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[[]],[]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[],[]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[]]]]]]]]]]
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[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[],[],[],[[]]]
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[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[],[],[[],[],[]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[],[],[[],[],[],[]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[],[],[]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[],[],[]]]
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[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[],[],[[[]]]]
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[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[],[],[],[[[]],[],[],[]]]
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[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[],[],[]],[[[]]],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[],[],[]],[[[]],[]],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[]],[[[]],[],[]],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[[]],[],[],[]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[],[]],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[],[],[]],[[[],[]]],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[],[]],[[[],[]],[]],[]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[],[],[]],[[[[]]]],[]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[]],[[[],[]],[],[]],[]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[],[]],[[[[]]],[]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[],[]],[],[],[]],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[]],[[[[]]],[],[]],[]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[],[[[[]]],[],[],[]],[]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[[]],[]]],[[]],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[],[[]],[[]],[]]],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[[],[[]],[[]]],[]],[]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[],[],[[]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[],[[]],[[]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[],[],[],[[]]],[[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[],[],[[]],[[]]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[],[],[[]]]],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[[[]]]],[[[[]]],[]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[],[]]],[],[],[],[]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[],[]],[],[],[[[[]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[[]]],[[]]],[[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[]],[[]]]],[[]],[]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[],[[],[[]]]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[]],[]],[]],[[]],[]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[],[[],[]],[]],[[]],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[],[[[],[],[],[]]],[[]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[[],[],[],[]]],[],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[],[]],[],[],[]],[],[]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[],[],[[],[],[]],[]],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[],[],[[]],[],[]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[]],[[],[],[],[]],[],[]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[],[]],[[[[[]]]]],[]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[],[]]],[[[[]]]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[],[]]]],[[[]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[],[]]]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[]],[]],[[[[]]]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[]],[]]],[[[]]],[]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[[],[]],[[[[]]]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[[[[]],[]]]],[[]],[]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[],[]]],[[[]]],[]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[],[]]]],[[]],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[],[],[]],[[],[],[]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[],[],[]]],[[]],[]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[],[[[[]],[],[[],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[]]],[],[[],[],[],[]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[[]],[],[],[[],[],[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[],[],[[[]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[],[],[[],[],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[],[[]],[]],[[]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[]],[[],[[]]],[[]],[]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[[]],[]],[[]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[]],[[],[[]],[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[]],[[],[[]],[],[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[]],[]],[[],[[]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]],[],[[]]],[[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[],[],[[],[],[],[[],[]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[],[[[[],[]]]],[]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[]]],[[[]]]],[],[]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[],[[[[]]]]],[[[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[],[],[]],[[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[[]],[],[],[]],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[]],[[]],[[],[[]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[]],[[],[[]],[[]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[],[[],[[]],[[]],[[]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[[]],[[]],[[]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[]],[[]],[[[]],[[]]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[]],[[],[[[]],[]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[],[[],[[[]],[]],[[]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[[]],[]],[[[]],[[]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[]],[[]],[[[]],[]],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[],[],[],[[]],[]],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[[]],[]],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[],[],[[],[[[],[]]]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[],[[[[]],[[],[],[]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[],[[[[[]],[],[]],[]]]]
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[],[[[[]],[[],[[]]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[[]]],[[],[[],[[]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[],[],[]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[],[[],[[],[],[],[[]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[],[[[[]],[],[],[]],[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[],[[[]],[[],[],[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[]],[[[[]]],[[]]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[]],[]]],[[]],[[]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[[]]],[[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[[]],[[]],[]],[[]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[],[],[]],[]]],[],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[],[],[]],[],[]]],[]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[[]],[[],[[]]]],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[]],[[[],[],[[]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[],[[],[]]],[[[[]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[]],[[]],[],[[]]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[[[]],[]],[],[[]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[],[[[],[]],[[]],[[]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[[[]],[],[[]]],[]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[],[[]],[],[[[],[[]]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[]],[[[],[[]]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[],[[],[[]],[[]]],[[]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[],[[],[[]],[[]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[[]],[]],[[]],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[],[]],[[]],[[]],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[],[[],[[[]],[]]],[[]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[[]],[[[]],[]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[[]],[[]],[],[]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[[]],[]],[[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[],[[],[]],[[[]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[[]],[]],[[]],[]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[],[[],[[[]],[[]],[]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[[],[[[],[[]]],[]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[[],[],[],[]],[[]]],[]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[],[],[[]]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[[]],[],[],[]],[]],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[]],[[],[],[],[]]],[]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[],[],[]]]],[],[],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[],[]],[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[[]],[[]],[]],[[[]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[[]],[]],[[[]],[]],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[]],[[[]],[]],[[]],[]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[[]],[[],[[]]],[[]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[],[[],[],[[]]],[],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[],[],[[],[]],[],[],[[]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[]],[[[],[]],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[[]],[],[[],[],[]]],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[[[]]],[[],[],[]]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[]],[[[],[]]]],[],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[]],[],[[],[]]],[],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[]]],[[],[]]],[],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[[[]]]],[]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[[[]]],[],[]],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[],[],[]],[],[]],[]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[],[],[],[]],[]],[[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[]],[[[],[]],[],[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[]],[[[[]],[],[],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[],[[[]],[]]],[]],[]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[[[],[[]]],[[]],[]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[],[[[],[]],[[]]],[[]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[],[],[]],[[],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[],[]],[],[[],[[]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[]],[],[],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[],[[],[],[[]]]]],[]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[],[]],[[]]]],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[],[],[[[[],[]]]],[],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[[]],[]],[]],[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[]],[]],[]],[[],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[]],[]],[[[],[]],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[],[]],[]],[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[[]],[]],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[],[]],[[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[],[]],[]],[[[]],[]]]
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[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[[[]],[]],[[],[[]],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[],[[]],[]],[]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[],[],[]],[]],[]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]]],[[[[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[],[]],[[]],[]],[[]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[],[],[]]],[[]],[[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[],[[[[[]]]]],[]],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[],[[]]],[[],[[]]],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[[],[],[],[]],[]],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[],[[[],[[[]]],[],[]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[],[[],[[[[]]]],[],[]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[],[]],[[]],[[]],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[[]],[],[],[],[[[]],[]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[[],[]]],[[],[],[],[]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[],[[],[[[]],[[]]],[]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[],[[],[[[]]],[]],[[]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[],[],[]],[[]],[[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[],[[]]],[]]],[[]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[],[],[]]],[]],[[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[],[],[]],[[]],[[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[]],[],[[]],[[]],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[[]]],[[],[],[[],[]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[[]],[],[]],[[[],[]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[]]],[],[],[[[],[]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[]]]],[],[[[],[]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]],[],[[]]],[[]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[[]],[[]]],[[],[]]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[],[],[[[],[]]],[]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[],[[],[[[],[],[]]],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[]],[[[[[]],[],[]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[]],[[[]],[],[],[],[]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[[[]]],[],[]],[]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0,1,0]=>[[[[[[]],[]]],[],[]],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[[[]]],[]],[],[]],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0,1,0]=>[[[[[[]]]],[],[],[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[[[]],[]],[]]],[],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[[[]]],[],[]]],[],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[[]],[]]],[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[[]]],[]],[]],[],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[[[]],[]]]],[],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[[[]]],[]]],[],[],[]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[],[],[[[[]],[[],[]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[],[[],[]]]],[]],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[]],[[],[],[]],[],[]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[],[[[]]]],[[],[]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[],[],[]],[[],[[[]]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[[]],[[[]]]],[[]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[],[[[[]]]],[]],[[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[]],[[],[[[]]],[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[]],[[],[],[],[[[]]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[]],[[[]],[[[]]],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[]],[[[[[]]]],[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[]],[[],[],[[[[]]]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[[[],[]]],[[[],[],[]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[],[[],[[],[[]]]],[[]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[],[[],[[]],[[],[[]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[],[],[],[[]],[],[[],[]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[[[[]]],[]]],[[]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[],[]]],[]],[[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[],[]],[]],[]],[],[]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[],[[],[[[[]],[]],[]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[],[[],[[],[[[]],[]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[],[],[[[[]],[]],[]],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[],[[[[]],[]],[]]],[]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[],[]]],[]],[[],[]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[[[]]],[]],[[],[],[]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[[]],[]],[[],[],[],[]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[],[],[[]]],[[]],[[]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[]]],[]],[[]],[[]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[],[[]]]],[],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[],[[[],[[]]]],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[],[],[[],[],[[],[]]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[],[],[[],[],[[[],[]]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[],[[],[],[[[[],[]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[],[[[]]]],[[[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[]],[[],[[]]],[[[]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[],[[[]]],[[]]],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[[]]],[[]],[[],[[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[]],[[],[[]],[[]]],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[[],[]]],[[[]]],[[]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[]]],[],[],[[],[]],[]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[],[],[[],[],[[[]]],[]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[],[[[]]]],[[],[]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[],[],[[]]],[[],[]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[],[]]],[]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[]],[]],[[[[[]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[[[]]],[]],[[[[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[[[[[[]]]],[]],[[[]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[],[[]]],[]],[]],[]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[[],[[[]],[[]]],[]],[]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[],[[[[]],[]],[[]]],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[[]],[]],[[]],[],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[[]]]],[[],[[[]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[]],[[[]]]],[[[]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[[[[[[]]],[[]]]],[[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[]],[[[[[]],[[]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[[],[],[],[]]],[]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[[]],[],[],[[],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[],[],[]],[[[]],[]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[],[[],[],[],[]],[[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[],[],[]],[],[[[]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[],[],[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[],[[],[]],[],[],[[[]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[],[[[],[]]],[[],[[]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[[]]],[],[[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[],[[[[],[]]]],[]],[]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[[]],[]],[],[[]],[]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[],[],[[[],[]]]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[],[[[[],[[]]],[],[]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[],[[[[],[]],[],[],[]]]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[],[[],[[],[[[[]]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[],[[],[[],[],[[[]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[],[[],[[],[[],[],[]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[]]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[[]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[],[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[],[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[]],[]]]]]]],[]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[],[[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[],[[[[[[[[]],[]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[[],[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[[[]]],[]]]]]],[]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[[],[],[]]]]]]],[]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[],[[[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[],[[[[[[[[]]],[]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[],[[[[[[[],[],[]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[],[[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[[[[[[[[[]]]],[]]]]],[]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[[],[]],[]]]]]],[]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[],[[],[]]]]]]],[]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[],[[[[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[],[[[[[[[[]]]],[]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[[],[[[[[[[],[]],[]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[[],[[[[[[[]],[[]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[],[[[[[[],[[],[]]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[],[[[[[],[[[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[[[]]]]],[]]]],[]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[[]],[],[]]]]]],[]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[],[],[[]]]]]]],[]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[],[[[[[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[],[[[[[[[[]]]]],[]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[[],[[[[[[[]],[],[]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[[],[[[[[[],[[]],[]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[],[[[[[[],[],[[]]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[],[[[[],[[[[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[[[[[[[[[]]]]]],[]]],[]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[[[]]],[[]]]]]],[]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[],[],[]]]]]],[]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[]],[[[]]]]]]],[]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[[],[[[[[[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[],[[[[[[[[]]]]]],[]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[[],[[[[[[[]]],[[]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[],[[[[[[],[],[],[]]]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[],[[[[[],[[],[[]]]]]]]]
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[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[[]],[[]],[[]],[[]],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]],[[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[]],[[]],[[[]]],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[]],[[]],[[[[]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[]],[[]],[[[]]],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[]],[[]],[[[]]],[[[]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[[[]]],[],[],[],[],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[]],[[[]]],[[[]]],[[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[]],[[[[]]]],[[[]]],[]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[[[]]]],[[[[]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[]],[[[[[[]]]]]],[],[]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[]],[[[[[[]]]]]],[[]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[]],[[[[[[[]]]]]]],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[],[],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[]]],[],[],[],[],[],[[]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[[]]],[],[],[],[],[[]],[]]
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[]]],[],[[[[[]]]]],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]]],[[]],[],[],[],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[]]],[[]],[[]],[[]],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[]]],[[]],[[]],[[[]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[]]],[[[]]],[[]],[[]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[]]],[[[]]],[[[[]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[]]],[[[[]]]],[[[]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[]]],[[[[[[]]]]]],[]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[]]],[[[[[[[]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[]]]],[],[],[],[],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[]]]],[],[],[],[],[[]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[]]]],[],[],[[[[]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[]]]],[],[[[[]]]],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[]]]],[[]],[[]],[[]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[[]]]],[[]],[[[[]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[[[]]]],[[[]]],[[[]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[]]]],[[[[]]]],[],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[]]]],[[[[]]]],[[]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[]]]],[[[[[]]]]],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[]]]],[[[[[[]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[]]]]],[],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[]]]]],[],[],[],[[]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[[[]]]]],[],[[[]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[]]]]],[],[[[[]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[[[]]]]],[[]],[[]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[]]]]],[[[[]]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]],[[[[[]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[]]]]]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[[[[]]]]]],[],[],[[]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[[[]]]]]],[],[[]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[[[[[[[]]]]]],[],[[[]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[[[]]]]]],[[[]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[[[[]]]]]],[[[[]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[[[]]]]]]],[],[],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[[[[]]]]]]],[],[[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[[[]]]]]]],[[]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[[[[]]]]]]],[[[]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[]]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[],[]],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[],[],[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[],[],[],[],[]],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[],[],[],[],[],[]],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[],[],[],[],[],[],[]],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[],[],[],[]],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[],[],[],[[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[[]],[],[],[],[]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[],[],[],[[]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[]],[],[],[],[],[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[],[],[],[[]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[],[[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[[]],[]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[],[],[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[[]],[],[]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[]],[],[],[],[],[],[[],[]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[],[[[[[[[[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[[]]]]]]]],[]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[],[]]]]]]],[]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[],[]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[],[[[]]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[],[[[[]]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[],[[[[[]]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[],[[[[[[]]]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[],[[[[[[[]]]]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[],[],[],[]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[],[],[[],[]],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[],[],[[],[],[]],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[[],[],[]],[],[],[],[]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[[],[]],[],[],[],[]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[[]],[],[],[],[]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[],[],[],[],[]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[],[],[],[],[],[],[[[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[],[],[],[],[],[[[],[]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[],[],[],[],[[[],[],[]]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[],[],[[[],[],[],[]]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[],[[[],[],[],[],[]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[],[],[],[]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[],[],[],[]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[[]]]]]]],[]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[[[[[[[[[[]]]]]],[]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[[[[[[[[[[]]]]],[]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[[[[[[[[[[]]]],[]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[[[]]],[]]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[[],[]],[],[],[],[],[]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[],[],[]],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[],[],[[],[],[],[]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[],[],[],[[],[],[]],[]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[],[],[],[],[[],[]],[],[]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[[]],[],[],[]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[],[],[]]]]]],[]]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[],[[[[[[],[],[]]]]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[[]]],[[]],[[]],[[]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[],[[]],[[]]],[[]],[[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[],[[]],[[]],[[]]],[[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[],[[]],[[]],[[]],[[]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[],[[]],[[]],[[]],[]],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[],[[]],[[]],[]],[[]],[]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[[]],[]],[[]],[[]],[]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[]],[[]],[[]],[[]],[]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[],[],[[[[[[[]]]]]]]]]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[],[],[],[[[[[[]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[],[],[],[],[[[[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[],[],[],[],[],[[[[]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[],[],[],[[],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[],[],[],[[],[],[]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[],[[],[],[],[],[]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[[],[],[],[],[],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[],[],[],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[],[],[],[],[],[[[]],[]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[],[],[],[],[[[]],[],[]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[],[],[],[[[]],[],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[[[]],[],[],[],[]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[[[]],[],[],[],[],[]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[]],[],[],[],[],[],[]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[]],[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[[[]]],[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[[]]],[[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[[[[]]]],[[[]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[[[[]]]],[[[[]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[[[]]]]],[[[[]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[[],[[],[[],[]]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[],[[[],[]],[[],[]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[]],[[],[[],[]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[],[[],[]]],[[],[]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[[],[]],[]],[[],[]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[],[[],[[],[]]]],[]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[],[[[],[[[],[]],[]]],[]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[]],[[],[]]],[]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[],[[],[]]],[]],[]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[],[[],[[],[]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[]],[[[],[]],[[],[]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[]],[[[],[[],[]]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[]],[[[[],[]],[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[]]],[[],[[],[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]]],[[[],[]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[]],[[],[[],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]],[[[],[]],[]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[],[[],[]]]],[[],[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[[],[]],[]]],[[],[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[],[]]],[[],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[[],[]]],[]],[[],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[],[]],[]],[]],[[],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[[],[]],[]],[]],[]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[],[],[],[]]],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[],[],[],[]]]]],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[],[],[],[]]]],[]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[],[[],[]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[],[[[[[[[],[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[]],[]]]]]],[]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[],[[]]]]]]],[]]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[[],[[[[[[[]],[]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[],[[[[[[],[[]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[],[]],[],[],[],[],[],[[]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[],[],[],[]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[[]],[],[],[]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[]]],[[[[[],[],[]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[[]]]],[[[],[],[],[]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[[],[]],[]]]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[],[[[[],[],[],[],[]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[],[[[[[],[],[],[]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[],[],[[[[[[[],[]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[],[],[[[[[[],[]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[[[]]]]]],[[[]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[[[[[[[[[]]]]]],[[]]]]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[],[[[[[],[]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[],[[[[[]],[]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[[[[],[[[[[]]],[]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[[[[],[[[[[]]]],[]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[],[[[[[[]]]]]],[],[]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[],[],[[[[]]]],[],[],[]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[[]],[],[],[],[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[]],[[],[],[],[],[],[],[]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[],[],[]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[],[],[],[],[[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[],[],[],[],[[]],[],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[],[],[],[],[[[]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[],[],[],[]],[[],[],[]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[],[[[],[],[]]],[],[],[]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[],[],[[[],[]]],[],[],[]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[],[],[],[[[]]],[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[],[],[[],[]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[[],[],[],[],[],[]],[],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[],[],[],[],[],[]],[]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[[],[]],[],[],[],[[]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[],[[],[],[]],[],[],[],[[]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[],[],[],[]],[],[],[],[[]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[],[],[],[]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[],[],[],[]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[[],[],[]]]]],[]]]]
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[],[[[[[],[],[]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[],[],[],[[[]]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[],[],[],[[[[]]]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[],[],[],[[[[[]]]]]]]]
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[],[],[[[[[[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[[[]]]]]]],[[]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[]]]],[[[[[]]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[]]],[[[[[[]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[]],[[[[[[[]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[[],[[[[[[[]]],[]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[[[],[[[[[[]]]],[]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[[[[[],[[[[[]]]]],[]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[[],[[[[]]]]]],[]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[],[[[]]]]]]],[]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[[],[],[],[]],[],[],[]],[]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[],[[],[],[]],[],[],[]],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[[],[]],[],[],[]],[]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[[]],[],[],[]],[]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[],[[],[],[],[],[]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[],[],[],[]],[]]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[],[[[],[],[],[],[]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[],[],[]],[],[]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[[],[]],[],[],[]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[[[[[[[[[]],[]],[]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[]],[],[],[],[],[[],[]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[[],[],[],[],[],[]]],[],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[[],[],[],[],[]]],[],[],[]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[[],[],[],[]]],[],[],[],[]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[],[],[]]],[],[],[],[],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[],[]]],[],[],[],[],[],[]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[],[],[],[]],[[]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[],[]]]]],[],[],[],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[[[],[]]]]]],[],[],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[],[],[],[]]]],[],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[[],[],[],[],[]],[],[]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[],[],[],[[],[]]]]]]
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[],[],[[[[[]]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[[]],[[]],[[]],[[],[]],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[],[]]],[[]],[[]],[[]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[],[],[],[],[]],[]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[[],[],[],[]]],[]]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[],[[[],[],[],[]]]]]]]
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[[[],[],[[[[]]]]]]]]
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[[],[],[[[[[]]]]]]]]
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[],[],[[[[[[]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[],[],[],[],[[],[]],[],[],[]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[],[],[[],[]],[],[],[],[]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[],[]],[],[],[],[],[],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[[[],[]]]]],[[[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[],[],[]],[]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[],[],[]],[],[],[],[]]
[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]=>[[],[],[],[],[],[],[[],[[]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[[],[],[],[[],[]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[[],[],[],[],[]]]],[]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[],[],[[],[],[]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[[],[],[],[],[]]],[]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[],[[],[],[],[]]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[[],[]],[],[],[],[],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[]],[],[],[],[[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[],[],[]],[],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[],[],[],[[[]],[],[],[]],[]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[[],[],[],[],[]],[],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[],[],[]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[]]],[[[]]]],[[[]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[],[],[[],[],[],[],[[[]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[],[],[],[],[[],[],[[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[],[[],[],[],[],[],[]],[[]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[]],[[],[]],[],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[[]],[]]]]]],[[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[]],[[]],[[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[[]],[]],[[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[]],[[]],[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[[]],[[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[[]],[[]],[[]],[[]]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[[]],[[]],[[]]],[[]],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[]],[[]]],[[]],[[]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[]],[],[],[],[],[],[]],[]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[],[[]]],[],[],[],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[],[],[[]]],[],[],[],[]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[],[],[],[[]]],[],[],[],[]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[],[[[[[]],[],[],[],[]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[[[],[[[[[]]],[],[],[]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[],[],[[[[]]],[],[],[]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[],[],[[[[]]]],[],[]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[],[],[],[[[]]]]],[]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[],[],[],[[]]]]],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[],[],[],[],[]],[],[[]],[]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[],[],[],[]],[],[[],[]],[]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[],[[],[],[]],[]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[]],[],[[],[],[],[]],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[],[[],[],[],[],[]],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[[[[[[[[],[]]]]]]],[],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[[],[]]]]]],[],[]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[[[[[[[[],[]]]]],[],[]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[[[[[[[[],[]]]],[],[]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[[[[[[[[],[]]],[],[]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[[],[]],[],[]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[]],[[[]]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[[],[[[[[[]]]]],[[[]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[[],[[[[[[[]]]]],[[]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[]],[[],[],[],[]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[],[],[],[],[],[[[]],[]],[]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[]],[[[],[],[],[],[],[]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[],[]],[],[],[],[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[[],[],[],[],[],[[],[]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[],[]],[],[],[],[],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[],[],[],[],[],[],[[]],[]]]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[]],[[[[[[]]]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[]]]],[[[[]],[[]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[[[[]]]]],[[[[]],[]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[[[[[]]]]],[[[],[[]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[]]],[[[[[]]],[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[],[],[],[[]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[],[]]]]]],[]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[[[[[[[[[],[]]]]],[]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[[[[[[[[[],[]]]],[]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[[[[[[[[[],[]]],[]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[],[[[],[]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[],[[[[],[]]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[[[],[[[[[[],[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[[[]]]]]]],[],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[[[]]]]]],[],[],[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[]],[[]],[[[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[]],[[[]],[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[]],[[]],[[]],[]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[],[[],[[]],[[]],[[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[]],[[]],[[],[]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[[],[]]]],[],[],[],[]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[],[],[[[],[]]],[],[],[],[]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[[]]],[],[],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[[[]]],[],[],[],[]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[[]],[],[],[],[]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[]],[[],[],[],[]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[[[],[]]],[[[],[],[]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[],[],[[],[]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[]],[[[[[[],[]]]]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[],[],[],[[[]]],[[]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[],[[]],[[[]]],[],[],[]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[],[],[],[]],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]],[]],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[]],[[],[[],[[],[[]]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[[]]],[[],[[],[[]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[],[[]],[[]]],[[],[[]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[],[[]],[[]],[[]]],[],[]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[],[[]],[[]],[[]],[],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[],[[]],[[]],[],[[],[]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[]],[],[[],[[],[]]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[],[],[[],[[],[[],[]]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[],[[],[[],[[],[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[],[],[],[],[],[],[[]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[],[],[],[]]],[]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[[[],[]],[]],[]],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[[]],[],[],[],[],[]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[[[]]],[],[],[],[],[]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[]],[[[[[[],[]]]]]],[]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[[],[[[[[[],[]]]]]],[[]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[],[],[],[],[[],[],[]]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[],[[],[],[],[],[],[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[[],[],[],[],[],[[[]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[],[],[],[[[],[]]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[[]],[[]],[[]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[],[[]],[[[]],[[]],[[]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[],[[]],[[]],[[[]],[[]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[]],[],[],[],[[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[],[],[],[],[[],[[]]],[[]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[],[],[],[],[[[]],[]],[[]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[],[[],[[]]],[[]],[]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[],[],[],[[[]],[]],[[]],[]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[],[[[[[[[]]]]]]],[]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[[[],[],[],[],[],[]]],[]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[],[],[],[],[]]],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[[]]],[],[],[],[[],[]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[],[],[],[]],[[]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[],[],[],[]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[]],[]],[]],[[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[[]],[]],[[]],[[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[[]],[]],[]],[[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[[]],[]],[]],[[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[[]],[]],[]],[[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[]],[]],[]],[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[]],[[[]],[]],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[[]],[]],[[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[]],[[]],[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[[]],[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[]],[[[[]],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[]],[[[[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[[[]],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[]],[[[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[]],[[[]],[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[]],[[]],[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[]],[[]],[]],[]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[[]],[]],[]],[]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[[]],[]],[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[[]],[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[]],[[]],[]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[]],[]],[]],[]],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[[]],[]],[]],[]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[[]],[]],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[]],[[]],[[[]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[]],[]],[]],[[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[]],[[[]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[[]],[]],[[[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[[]],[]],[[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[[]],[]],[[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[[]],[]],[]],[[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[]],[[[]],[[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[]],[[]],[[]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[],[],[],[],[],[]],[[]],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[],[],[],[],[]],[[],[]],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[]],[[],[],[]],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[[],[],[],[]],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[]],[[],[],[],[],[]],[]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[],[],[],[]],[[[]]],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[],[],[],[]],[[[]],[]],[]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[],[]],[[[]],[],[]],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[],[]],[[[]],[],[],[]],[]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[[]],[],[],[],[]],[]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[[]],[],[],[],[],[]],[]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[[]],[],[],[],[],[],[]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[],[],[],[],[[]],[[]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[],[],[[]],[[]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[]],[[]],[[]],[[]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[],[[]]]]]]],[[]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[],[[],[],[],[]],[]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[],[],[[],[],[]]],[]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[],[],[[],[]]]],[]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[],[],[[[],[]]]],[]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[],[[[],[],[]]],[]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0,0]=>[[[[[[[[[]]]]]],[]],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[[[[]]]]],[]],[],[]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[[[[]]]],[]],[],[],[]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[[]]],[]],[],[],[],[]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[]],[]],[],[],[],[],[]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[],[],[],[]],[]],[]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[],[],[]],[]],[]],[]]]
[1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[[[[],[[[[[[]],[]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[[[[],[[[[[[]]]]]]],[]]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[],[[]],[]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[[[[[[[],[[[]]],[]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[[[[[[],[[[[]]]],[]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[]]],[[]]],[[]],[[]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[],[],[],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[],[],[],[]]],[[]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[[],[],[],[]]]]],[]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[]],[[[[[[]]]]]],[]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[],[[[[[[]]]]]],[[]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[],[],[],[[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[],[]],[[]],[[]],[[]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[],[]],[[[[[[]]]]]],[]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[],[]]],[[[[[]]]]],[]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[],[]]]],[[[[]]]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[[],[]]]]],[[[]]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[[],[]]]]]],[[]],[]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[[[],[[[[[[]],[],[]]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[[],[[[[[]],[],[],[]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[[[[]],[],[],[],[]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[[]],[],[],[],[],[]],[]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[[]],[],[],[],[],[]],[[]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[],[[],[[],[]]]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[]],[],[[[],[[],[]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[],[[[],[[],[]]]],[]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[],[[],[]]]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[[]],[],[[[],[]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[]],[],[[[],[]]]],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[],[[],[[[],[]]]],[],[[]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[[],[]]]],[],[[]],[]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[],[[],[[[],[]]],[]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[],[[[],[[[],[]]],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[]],[],[[[[],[]]],[]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[],[[[[],[]]],[]],[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[[],[]]],[]],[]],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[],[[],[[]],[],[[]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[]],[],[[]]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[]],[],[[[]],[],[[]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[],[[],[[[]],[],[[]]],[]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[[[]],[],[[]]],[]],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[]]],[],[[],[[]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[],[[[]]],[],[[],[[]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[],[[],[[]],[]],[],[[[]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[],[[[]],[]],[],[[[]]],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[],[[],[[],[[]]],[],[[]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[],[[]]],[],[[]]],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[[[]]],[],[[]],[]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[[[]]],[],[[]],[]],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[[],[[],[[],[[]],[]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[[]],[]]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[]],[],[[[],[[]],[]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[],[[],[[[],[[]],[]]],[]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[[]],[]]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[],[[],[[]],[],[[[]],[]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[],[[[]],[],[[[]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[],[[],[[[]],[]]],[],[[]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[[]],[]]],[],[[]],[]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[],[[],[[],[[[]],[]],[]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[[]],[]],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[],[[]],[],[[[[]],[]],[]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[],[[[[]],[]],[]],[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[[]],[]],[]],[]],[]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[],[[[],[],[],[],[]],[]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[],[],[[[],[],[]],[],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[[]],[],[[],[],[]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[[]],[],[],[],[[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[]],[],[],[],[],[],[[]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[[[[[[[[]]]]]]],[[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[[[[[[[]]]]]],[[],[],[]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[[]]]]],[[],[],[],[]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[]]]],[[],[],[],[],[]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[]]],[[],[],[],[],[],[]]]
[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[],[],[[]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[[]],[],[],[],[],[[],[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[],[],[],[],[[]],[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[],[],[],[],[],[[],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[],[[]]],[[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[]],[[]],[[],[[]]],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[]],[[]],[[]],[[],[[]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[]],[[]],[[],[[]],[]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[]],[[],[[]],[]],[[]],[]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[[[],[[[[[[],[]]]]]],[]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[[],[[[[[[],[]]]]]],[],[]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[],[],[[[[[[],[]]]]]],[]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[[],[[[[[[[],[]]]]]]],[]]
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[],[],[[[[[[],[[]]]]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[],[]],[[[[[[]]]]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[],[]]],[[[[[]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[[],[]]]],[[[[]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[[],[]]]]],[[[]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[[],[]]]]]],[[]]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[],[[],[[]]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[],[[],[],[]]]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[],[[]]],[]],[[]],[[]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[[[],[[[[]]]],[[]]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[],[[]],[[]],[[]]],[]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[]],[[],[[]],[[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[]],[[],[[]],[[]],[[]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[]],[[[],[],[[]],[],[]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[]],[],[]],[[[]]],[]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[],[[]],[],[]]],[[]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[[]],[],[],[]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[[],[[],[[],[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[],[],[],[],[]],[],[[],[]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[],[],[],[],[]],[],[],[[]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[],[],[]]]],[],[],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[],[],[],[[]]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[],[[[[]],[],[],[],[],[]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[[]],[]],[[]],[[]],[]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[],[[],[[]]]],[[],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[],[[],[[]]]],[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[],[[[],[[]]],[[],[]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[],[[[],[[]]],[]]],[],[]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[],[[]]],[]],[]],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[],[]],[[]]],[[],[]],[]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[],[]],[[]]],[],[[],[]]]
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[],[[],[[[]],[[],[]]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[],[]],[[[]],[[],[]]],[]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[],[[],[[[]],[]]]],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[],[[[],[[[]],[]]],[]],[]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[[]],[]],[[],[]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[[]],[]],[]]],[]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[],[[[[[]],[]],[]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[],[[[],[]]]],[[],[]],[]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[],[[[],[]]]],[],[[],[]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[],[[[[],[]]],[[],[]]],[]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[],[[[[],[]]],[]],[[],[]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[],[]]],[]],[]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[],[[],[[],[[[],[]]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[],[]],[[],[[[],[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[],[]],[[[],[]]]],[]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[]],[],[[[[],[]]],[]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[],[[],[]],[[[[],[]]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[],[[],[[],[[]]]]],[],[]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[],[[[],[[],[[]]]],[]],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[],[]],[[],[[]]],[[],[]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[],[[[],[[]]],[]]],[]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[],[],[[[[],[[]]],[]],[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[],[[[],[]],[[]]],[[],[]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[[],[]],[[]]],[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[[],[]],[],[[[]],[[],[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[],[[],[]],[[[]],[[],[]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[],[[],[[],[[[]],[]]]],[]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[],[]],[[[]],[]]],[]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[],[],[[],[[[[]],[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[],[]],[[[[]],[]],[]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[],[],[[[],[],[]]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[],[],[[[],[],[],[]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[],[],[],[]],[[[]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[[],[],[],[]],[[[[]]]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[],[],[]],[[[[],[]]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[]],[[[[],[],[]]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[]],[[[[],[],[],[]]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[],[[[],[[[]],[]]],[]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[],[[[],[[]],[[],[]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[],[[[]],[[[[]]]],[]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[],[[[],[[],[]],[[]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[],[[[]],[[[],[[]]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[[],[[],[],[[]]],[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[],[[],[[],[]],[[[]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[],[[[[]]],[[],[]],[]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[],[[],[[[]],[],[]],[]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[[[],[[[[[]],[]]],[[]]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[],[[[[]],[[],[]],[]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[],[[],[[[[]]]],[[]]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[],[[[[],[]],[[]],[]]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[],[[],[[[],[[]]],[]]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[]],[],[[[],[[]]],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[]],[],[[[]],[[[]]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[]],[],[[],[[],[]],[]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[]],[],[[[[]]],[[]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[]],[],[[],[[[]],[]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[]],[]],[],[[[]],[]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[[]],[]],[],[[],[[]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[],[[]]],[],[[[]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[],[[]]],[],[[],[[]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[],[[]]],[]],[],[[]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[]],[[[]]]],[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[[],[]],[]],[],[[]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[[]]],[[]]],[],[[]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[[]],[]]],[],[[]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[],[[[]],[]]],[]],[]]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[[]],[[],[]]]],[]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[]],[[[[]]]],[]],[]]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[[],[]],[[]]]],[]]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[]],[[[],[[]]]]],[]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[],[[],[],[[]]],[]],[]]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[[],[]],[[[]]]],[]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]]],[[],[]],[]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[[[]],[],[]],[]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[[[]],[]]],[[]]],[]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[[],[]],[]]],[]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[],[]],[[]],[]]],[]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[],[[[],[[]]],[]]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[[]],[]],[[]],[[]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[],[[[]],[],[[[]],[[]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[],[[[]],[],[[[]]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[],[[[]],[],[],[[]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[],[[[]],[],[[]],[],[[]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[],[[[]],[],[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[],[[]],[]],[],[[]],[[]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[]],[[],[]],[],[[]],[[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[],[],[],[],[],[[]],[[]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[[[[]]]]]],[[],[]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[[[[]]]]],[[[],[]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[[]]]],[[[[],[]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[]]],[[[[[],[]]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[],[[],[[],[[],[[]]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[],[[]]],[[]],[[]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[]],[[]]],[[]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[],[[],[[]],[[]],[[]]],[]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[],[[],[[]],[[]],[]],[[]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[],[[]],[]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[],[[],[[[]],[]]],[[]],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[],[],[],[]]]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[[],[],[],[],[],[[]]]],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[[]]],[[[]]],[[[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[],[],[],[],[],[]],[[],[]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[[]],[],[],[],[],[]],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[[],[]],[],[],[],[],[]],[]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[]],[[],[[],[[],[],[]]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[]],[[],[[[],[],[]],[]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[]],[[[],[[],[],[]]],[]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[],[],[]],[]],[]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[],[[]],[[],[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[]],[],[[[]],[],[]],[]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[]],[[],[],[[]]],[],[]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[[]],[],[]],[[]],[],[]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[]],[[],[[],[],[]]]],[]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[]],[[[],[],[]],[]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[]],[],[[]],[],[]]],[]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[]],[[],[],[]]],[]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[[]],[],[]],[]],[]],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[],[[]],[[],[[],[],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[],[[]],[[[],[],[]],[]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[],[],[[[]],[],[[]],[],[]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[[[]],[[],[],[]]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[],[],[[[[]],[],[]],[]],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[],[[],[],[[]]],[[],[],[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[],[],[[[]]],[],[]],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[],[]],[[]],[[],[],[]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[],[],[[]]]],[],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[],[],[]],[[]]],[],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[[]],[],[[]]],[],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[[],[],[]]],[[]],[],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[],[],[]],[]],[[]],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[],[[],[[],[],[[]]]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[],[[],[[[],[],[]],[[]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[[],[],[[]],[],[[]]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[],[[],[],[]]],[[]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[],[[[[],[],[]],[]],[[]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[],[],[[]],[[],[],[[]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[],[],[[[]],[],[]],[[]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[],[[],[],[[]]],[],[[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[],[],[]],[[]],[],[[]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[],[[],[[],[],[]]]],[[]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[],[[[],[],[]],[]]],[[]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[],[[],[],[]]],[]],[[]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[],[],[]],[]],[]],[[]]]
[1,1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[]],[[],[[[[[]]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[[[[[],[[[[]]]]]],[[]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[]]],[[[],[[[]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[],[[]]]]],[[[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[],[],[],[],[],[[],[]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[],[],[],[[],[[]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[[],[],[],[]],[],[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[]],[[],[],[]],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[],[[]],[[],[]],[],[],[],[]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[],[[]],[[]],[]],[]],[]]
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[[],[[[],[[[],[]]]]]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[[],[[[],[[[]],[]]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[],[[[]],[]]],[]],[[]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[],[],[],[[[],[]]]]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[],[],[[[],[],[]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[],[],[]]],[[],[]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[],[],[]]],[[[[]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[]],[[[[[],[],[]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[],[],[],[[]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[],[[],[],[],[],[[]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[],[],[[],[],[],[[]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[],[],[],[[],[],[[]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[],[],[[]]]]]],[]]
[1,1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[[],[]],[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0]=>[[[[[[[[]],[[],[]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[],[[],[],[],[],[],[[[]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[],[[],[],[],[]]]]],[]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[[],[],[],[]],[]]]],[]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[],[[],[],[],[]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[[],[[[[[],[],[],[]],[]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[]],[[]],[[],[],[],[],[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[]],[[]],[[]],[[],[],[]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[],[],[],[[]],[],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[],[],[],[[],[]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[],[],[],[[[]]],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[],[],[],[[],[[]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[[],[],[],[]],[],[],[[]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[],[],[]],[],[],[]]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[[],[]],[],[],[],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[[]],[[]],[],[],[],[]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[]],[[[],[[[]],[],[]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[]],[[[[],[],[[]]],[]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[]],[[[[[],[],[],[]]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[],[]]],[[]],[[[],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[],[[[]],[],[]]]],[[]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[],[],[[]]],[]]],[[]]]
[1,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[]],[],[[[[[[]]]]]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[[],[]],[],[[[[],[]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]],[],[[[[]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[[[],[]]]],[],[[],[]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[[[[]]]]]],[],[[]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[[],[],[],[]],[[]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[[],[],[],[]],[],[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[[],[],[],[],[],[]],[]],[]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[[],[[[[],[[[[]]]],[]]]]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[],[[[],[[[[[]]]]],[]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[[],[[],[[[[[[]]]]]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[],[],[]],[[]],[[]],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[[]]],[],[],[],[],[]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[],[[[]],[[]],[]]],[]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[],[[],[[[]],[[]],[[]]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[],[[],[[[]],[[]]],[]],[]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[],[[],[[[]]],[]],[[]],[]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[],[],[]],[[]],[[]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[[]],[],[],[],[],[[]],[]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[],[],[],[[],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[],[],[],[],[[]],[]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[[]],[[]],[]],[],[]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[]],[[[]],[],[]]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[[[]],[]],[[],[]],[]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[[]],[[]],[[],[],[]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[]],[[[[],[]]],[]],[]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[]],[[[],[[]]],[],[]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[]],[],[[[]],[]]],[]]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[]],[[],[[[],[]]]],[]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[[]],[],[]],[[]],[]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[]],[[],[]],[[],[]]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[]],[[[],[],[[]]],[]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[]],[],[[],[[]],[]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[]],[[],[[],[[],[]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[[[]]],[]],[]],[]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[],[[[[]]],[[]],[],[]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[]]],[[[],[]]],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[],[[[[]]],[],[[]],[]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[[]]],[[],[[],[]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[],[]],[[[[]]],[]],[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[],[]],[[[]]],[[],[]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[],[[],[[[[]]]],[]],[]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[],[[],[[[]]]],[[],[]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[],[]],[]],[[[]]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[[]],[],[[[]]]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[],[[[],[]]],[[[]]],[]]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[],[[]],[[[]]]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[],[[],[[],[[[]]]]],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[[],[]],[]],[]],[[]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[],[[]],[]],[],[[]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[],[[[]],[],[]]],[[]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[]],[[],[]],[[]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[],[[]],[[],[],[[]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[],[[[[],[]]],[]],[[]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[],[[[],[[]]],[],[[]]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[],[],[[[]],[]]],[[]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[],[[],[[[],[]]]],[[]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[],[],[]],[[]],[[]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[],[[],[]],[[],[[]]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[],[[[],[],[[]]],[[]]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[],[],[[],[[]],[[]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[]],[[[[[[[]],[]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[[],[],[[[[[[[]]],[]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[]],[],[],[],[],[[],[],[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[]],[[[[[[],[],[]]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[]],[[[[],[],[],[],[]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[],[[],[],[],[[]]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[]],[[[[[],[]],[]]],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[]],[[],[],[[],[]],[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[]],[[],[[[],[[],[]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[]],[[[]]],[]],[],[]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[[]],[[]]],[],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[[]],[],[[],[[[]]],[]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[]],[[[]],[],[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[[[]],[]],[]]],[]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[[]],[],[[],[]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[]],[[[],[[],[]]]]],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[[]],[],[[]]],[]]],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[],[[]],[[[],[]],[],[]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[],[[]],[[],[],[[],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[],[],[[[[]],[[[]]],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[[]],[]],[],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[],[[[]],[],[[],[]]],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[],[[[],[[]]]],[[[],[]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[],[[[],[[[[]]]],[]]],[]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[],[]]],[[[[]],[]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[[],[]],[],[[]]],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[],[[],[[]]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[[[]]],[[]]]],[],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[],[]],[],[]],[[]],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[],[[],[]]],[[]],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[],[[[],[[[]],[],[[]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[[],[]],[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[],[[],[],[[],[]],[],[[]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[],[[[],[[],[[]]]]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[],[[[[],[],[[]]],[[]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[[[]]],[]],[],[[]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[[],[]],[],[[[]],[[]]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[],[],[[],[[[]]],[[]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[[],[]],[]]],[]],[[]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[[],[]],[],[]],[[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[],[[[],[[],[]]]]],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[]],[]],[[[[]]]],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[]],[],[[],[[[]]]],[[]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[]],[],[]],[[[[]]]],[]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[]],[[],[[[]]]],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[],[]]],[],[[[[]]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[],[[],[]]],[[[[]]]],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[[]]],[],[[],[[[]]],[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[[[],[]]],[],[[[[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[[]],[],[[[]]]],[[]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[[]],[],[]],[[[[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[],[[],[]],[[[]]]],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[]],[]],[[[[]]],[],[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[[]]]],[[],[]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[[]],[]]]],[],[[]],[]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[],[[[[]],[]]]],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[[]],[]]]],[],[[],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[],[[[[]],[]]],[]],[[]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[[]],[]]],[]],[[],[]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[]],[],[[[[]],[],[[]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[],[]],[[[[]],[],[[]]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[]],[],[[[[],[]],[[]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[],[]],[[[[],[]],[[]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[[[]]],[],[[]],[]]],[]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[[],[[]]],[[]],[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[[]]],[],[[],[]]]],[]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[[]],[]],[[]]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[]],[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[]],[],[[[]]],[],[[]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[[[]],[]],[[[]]],[],[]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[]],[],[[],[[]]],[[]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[]],[[],[[]]],[[]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[[],[]]],[],[[[]]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[[],[]]],[[[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[[[]]],[],[[],[[]],[]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[],[]]],[],[[[]],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[[]],[],[[]]],[[]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[[[]],[],[]],[[[]],[]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[[],[]],[[]]],[[]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[]],[]],[[[]],[],[]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[]],[[]]],[[],[]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[],[[]]]]]],[],[]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[[[[[[],[[[]]]]],[],[]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[[[[[],[[[[]]]],[],[]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[[[[],[[[[[]]],[],[]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[[[[[[[[[]]]]],[[]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[[[[[[[[[]]]],[[]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[]],[]]]]],[]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[],[[]]]]]],[]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[[],[]],[]],[]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[[[],[[[[[]],[]],[]],[]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[],[[],[[[[]],[]],[]]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[],[[],[[],[[[]],[]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[],[],[],[[]]]],[],[]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[],[],[],[[]]]],[],[],[]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[],[],[[]]]],[],[],[],[]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[[],[[]]]],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[],[],[],[],[],[[],[[],[]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[],[],[],[[],[[[],[]]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[],[],[],[[],[[[[],[]]]]]]
[1,0,1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[],[[],[[[[[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[[[]],[],[],[]],[]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[[[[]]]],[[[]]]],[],[]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[]],[[[[]]],[[[]]]],[]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[[]],[[]],[[[[]]],[[]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[[[]],[[]]]],[[]],[[]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[]]],[[[[]],[]]],[[]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[[]]],[[[]]],[[[],[]]]]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[],[],[[[]]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[[]],[],[[]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[[],[]],[],[],[],[[],[]],[]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[[]],[],[],[],[[],[]],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[[],[]],[],[],[],[],[[]],[]]
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[],[[],[[[[[[]]]]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[],[[],[[[],[[]],[]]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[],[[[],[[],[[]]],[]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[[],[]],[[[[]],[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[],[]],[[[],[[]],[]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[],[],[[],[[],[[[]]]],[]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[],[],[],[[[]],[[[]]],[]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[]],[[],[[[]]],[]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[],[],[],[[[[]]],[[]],[]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[],[[]],[[]],[[[]],[]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[]],[],[[[],[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[]],[],[[],[[[]]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[]],[],[[]],[[[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[],[[],[]]],[],[[[]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[],[]],[]],[],[[[]],[]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[],[[],[[],[[]]]]],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[]],[[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[]],[[],[[]]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[[],[]]],[[[]]],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[]],[[[]]],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[]],[[],[[],[[]]]],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[]],[[],[]],[[[]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[],[[],[]]],[[],[[]]],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[],[]],[]],[[],[[]]],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[],[[],[]]]],[[]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[[]],[]]],[[]],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[],[]],[[[],[]]],[[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[[[]]],[]],[[]],[]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[],[],[],[],[],[[[],[]]],[]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[],[],[],[],[[[],[],[]]],[]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[],[],[],[[[],[],[],[]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[]],[[],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[],[]],[]],[[]],[[],[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[],[],[],[[]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[[]],[],[],[],[],[[]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[],[[]]],[]],[]],[]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[],[[]],[[]]],[]],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[],[[]],[]],[]],[]],[]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[],[[],[[],[],[],[],[],[]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[[],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[],[],[],[]],[[]],[[]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[],[],[]],[[]],[[]],[[]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[],[[[],[],[],[],[]],[[]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[],[[],[],[],[]],[[],[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[],[],[]],[],[[],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[],[]],[],[],[[],[[]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[]],[],[],[],[[],[[]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[[[[],[[[[[[]]]]]],[]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[],[],[],[]]],[[]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[]],[[[],[],[],[],[]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[]],[[]],[[[],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[]],[[[],[]]],[[],[]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[]],[[[],[[],[]]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[]],[[[[],[]],[]],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[[],[]]],[[]],[[],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[]]],[[[],[]],[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[[],[[],[]]]],[[],[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[[[],[]],[]]],[[],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[]],[[]],[[],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[]],[[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[]],[[[],[]]],[[],[]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[[],[[],[[],[]]]],[]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[],[[],[[[],[]],[]]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[],[[],[]]],[]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[]],[[],[[],[]]],[]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[]],[[[],[]],[]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[],[[],[]]],[[],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[[],[]],[]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[],[[],[[],[]]]],[],[]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[],[[[],[]],[]]],[],[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[]],[[],[]]],[],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[],[[],[]]],[]],[],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[[],[]],[]],[]],[],[]]]
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[],[[],[[],[[[[[]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[],[[],[[],[[],[[[]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[],[[],[],[],[],[],[[]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[[]]]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[[[]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[],[]]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[[],[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[]],[]]]]]]]],[]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[],[[]]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[[]],[]]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[],[[]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[],[],[]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[[],[[[[[[[[[]]],[]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[],[],[]]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[],[[[]]]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[],[[[[]]]]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[[],[[[[[]]]]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[[],[[[[[[]]]]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[[],[[[[[[[]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[],[],[],[],[],[],[],[],[[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[],[],[],[],[[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[],[],[],[],[],[],[],[[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[],[],[],[],[],[],[[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[],[],[],[[],[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[],[],[[],[],[],[],[],[]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[],[[],[],[],[],[],[],[]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[],[[],[],[],[],[],[],[],[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[],[],[],[],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[],[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[],[],[],[],[[[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[],[],[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[],[],[],[],[],[],[],[[[],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[],[]],[],[],[],[],[],[],[]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[]]],[],[],[],[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[],[],[],[],[],[[[[],[]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[],[],[]],[],[],[],[],[],[]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[],[],[],[]],[],[],[],[],[]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[]]]],[],[],[],[],[],[]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[[],[],[],[],[]],[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[],[],[],[],[],[[[[[],[]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[[],[],[],[],[],[]],[],[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[[[]]]]],[],[],[],[],[]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[[],[],[],[],[],[[]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[[]],[],[],[],[],[]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[],[],[],[],[]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[],[[]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[]],[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[[[]]]]]]]]],[]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[],[]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[[],[]]]]]]]],[]]]
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[],[[[[[[[[],[]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[],[],[],[],[[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[],[],[],[],[[],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[],[],[],[],[[],[],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[],[],[],[[],[],[],[]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[],[],[[],[],[],[],[]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[],[[],[],[],[],[],[]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[],[[],[],[],[],[],[],[]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[],[[],[],[],[],[],[],[],[]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[],[],[],[],[]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[[]]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[]],[[[[[[[[[]]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[],[[[[[[[[[]]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[],[],[],[],[]]
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[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[],[[]],[],[],[]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[],[],[]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[],[],[],[],[],[],[],[[[]]],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[],[],[],[[]],[]]
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[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[],[[[[[[[[[]]]]]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[],[],[],[],[]],[]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[]]],[]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[],[],[]]]]]],[]]]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[],[[[[[[],[],[]]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[],[[]],[],[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[],[],[],[],[[[[[[],[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[],[],[],[],[[[[[[]]]]]],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[[],[],[],[],[],[],[],[]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[[],[]],[]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[],[],[],[[],[]],[]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[],[[[[[[]]]]]],[],[],[],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[[[],[]]]]]],[],[],[],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[],[[]],[[]],[[]],[[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[]],[[]],[[]],[[]],[[],[]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[[],[],[],[],[]],[]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[],[[],[],[],[],[]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[[],[],[],[],[],[],[],[]]],[]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[],[[[],[],[],[],[],[],[],[]]]]
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[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[[],[],[],[],[],[]]]]],[]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[[],[],[],[],[],[],[]],[],[]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[[],[],[],[],[],[],[],[]],[]]]
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[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[[]],[],[],[],[],[]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[[],[],[],[],[],[],[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[],[],[],[[],[],[],[],[]],[],[]]
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[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[]],[[],[],[]],[]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[]],[[],[],[],[]],[]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[]],[[],[],[],[],[]],[]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[]],[[],[],[],[],[],[]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[]],[[],[],[],[],[],[],[]],[]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[],[[],[],[],[],[],[],[],[]],[]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[],[[[[[[[[[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0]=>[[[[[[[[[[]]]]]]]],[],[]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[[[[[]]]]]]],[],[],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[[[[[]]]]]],[],[],[],[]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[[[],[[[[[[[[]],[]]]]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[[]],[[]]],[[]],[[]],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[],[[]]],[[]],[[]],[[]],[]]
[1,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[],[[[[[[[[]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[[[]]]]]]]],[]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[[],[],[],[],[],[[[]]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[[]],[],[],[],[],[[]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[[[]],[[[[[[[[]]]]]]]],[]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[]]],[[[[[[[]]]]]]],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[]]]],[[[[[[]]]]]],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[[]]]]],[[[[[]]]]],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[[[[[]]]]]],[[[[]]]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[[[[[[]]]]]]],[[[]]],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[[[[[]]]]]]]],[[]],[]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[],[[[[[[[],[],[]]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[[[],[[[[[[],[],[],[]]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[],[[[[[],[],[],[],[]]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[],[[[[],[],[],[],[],[]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[],[[[],[],[],[],[],[],[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[],[],[],[],[],[],[],[]],[[]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[]],[],[],[],[],[],[],[],[[]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[],[[]],[],[],[],[],[],[],[[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[[],[],[],[],[],[],[],[[]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[]]]]],[[[[[[]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[],[],[[[[[[[[],[]]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[[[]],[[[[[[[[]]]]]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[[[]]],[[[[[[[]]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[]]]],[[[[[[]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[[]]]]],[[[[[]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[[[[[]]]]]],[[[[]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[[[[[]]]]]]],[[[]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0]=>[[[[[[[[[[]]]]]]]],[[]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[]],[[]]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[],[],[],[],[],[]]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[],[[[[[[]],[],[],[],[]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[[],[],[],[],[],[[]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[],[[[[[]],[],[],[],[],[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[[],[],[],[],[],[[[],[]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[],[],[],[],[[[],[],[]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[],[],[],[[[],[],[],[]]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[],[],[[[],[],[],[],[]]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[],[[[],[],[],[],[],[]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[],[[],[[[[[[[[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,0]=>[[[[[[[[[[[]]]]]]],[]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,0]=>[[[[[[[[[[[]]]]]],[]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0]=>[[[[[[[[[[[]]]]],[]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[[[[]]]],[]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[[],[],[],[],[],[[]]]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[],[],[],[],[]]]],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[]],[]],[[]],[[]],[[]],[]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[[]]]],[[[[]]]],[[[]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[],[],[],[],[],[],[[]],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[],[],[],[],[],[],[[],[]],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[],[],[],[],[],[],[[],[],[]],[]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[[],[],[],[]],[],[],[],[]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[[],[],[]],[],[],[],[]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[[],[]],[],[],[],[]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[],[],[],[],[[]],[],[],[],[]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[],[],[],[],[],[],[]]]],[]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[[],[],[],[],[],[],[]],[]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[],[],[],[],[],[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[],[],[],[],[[[],[]]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[],[],[],[[[],[],[]]]]]]]
[1,1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[],[],[[[],[],[],[]]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[],[[[],[],[],[],[]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[[]]],[[]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[[],[],[],[],[[]]]]]],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[],[],[],[],[],[],[],[[],[[]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[],[],[],[],[],[],[[],[],[[]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[],[],[],[[],[],[],[[]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[],[],[[],[],[],[],[[]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[],[[],[],[],[],[],[[]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[],[],[[],[],[],[],[],[],[[]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[],[],[[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0]=>[[[[[[[[[[]],[],[]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[[[],[[[[[[[[]]]]]]]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[],[],[],[],[[],[],[]],[]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[[],[],[],[]],[],[],[],[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[[],[],[]],[],[],[],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[[],[]],[],[],[],[]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[[]],[],[],[],[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[]],[],[],[],[],[],[],[[]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[[],[[[[[[[[]]]]]]]],[[]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[[],[]]]]]]],[]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0]=>[[[[[[[[[[],[]]]]]],[]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]=>[[[[[[[[[[],[]]]]],[]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0]=>[[[[[[[[[[],[]]]],[]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]=>[[[[[[[[[[],[]]],[]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[],[],[],[[[[[[[],[]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[],[],[],[[]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[[]],[],[],[],[]]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[],[[[[[]]]]],[[[[[]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[]]]]],[],[[[[[]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[]],[[[[[]]]]],[[[[]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[[[]]]]],[[]],[[[[]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[[[]]]]],[[[[]]]],[[]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[[[[]]],[[[[]]]],[[[[]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[[[]]]],[[[]]],[[[[]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[],[],[],[],[[],[]]]]
[1,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[],[[[[]]]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[],[[[[[]]]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[],[[[[[[]]]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[],[[[[[[[]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[[[]]]]]]]]]]],[]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[[[[[[[[[[[],[]]]]]]]]]],[]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[[],[[[[[[[[[[],[]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[],[],[],[],[],[],[],[],[],[[],[]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[],[[],[],[],[],[],[],[],[],[],[]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[],[],[],[],[],[],[],[],[],[[[]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[]],[],[],[],[],[],[],[],[],[]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[],[[],[[],[[],[[],[[],[]]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[[],[[[],[]],[[],[]]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[[[],[]],[[],[[],[]]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[],[[],[[[],[[],[]]],[[],[]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[],[[[[],[]],[]],[[],[]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[[],[]],[[],[[],[[],[]]]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[],[[[],[]],[[[],[]],[[],[]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[],[[],[]]],[[],[[],[]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[[[],[]],[]],[[],[[],[]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[[],[[[],[[],[[],[]]]],[[],[]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[],[[[],[]],[]]],[[],[]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[],[[[[],[]],[[],[]]],[[],[]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[[],[[],[]]],[]],[[],[]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[],[[[[[],[]],[]],[]],[[],[]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[],[[[],[[],[[],[[],[]]]]],[]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[],[[[],[[],[[[],[]],[]]]],[]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[],[[[],[]],[[],[]]]],[]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[],[[[],[[[],[[],[]]],[]]],[]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[],[[[],[[[[],[]],[]],[]]],[]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[[[],[]],[[],[[],[]]]],[]]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[],[[[[],[]],[[[],[]],[]]],[]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[],[[],[]]],[[],[]]],[]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[[[],[]],[]],[[],[]]],[]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[],[[[[],[[],[[],[]]]],[]],[]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[],[[[],[]],[]]],[]],[]]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[[[[],[]],[[],[]]],[]],[]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[[],[[],[]]],[]],[]],[]]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[[[[[],[]],[]],[]],[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[],[]],[[],[[],[[],[[],[]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[],[[[],[]],[[],[]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[[],[]],[[],[[],[]]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[],[]],[[[],[[],[]]],[[],[]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[]],[[[[],[]],[]],[[],[]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[]],[[[],[[],[[],[]]]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[],[]],[[[],[[[],[]],[]]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[]],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[],[]],[[[[],[[],[]]],[]],[]]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[]],[[[[[],[]],[]],[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[]]],[[],[[],[[],[]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[],[[],[]]],[[[],[]],[[],[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[],[]]],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[[],[]]],[[[[],[]],[]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[],[]],[]],[[],[[],[[],[]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[[],[]],[]],[[[],[]],[[],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[]],[]],[[[],[[],[]]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[]],[]],[[[[],[]],[]],[]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[[],[[],[]]]],[[],[[],[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[[],[[],[]]]],[[[],[]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[],[[[],[]],[]]],[[],[[],[]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[[[],[]],[]]],[[[],[]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[],[]],[[],[]]],[[],[[],[]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[[],[]]],[[[],[]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[],[[],[]]],[]],[[],[[],[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[],[[],[]]],[]],[[[],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[],[]],[]],[]],[[],[[],[]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[]],[[[],[]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[],[[],[[],[[],[]]]]],[[],[]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[],[[[],[]],[]]]],[[],[]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[[[],[]],[[],[]]]],[[],[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[[],[[],[]]],[]]],[[],[]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[[[],[]],[]],[]]],[[],[]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[],[[],[]]]],[[],[]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[[],[]],[]]],[[],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[[],[]]],[[],[]]],[[],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[[],[]],[]],[[],[]]],[[],[]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[[],[[],[]]]],[]],[[],[]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[[[],[]],[]]],[]],[[],[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[],[]],[[],[]]],[]],[[],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[],[[],[]]],[]],[]],[[],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[[],[]],[]],[]],[]],[[],[]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[[[[[[[[[[[[]]]]]]]]]],[]]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[],[[[[[[[[[[]]]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[],[],[],[],[],[],[],[],[],[]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[],[],[],[],[],[],[],[],[],[[]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[]]],[],[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[]],[[]],[[]],[[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[]],[[]],[[]],[[]],[[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[]],[]],[]],[[]],[[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[[]],[]],[[]],[[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[[]],[]],[[]],[[]],[[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[[[]],[]],[]],[[]],[[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[[[]],[]],[]],[[]],[[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[]],[[]],[]],[]],[[]],[[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[[]],[]],[]],[]],[[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[]],[[[]],[]],[[]],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[]],[[[]],[]],[[]],[[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[[]],[]],[[]],[]],[[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[]],[[[]],[[]],[]],[[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[[]],[[]],[[]],[]],[[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[]],[[[[]],[]],[]],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[[[]],[]],[]],[[]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[]],[[[]],[]],[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[[[]],[]],[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[]],[[[]],[]],[]],[[]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[[]],[[]],[]],[]],[[]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[]],[]],[[]],[]],[]],[[]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[[[]],[]],[]],[]],[[]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[]],[[]],[]],[]],[]],[[]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[[]],[[]],[]],[]],[[]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[[]],[[]],[]],[]],[[]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[[]],[]],[]],[]],[]],[[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[[[]],[]],[]],[]],[[]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[[[]],[]],[]],[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[]],[[]],[[[]],[]],[[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[]],[[[]],[]],[[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[]],[]],[[[]],[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[]],[[[]],[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[]],[]],[[[]],[]],[[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[[]],[]],[[]],[]],[[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[[]],[]],[[]],[]],[[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[[]],[]],[[]],[]],[[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[[]],[]],[]],[[]],[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[]],[[[]],[[]],[]],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[]],[[[]],[[]],[]],[[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[[]],[]],[[]],[[]],[]],[[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[]],[[[]],[[]],[[]],[]],[[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[[]],[[]],[[]],[[]],[]],[[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[]],[[]],[[[[]],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[]],[[]],[[[[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[]],[[[[]],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[]],[]],[[[[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[]],[]],[[[[]],[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[[[]],[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[]],[]],[[[]],[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[]],[]],[[[]],[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[]],[]],[[[]],[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[]],[[[]],[[[]],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[]],[[[]],[[[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[[]],[[[]],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[]],[[]],[[[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[]],[[]],[[[]],[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[[]],[[]],[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[]],[[]],[[]],[]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[[[]],[]],[]],[[]],[]],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[[]],[]],[[]],[]],[]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[[]],[]],[[]],[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[]],[[[]],[]],[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[]],[[[]],[]],[]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[]],[]],[[]],[]],[]],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[[]],[[]],[]],[]],[]]]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[[]],[[]],[]],[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[]],[[]],[[]],[]],[]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[[]],[]],[[]],[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[]],[[]],[[]],[]],[]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[[]],[]],[[]],[]],[]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[]],[[]],[]],[]],[]],[]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[[]],[]],[]],[]],[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[]],[[[]],[]],[]],[]]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[[]],[[]],[]],[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[]],[[[]],[]],[]],[]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[[]],[[]],[]],[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[]],[[[[]],[[]],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[]],[[[[]],[[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[[[]],[[]],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[]],[[[]],[[[]],[[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[]],[[]],[[[]],[[]],[]],[]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[[[]],[]],[]],[]],[]]]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[[[]],[]],[]],[]],[]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[]],[[[[]],[]],[]],[]],[]]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[[[]],[]],[]],[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[]],[[[[[]],[]],[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[]],[[[[[]],[]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[]],[]],[[[[]],[]],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[]],[[[[]],[]],[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[[]],[[[[]],[]],[]],[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[]],[[]],[[]],[[[]],[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[]],[[]],[[]],[[[]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[]],[]],[]],[[]],[[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[]],[[]],[[[]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[[]],[]],[[]],[[[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[]],[[[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[[[]],[]],[]],[[[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[]],[[]],[]],[]],[[[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[[]],[]],[]],[]],[[[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[]],[[[]],[]],[[[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[]],[[[]],[]],[[[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[[]],[]],[[]],[]],[[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[]],[[[]],[[]],[]],[[[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[[]],[[]],[[]],[]],[[[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[]],[[[[]],[]],[[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[]],[[[[]],[]],[[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[]],[[[]],[]],[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[]],[[[]],[]],[[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[[[]],[]],[[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[[]],[[]],[]],[[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[[]],[]],[[]],[]],[[]],[]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[[[]],[]],[]],[[]],[]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[[]],[[]],[]],[]],[[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[[]],[[]],[]],[[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[[]],[[]],[]],[[]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[[[]],[]],[]],[]],[[]],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[[[]],[]],[]],[[]],[]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[[[]],[]],[]],[[]],[]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[]],[[]],[[[]],[[]],[]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[]],[[]],[[[]],[[]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[]],[]],[[[]],[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[]],[]],[[[]],[[]],[]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[]],[[[]],[[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[[]],[]],[[]],[[]],[]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[[]],[]],[[]],[[]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[[]],[]],[[]],[[]],[]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[[[]],[]],[]],[[]],[[]],[]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[]],[[[]],[[]],[[]],[]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[]],[[[]],[[]],[[]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[[]],[]],[[]],[[]],[[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[]],[[[]],[[]],[[]],[[]],[]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[[]],[[]],[[]],[[]],[[]],[]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[[[[[[[[[[[]]]]]]]]]],[[]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[[]],[]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[[],[]]]]]]]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[[],[[[],[[],[[],[[],[]]]]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[]],[],[[[],[[],[[],[]]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[],[[],[[[],[[],[[],[]]]]],[]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[[],[[[[],[[],[[],[]]]]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[[]],[],[[[],[[],[]]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[]],[],[[[],[[],[]]]]],[]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[[],[[],[[[],[[],[]]]]],[],[[]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[[],[[],[]]]]],[],[[]],[]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[],[[],[[],[[[],[[],[]]]],[]]]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[[],[[[],[[[],[[],[]]]],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[]],[],[[[[],[[],[]]]],[]]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[],[[],[[[[],[[],[]]]],[]],[]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[[],[[],[]]]],[]],[]],[]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[],[[],[[],[[]],[],[[[],[]]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[[],[[]],[],[[[],[]]]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[]],[],[[[]],[],[[[],[]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[],[[[]],[],[[[],[]]]],[]]]
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[]],[],[[[],[]]]],[]],[]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[],[[],[[]]],[],[[],[[[],[]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[]]],[],[[],[[[],[]]]],[]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[],[[],[[]],[]],[],[[[[],[]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[],[[[]],[]],[],[[[[],[]]]],[]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[[],[[],[[],[[[],[]]]],[],[[]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0]=>[[],[[[],[[[],[]]]],[],[[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[],[[]],[],[[[[],[]]]],[],[[]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0]=>[[],[[],[[[[],[]]]],[],[[]],[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[],[[[[[],[]]]],[],[[]],[]],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[],[[],[[],[[],[[[],[]]],[]]]]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[[],[[[],[[],[[[],[]]],[]]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[]],[],[[[],[[[],[]]],[]]]]
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[],[[],[[[],[[[],[]]],[]]],[]]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[[[],[]]],[]]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[],[[],[[]],[],[[[[],[]]],[]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[],[[[]],[],[[[[],[]]],[]]],[]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0]=>[[],[[],[[[[],[]]],[]]],[],[[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[],[[[[[],[]]],[]]],[],[[]],[]]
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[[],[[],[[],[[[[],[]]],[]],[]]]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[[[],[]]],[]],[]]],[]]
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[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[],[[],[[],[[]]]],[],[[],[[]]]]
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[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[],[[],[[],[[],[[]]],[],[[]]]]]
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[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[],[[[],[[[]]],[],[[]],[]]],[]]
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[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[[],[[[],[[],[[],[[]],[]]]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[[]],[],[[[],[[],[[]],[]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[[],[[],[[[],[[],[[]],[]]]],[]]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[[],[[[[],[[],[[]],[]]]],[]],[]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[[],[[]],[],[[[],[[]],[]]]]]
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[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[[],[[],[[[],[[]],[]]]],[],[[]]]
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[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[[],[[[],[[[],[[]],[]]],[]]],[]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[],[[]],[],[[[[],[[]],[]]],[]]]
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[],[[[[],[[]],[]]],[]],[]]]
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[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[],[[],[[],[[]],[],[[[]],[]]]]]
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[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[[],[]],[[]]],[]],[]],[],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[],[]],[],[[[]],[[[],[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[]],[],[[[]],[[],[[],[]]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[],[[],[]],[[[]],[[[],[]],[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[[],[]],[[[]],[[],[[],[]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[[],[[],[[],[[[]],[[],[]]]]],[]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[],[[[],[[[]],[[],[]]]],[]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[]],[[[]],[[],[]]]],[]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[],[],[[],[[[[]],[[],[]]],[]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[],[[],[[[]],[]]]],[[],[]]]
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[],[[],[[[]],[]]]],[]],[]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[],[],[[[],[[[]],[]]],[[],[]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[[[[],[[[],[[[]],[]]],[]]],[]]]
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[[[],[[[[],[[[]],[]]],[]],[]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[]],[[[]],[]]],[[],[]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[[],[]],[[[]],[]]],[]],[],[]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[],[],[[],[[[[]],[]],[[],[]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[],[]],[[[[]],[]],[[],[]]]]]
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[[[[],[[],[[[[]],[]],[]]]],[]]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[],[[[],[[[[]],[]],[]]],[]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[],[]],[[[[]],[]],[]]],[],[]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[[[],[[],[[[[[]],[]],[]],[]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[],[]],[[[[[]],[]],[]],[]],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[],[[[],[]]]],[[[],[]],[]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[],[[],[[[],[]]]],[[],[[],[]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[],[[[],[]]]],[[],[]]],[]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[[],[[[],[]]]],[]],[[],[]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[[],[[[],[]]]],[]],[]],[],[]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[],[],[[[[],[]]],[[[],[]],[]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[],[],[[[[],[]]],[[],[[],[]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[],[[[[],[]]],[[],[]]]],[]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[],[[[[[],[]]],[[],[]]],[]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[],[[[[],[]]],[]]],[[],[]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[],[[[[],[]]],[]]],[]],[],[]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[],[[[[[],[]]],[]],[[],[]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[],[[[[[],[]]],[]],[]]],[],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[[],[]],[]]],[[[],[]],[]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[[[],[]],[]]],[[],[[],[]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[[],[]],[]]],[[],[]]],[],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[[],[]],[]]],[]],[[],[]],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[[[],[]],[]]],[]],[],[[],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[[[],[[],[]]]],[[[],[]],[]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[[],[[],[]]]],[[],[[],[]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[],[[],[]]]],[[],[]]],[],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[[[],[[],[]]]],[]],[[],[]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[[[],[[],[]]]],[]],[],[[],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[],[]],[],[[],[[[[],[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[],[]],[],[[],[[[],[[],[]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[],[[],[]],[[],[[[[],[]],[]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[[],[]],[[],[[[],[[],[]]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[],[],[[[],[]],[[[[],[]],[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[],[[[],[]],[[[],[[],[]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[],[]],[]],[[[[],[]],[]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[],[]],[]],[[[],[[],[]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[],[[],[]]],[[[[],[]],[]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[],[[],[]]],[[[],[[],[]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[],[[],[[],[[],[[[],[]]]]]],[]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[],[],[[[],[[],[[[],[]]]]],[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[],[]],[[],[[[],[]]]]],[]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[],[],[[],[[[],[[[],[]]]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[],[]],[[[],[[[],[]]]],[]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[],[[[],[]],[[[],[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[],[[[[],[]],[[[],[]]]],[]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[[],[]],[]],[[[],[]]]],[],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[],[[],[]]],[[[],[]]]],[],[]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[],[],[[],[[],[[[[],[]]],[]]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[],[]],[[],[[[[],[]]],[]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[],[[[],[]],[[[[],[]]],[]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[],[]],[]],[[[[],[]]],[]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[],[[],[]]],[[[[],[]]],[]],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[],[[],[[],[[],[[]]]]],[[],[]]]
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[[[],[[],[[],[[]]]]],[]],[]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[],[],[[[],[[],[[]]]],[[],[]]]]
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[[[[],[[[],[[],[[]]]],[]]],[]]]
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0]=>[[[],[[[[],[[],[[]]]],[]],[]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[]],[[],[[]]]],[[],[]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[],[]],[[],[[]]]],[]],[],[]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[],[],[[],[[[],[[]]],[[],[]]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[],[]],[[[],[[]]],[[],[]]]]]
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[[[[],[[],[[[],[[]]],[]]]],[]]]
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[[[],[[[],[[[],[[]]],[]]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[],[]],[[[],[[]]],[]]],[],[]]
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[[[],[[],[[[[],[[]]],[]],[]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[],[]],[[[[],[[]]],[]],[]],[]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[],[[[],[]],[[]]]],[[],[]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[],[[[],[]],[[]]]],[]],[],[]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[],[[[[],[]],[[]]],[[],[]]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[],[[[[],[]],[[]]],[]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[],[[[[[],[]],[[]]],[]],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[[],[]],[]],[[]]],[[],[]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[],[]],[]],[[]]],[],[[],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[[],[[],[]]],[[]]],[[],[]],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[[],[[],[]]],[[]]],[],[[],[]]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[],[],[[],[[],[[[]],[[],[]]]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[],[]],[[],[[[]],[[],[]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[],[[[],[]],[[[]],[[],[]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[[],[]],[]],[[[]],[[],[]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[],[[],[]]],[[[]],[[],[]]],[]]
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[[[],[[],[[],[[[]],[]]]]],[]]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[[[],[[[],[[],[[[]],[]]]],[]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[],[]],[[],[[[]],[]]]],[],[]]
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[[[],[[],[[[],[[[]],[]]],[]]]]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[],[]],[[[],[[[]],[]]],[]],[]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[],[[[],[]],[[[]],[]]]],[],[]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[],[[[[],[]],[[[]],[]]],[]],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[],[]],[]],[[[]],[]],[[],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[[]],[]],[[],[]]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[[[],[[],[[],[[[[]],[]],[]]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[],[]],[[],[[[[]],[]],[]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[],[[[],[]],[[[[]],[]],[]]],[]]
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[]],[],[[[[[]],[]],[]],[]]]
[1,0,1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[],[]],[[[[[]],[]],[]],[]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[],[[[],[[[]],[[]],[],[]]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[],[[[],[[]],[[[[]]]]],[]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[],[[[],[[[]],[],[[]],[]]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[],[[[],[[]],[[],[[[]]]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[[[],[[[]],[[[[],[]],[]]],[]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[[[],[[[]],[[[[]]],[[],[]]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[],[[[],[[],[]],[[[]]]],[]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[],[[[]],[[[],[[],[]]]],[]]]]
[1,1,0,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,0]=>[[[],[[[],[[[[]]],[]],[[]]]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[[[],[[[],[[],[[]],[],[[]]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[[[],[[[]],[[[[[]]]],[[]]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[],[[[],[[],[],[[]],[[]]]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[[[],[[[]],[[[],[[[]],[]]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[],[[],[[],[],[[[]],[]]],[]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[],[[],[[],[],[[]],[[],[]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[],[[],[[],[]],[[[[]]]],[]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[],[[],[[],[],[[],[]],[[]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[],[[],[[],[]],[[[],[[]]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[[[[]]],[[],[],[[]]],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[],[[[[]]],[[],[]],[[[]]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[[],[[[]],[],[],[[]]],[]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[],[[],[[[]],[],[]],[[[]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[],[[[[[]],[]]],[[],[]],[]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[],[[[[]],[[],[]],[],[]],[]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[],[[],[[[[]]]],[[],[]],[]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[],[[[[],[]],[[]],[],[]],[]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,0]=>[[[],[[],[[[],[[]]],[],[]],[]]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,0]=>[[[],[[[[[],[[]]],[]]],[[]]]]]
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[[[],[[[[[]],[[]],[],[]],[]]]]]
[1,1,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[[[],[[[[]],[[[[]]]]],[[]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[],[[[[[]],[],[[]],[]],[]]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[[[],[[[[]],[[],[[[]]]],[]]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[[[],[[],[[[[],[]],[]]],[[]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[],[[],[[[[]]],[[],[]],[]]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[],[[[[],[]],[[[]]]],[[]]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,0]=>[[[],[[],[[[],[[],[]]]],[[]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[],[[[[[[]]],[]],[[]],[]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[],[[[[],[[]],[],[[]]],[]]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,0]=>[[[],[[],[[[[[]]]],[[]],[]]]]]
[1,1,0,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,0]=>[[[],[[[[],[],[[]],[[]]],[]]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[]],[],[[[],[[[]],[]]],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[]],[],[[[],[[]],[[],[]]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[]],[],[[[]],[[[[]]]],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[]],[],[[[],[[],[]],[[]]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[]],[],[[[]],[[[],[[]]]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[]],[],[[],[[],[],[[]]],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[]],[],[[],[[],[]],[[[]]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[]],[],[[[[]]],[[],[]],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[]],[],[[],[[[]],[],[]],[]]]]
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0]=>[[[[]],[],[[[[[]],[]]],[[]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[]],[],[[[[]],[[],[]],[]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[]],[],[[],[[[[]]]],[[]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[]],[],[[[[],[]],[[]],[]]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[]],[],[[],[[[],[[]]],[]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[]],[]],[],[[[],[[]]],[]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[[]],[]],[],[[[]],[[[]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[[]],[]],[],[[],[[],[]],[]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[]],[]],[],[[[[]]],[[]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[[]],[]],[],[[],[[[]],[]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[],[[]]],[],[[[],[[]]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[],[[]]],[],[[[]],[[[]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[[],[[]]],[],[[],[[],[]],[]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[],[[]]],[],[[[[]]],[[]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[[],[[]]],[],[[],[[[]],[]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[],[[]]],[]],[],[[[]],[]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[[],[[]]],[]],[],[[],[[]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[]],[[[]]]],[],[[[]],[]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[[]],[[[]]]],[],[[],[[]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[],[[],[]],[]],[],[[[]],[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[],[[],[]],[]],[],[[],[[]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[[]]],[[]]],[],[[[]],[]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[[[]]],[[]]],[],[[],[[]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[],[[[]],[]]],[],[[[]],[]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[],[[[]],[]]],[],[[],[[]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[],[[[]],[]]],[]],[],[[]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[],[[]],[[],[]]]],[],[[]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[]],[[[[]]]],[]],[],[[]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[],[[],[]],[[]]]],[],[[]]]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[]],[[[],[[]]]]],[],[[]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[[],[],[[]]],[]],[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[],[]],[[[]]]],[],[[]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[[[]]],[[],[]],[]],[],[[]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[[[]],[],[]],[]],[],[[]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[[[]],[]]],[[]]],[],[[]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[[]],[[],[]],[]]],[],[[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[[[]]]],[[]]],[],[[]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[[[],[]],[[]],[]]],[],[[]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[],[[[],[[]]],[]]],[],[[]]]]
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[],[[[]],[[]],[],[]]]],[]]]
[1,1,1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[[[],[[]],[[[[]]]]],[]],[]]]
[1,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[],[[[]],[],[[]],[]]]],[]]]
[1,1,1,1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[[[],[[]],[[],[[[]]]]]],[]]]
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[]],[[[[],[]],[]]],[]],[]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[]],[[[[]]],[[],[]]]],[]]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[],[[],[]],[[[]]]],[]],[]]]
[1,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[]],[[[],[[],[]]]],[]],[]]]
[1,1,1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[],[[[[]]],[]],[[]]]],[]]]
[1,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[],[[],[[]],[],[[]]]]],[]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[]],[[[[[]]]],[[]]]],[]]]
[1,1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[],[[],[],[[]],[[]]]]],[]]]
[1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[[[[[]],[[[],[[[]],[]]]]],[]]]
[1,1,1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[],[[],[],[[[]],[]]],[]],[]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[],[[],[],[[]],[[],[]]]],[]]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[],[[],[]],[[[[]]]],[]],[]]]
[1,1,1,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[],[[],[],[[],[]],[[]]]],[]]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[],[]],[[[],[[]]]]],[]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[[]]],[[],[],[[]]],[]],[]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[[]]],[[],[]],[[[]]]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[],[[[]],[],[],[[]]],[]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[],[[[]],[],[]],[[[]]]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[[[]],[]]],[[],[]],[]],[]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[[]],[[],[]],[],[]],[]],[]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[[[[]]]],[[],[]],[]],[]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[[],[]],[[]],[],[]],[]],[]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[[[],[[]]],[],[]],[]],[]]]
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[[[],[[]]],[]]],[[]]],[]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[[]],[[]],[],[]],[]]],[]]]
[1,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[[]],[[[[]]]]],[[]]],[]]]
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[[]],[],[[]],[]],[]]],[]]]
[1,1,1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[[],[[[]]]],[]]],[]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[],[[[[],[]],[]]],[[]]],[]]]
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[],[[[[]]],[[],[]],[]]],[]]]
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[[],[]],[[[]]]],[[]]],[]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0]=>[[[[],[[[],[[],[]]]],[[]]],[]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[[[]]],[]],[[]],[]]],[]]]
[1,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[],[[]],[],[[]]],[]]],[]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[],[[[[[]]]],[[]],[]]],[]]]
[1,1,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[],[],[[]],[[]]],[]]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[],[[],[[],[[],[[],[[]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[],[]],[],[],[],[],[],[],[],[],[]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[]],[[],[[],[[],[[],[],[]]]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[]],[[],[[],[[[],[],[]],[]]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[]],[[],[[[],[],[[]],[],[]]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[]],[[],[[[],[[],[],[]]],[]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[]],[[],[[[[],[],[]],[]],[]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[]],[[[],[],[[]],[[],[],[]]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[]],[[[],[],[[[]],[],[]],[]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[]],[[[],[[],[],[[]]],[],[]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[]],[[[[],[],[]],[[]],[],[]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[]],[[[],[[],[[],[],[]]]],[]]]
[1,1,0,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[]],[[[],[[[],[],[]],[]]],[]]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[]],[[[[],[],[[]],[],[]]],[]]]
[1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[]],[[[[],[[],[],[]]],[]],[]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[]],[[[[[],[],[]],[]],[]],[]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[[]],[],[[]],[[],[[],[],[]]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[]],[],[[]],[[[],[],[]],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[[]],[],[[[]],[],[[]],[],[]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[]],[],[[[]],[[],[],[]]],[]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[],[[[[]],[],[]],[]],[]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[[]],[[],[],[[]]],[[],[],[]]]]
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[]],[[],[],[[[]]],[],[]],[]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[[[]],[],[]],[[]],[[],[],[]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[]],[[],[[],[],[[]]]],[],[]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[]],[[[],[],[]],[[]]],[],[]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[[[]],[],[[]],[],[[]]],[],[]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[[]],[[],[],[]]],[[]],[],[]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[[[[]],[],[]],[]],[[]],[],[]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[]],[[],[[],[[],[],[]]]]],[]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[]],[[],[[[],[],[]],[]]]],[]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[]],[[[],[],[[]],[],[]]]],[]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[]],[[[],[[],[],[]]],[]]],[]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[]],[[[[],[],[]],[]],[]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[]],[],[[]],[[],[],[]]]],[]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[[]],[],[[[]],[],[]],[]]],[]]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[]],[[],[],[[]]],[],[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[[]],[],[]],[[]],[],[]]],[]]
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[]],[[],[[],[],[]]]],[]],[]]
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[]],[[[],[],[]],[]]],[]],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[[]],[],[[]],[],[]]],[]],[]]
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[[]],[[],[],[]]],[]],[]],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[[[[[[[]],[],[]],[]],[]],[]],[]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[],[],[[]],[[],[[],[[],[],[]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[],[],[[]],[[],[[[],[],[]],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[],[],[[]],[[[],[[],[],[]]],[]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[],[],[[]],[[[[],[],[]],[]],[]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[],[],[[[]],[],[[]],[[],[],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[],[],[[[]],[],[[[]],[],[]],[]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[],[],[[[]],[[],[],[[]]],[],[]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[],[],[[[[]],[],[]],[[]],[],[]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[],[],[[[]],[[],[[],[],[]]]],[]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[],[],[[[]],[[[],[],[]],[]]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[],[],[[[[]],[],[[]],[],[]]],[]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[]],[[],[],[]]],[]],[]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[],[],[[[[[]],[],[]],[]],[]],[]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[],[[],[],[[]]],[[],[[],[],[]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[],[[],[],[[]]],[[[],[],[]],[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[],[[],[],[[[]]],[],[[]],[],[]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[],[[],[],[[[]]],[[],[],[]]],[]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[[],[[],[],[[[[]]],[],[]],[]],[]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[],[],[]],[[]],[[],[[],[],[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[[],[],[]],[[]],[[[],[],[]],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[],[],[]],[[[]],[],[[]],[],[]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[],[],[]],[[[]],[[],[],[]]],[]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[],[],[]],[[[[]],[],[]],[]],[]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[],[[],[[],[],[[]]]],[[],[],[]]]
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[],[[],[[],[],[[[]]]],[],[]],[]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[],[[[],[],[]],[[]]],[[],[],[]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[],[[[],[],[]],[[[]]],[],[]],[]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[],[],[[]],[],[[]]],[[],[],[]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[],[],[[]],[],[[[]]],[],[]],[]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[],[[],[],[]]],[[]],[[],[],[]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[],[[],[],[]]],[[[]],[],[]],[]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[[],[],[]],[]],[[]],[[],[],[]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[[],[],[]],[]],[[[]],[],[]],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[],[[],[[],[],[[]]]]],[],[]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[],[[[],[],[]],[[]]]],[],[]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[],[],[[]],[],[[]]]],[],[]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[],[[],[],[]]],[[]]],[],[]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[[],[],[]],[]],[[]]],[],[]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[],[],[[]],[[],[],[[]]]],[],[]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[],[],[[[]],[],[]],[[]]],[],[]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[],[[],[],[[]]],[],[[]]],[],[]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[],[],[]],[[]],[],[[]]],[],[]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[[],[[],[],[]]]],[[]],[],[]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[[[],[],[]],[]]],[[]],[],[]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[],[[],[],[]]],[]],[[]],[],[]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[],[],[]],[]],[]],[[]],[],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[],[[],[[],[[],[[],[],[[]]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[[],[[],[[],[[[],[],[]],[[]]]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[],[[],[[[],[],[[]],[],[[]]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0]=>[[],[[],[[[],[[],[],[]]],[[]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0]=>[[],[[],[[[[],[],[]],[]],[[]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[],[],[[]],[[],[],[[]]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[[],[[[],[],[[[]],[],[]],[[]]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[],[[[],[[],[],[[]]],[],[[]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[[[],[],[]],[[]],[],[[]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[[],[[[],[[],[[],[],[]]]],[[]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[],[[[],[[[],[],[]],[]]],[[]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[],[],[[]],[],[]]],[[]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[],[[[[],[[],[],[]]],[]],[[]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[],[[[[[],[],[]],[]],[]],[[]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[],[],[[]],[[],[[],[],[[]]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[],[],[[]],[[[],[],[]],[[]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[],[],[[[]],[],[[]],[],[[]]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[],[],[[[]],[[],[],[]]],[[]]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[],[],[[[[]],[],[]],[]],[[]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[],[[],[],[[[]]],[],[]],[[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[[],[],[]],[[]],[[],[],[[]]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[],[],[]],[[[]],[],[]],[[]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[],[[],[[],[],[[]]]],[],[[]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[],[[[],[],[]],[[]]],[],[[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[],[],[[]],[],[[]]],[],[[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[],[[],[],[]]],[[]],[],[[]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[[[],[],[]],[]],[[]],[],[[]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[],[[],[[],[[],[],[]]]]],[[]]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[],[[],[[[],[],[]],[]]]],[[]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[],[[[],[],[[]],[],[]]]],[[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[],[[[],[[],[],[]]],[]]],[[]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[],[[[[],[],[]],[]],[]]],[[]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[],[],[[]],[[],[],[]]]],[[]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[[[],[],[[[]],[],[]],[]]],[[]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[[],[],[[]]],[],[]]],[[]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[[],[],[]],[[]],[],[]]],[[]]]
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[],[[],[[],[],[]]]],[]],[[]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[],[[[],[],[]],[]]],[]],[[]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[],[],[[]],[],[]]],[]],[[]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[],[[],[],[]]],[]],[]],[[]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[],[],[]],[]],[]],[]],[[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[[]],[[]],[[]],[[]],[[]],[]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[[]]],[]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[[[[[[[[[[[],[[]]]]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[[],[],[],[],[],[]]]]]],[]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[],[[[[[[],[],[],[],[],[]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[[[]],[[]],[]],[]],[],[]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[[]],[[[]],[]],[],[]]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[[[]],[]],[[]],[],[]],[]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[[]],[[]],[[]],[],[],[]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[]],[[[[]],[],[]]],[]],[]]]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[]],[[[]],[[],[]]],[],[]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[]],[[[],[]],[]]],[]]]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[]],[[]],[[[],[],[]]]],[]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[[[]],[]],[],[[]],[]],[]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[[]],[[]],[],[[]],[],[]]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[]],[[[]],[],[[],[]]],[]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[[]],[]],[[],[[],[]],[]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[]],[[]],[[],[[],[],[]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[]],[[[[[],[]]],[]],[]],[]]]
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0]=>[[[[]],[[[[],[[]]],[]],[],[]]]]
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0]=>[[[[]],[[[],[[[]]],[],[]]],[]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[]],[[[[],[]]],[[],[]],[]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[]],[[[],[[]]],[[],[],[]]]]]
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[]],[],[[[[]],[]]],[]],[]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[]],[],[[[]],[[]]],[],[]]]]
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[[]],[[],[[[[],[]]]],[]],[]]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[]],[[],[[[],[[]]]],[],[]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[[]],[],[]],[[[]],[]]],[]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[]],[[],[]],[[[],[]]]],[]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[]],[[[],[],[[[]]],[]]],[]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[]],[],[[],[[[]],[]]]],[]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[]],[[],[[],[[[],[]]]]],[]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[[[]],[],[]],[]],[[]],[]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[[[]],[[],[]],[]],[[],[]]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[]],[[[],[]],[],[[]]],[]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[],[[]],[],[[]],[]]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[]],[[],[[]],[],[[],[]]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[]],[[[[],[],[]]],[[]],[]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[]],[[[],[[],[]]],[[],[]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[]],[],[[[],[]],[[]]],[]]]]
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[]],[[],[[[],[],[[]]]],[]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[[]],[],[],[[]],[[]],[]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[]],[[],[],[[]],[[],[]]]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[]],[[[],[],[[],[[]]],[]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[]],[],[[],[[],[[]],[]]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[]],[[],[[],[[],[[],[]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[[[[]]],[]],[]],[]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[],[[[[[]]],[[]],[]],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[],[[[[]]],[[[]],[],[]]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[],[[[[[]]],[]],[[],[]],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[],[[[[]]],[[]],[[],[],[]]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[]]],[[[[],[]]],[]],[]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[],[[[]]],[[[],[[]]],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[],[[[[]]],[],[[[]],[]]],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[[[]]],[[],[[[],[]]]],[]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[],[[[[[]]],[],[]],[[]],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[],[[[[]]],[[],[]],[[],[]]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[[[]]],[[[],[],[[]]],[]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[],[[[[]]],[],[[],[[]],[]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[],[[[]]],[[],[[],[[],[]]]]]]
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[[],[]],[[[[[]]],[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[],[]],[[[[]]],[[]],[],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[],[]],[[[]]],[[[],[]]],[]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[],[]],[[[[]]],[],[[]],[]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[[],[]],[[[]]],[[],[[],[]]]]]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[[],[[[[[]]]],[]],[]],[]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[],[[],[[[[]]]],[[]],[],[]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[],[[],[[[]]]],[[[],[]]],[]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[[[[]]]],[],[[]],[]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[],[[],[[[]]]],[[],[[],[]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[[[[]]],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[[],[]],[]],[[[]]],[[],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[],[[]],[],[[[[]]]],[]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[],[[]],[],[[[]]]],[[],[]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[],[]]],[[[[]]],[]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[],[[[],[]]],[[[]]],[[],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[],[],[[]],[[[[]]]],[]],[]]]
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[],[],[[]],[[[]]]],[[],[]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[[[],[[],[[],[[[[]]]]],[]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[[[],[[],[[],[[[]]]]],[[],[]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[[[],[]],[]],[]],[[[]]],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[],[[]],[]],[],[[[]]]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[[[]],[],[]]],[[[]]],[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[],[]],[[],[]],[[[]]]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[]],[[],[],[[[]]]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[],[[[[],[]]],[]],[[[]]],[]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[],[[[],[[]]],[],[[[]]]],[]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[],[[[]],[]]],[[[]]],[]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[],[[],[[[],[]]]],[[[]]],[]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[[],[],[]],[[]],[[[]]]],[]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[[],[]],[[],[[[]]]]],[]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[],[[[],[],[[]]],[[[]]]],[]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[],[],[[],[[]],[[[]]]]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[[[],[[],[[],[[],[[[]]]]]],[]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[[[[],[]],[]],[]],[]],[[]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[[],[[]],[]],[]],[],[[]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[[[]],[]],[],[]]],[[]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[[],[]],[[]],[],[]],[[]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]],[[]],[],[],[[]]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[],[[[[]],[],[]]],[]],[[]]]]
[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[],[[[]],[[],[]]],[],[[]]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[]],[[[],[]],[]]],[[]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[],[[]],[[[],[],[]]]],[[]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[[],[]],[],[[]],[]],[[]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[],[[]],[],[[]],[],[[]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[],[[[]],[],[[],[]]],[[]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[],[]],[[],[[],[]],[[]]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[]],[[],[[],[],[[]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[],[[[[[],[]]],[]],[]],[[]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[],[[[[],[[]]],[]],[],[[]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[],[[[],[[[]]],[],[]]],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[],[[[[],[]]],[[],[]],[[]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[[]]],[[],[],[[]]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[],[],[[[[]],[]]],[]],[[]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[],[],[[[]],[[]]],[],[[]]]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0]=>[[[],[[],[[[[],[]]]],[]],[[]]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0]=>[[[],[[],[[[],[[]]]],[],[[]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[],[],[]],[[[]],[]]],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[],[[],[]],[[[],[]]]],[[]]]]
[1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0]=>[[[],[[[],[],[[[]]],[]]],[[]]]]
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[[[[],[],[[],[[[]],[]]]],[[]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[[[],[[],[[],[[[],[]]]]],[[]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[[[],[],[]],[]],[[]],[[]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[[],[[],[]],[]],[[],[[]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[],[[[],[]],[],[[]]],[[]]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[],[],[[]],[],[[]],[[]]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[],[[]],[],[[],[[]]]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[],[[[[],[],[]]],[[]],[[]]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[],[[[],[[],[]]],[[],[[]]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[],[],[[[],[]],[[]]],[[]]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[],[[],[[[],[],[[]]]],[[]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[],[],[],[[]],[[]],[[]]]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[],[],[[]],[[],[[]]]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[],[[[],[],[[],[[]]],[[]]]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[],[],[[],[[],[[]],[[]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[[],[],[],[],[],[[]]]]]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[]],[[[],[[[]],[],[]],[],[]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[]],[[[],[[]],[],[[],[],[]]]]]
[1,1,0,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[[[]],[[[[[],[[[]],[]]],[]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[]],[[[[[],[]],[]],[],[]],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[]],[[[[],[]],[[],[],[]]],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[]],[[],[],[[],[[[]],[],[]]]]]
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[]],[[],[],[[[[],[]],[]]],[]]]
[1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[]],[[],[[[],[[],[]]]],[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[]],[[[[],[],[[]]],[]],[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[]],[[],[[[],[],[]],[[],[]]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[]],[[],[[],[],[[],[[],[]]]]]]
[1,1,0,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[[[]],[[[[],[[[],[[]]],[]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[]],[[[[],[],[]],[],[[]],[]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[]],[[[],[],[[],[],[[]]],[]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[]],[[[]]],[[[]],[],[]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[]],[[[[[]]],[]],[]]],[]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[[[]],[[]]],[],[[],[]],[],[]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[[]],[[]]],[[[],[[],[]]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[[]],[[[[]]],[],[[]]],[]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[]],[]],[],[[[]],[]],[],[]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[[[]],[]],[],[[]],[],[[],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[]],[],[[],[[[]]],[]],[],[]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[]],[],[[],[[]]],[],[[],[]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[]],[[[]],[],[[[]]]],[]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[[[[]],[]],[]]],[[[]],[]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[]],[],[[],[]],[],[[[]],[]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[[[[]],[[[],[[],[[[]]]]],[]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[[[]],[],[[]]],[[[]]],[]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[[]],[[[]],[],[]],[],[]]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[[]],[[]],[],[[],[],[]]]],[]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[[]],[[[]],[]]],[]]]],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[[[[[[]],[]],[]],[],[]],[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[[[]],[]],[[],[],[]]],[]],[]]
[1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[]],[],[[],[[[]],[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[]],[],[[[[],[]],[]]],[]],[]]
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[]],[[[],[[],[]]]],[],[]],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[[[]],[],[[]]],[]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[]],[[[],[],[]],[[],[]]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[]],[[],[],[[],[[],[]]]]],[]]
[1,1,1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[[[[[[]],[[[],[[]]],[]]]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[[[[]],[],[]],[],[[]],[]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[]],[],[[],[],[[]]],[]]],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[],[],[[]],[[[],[[[]],[],[]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[],[],[[]],[[[[[],[]],[]]],[]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[],[],[[]],[[],[],[[],[]],[],[]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[],[],[[]],[[],[[[],[[],[]]]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[],[],[[]],[[[[],[],[[]]],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[],[],[[[[]],[[[]]],[]],[],[]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[],[],[[[[]],[[]]],[],[[],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[],[],[[[[]],[]],[],[[[]],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[],[],[[[]],[],[[],[[[]]],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[],[],[[[[]],[[[]],[],[]]]],[]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[[],[],[[[[[[]],[]],[]]],[]],[]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[],[],[[[]],[],[[],[]],[],[]],[]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[],[],[[[]],[[[],[[],[]]]]],[]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[],[],[[[[[]],[],[[]]],[]]],[]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[],[[[],[[]]]],[[[],[]],[],[]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[],[[[],[[]]]],[[],[],[[],[]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[[],[[[],[[[[]]]],[[[]]],[]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0,1,0]=>[[],[[[],[[[[]]]],[]],[],[]],[]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[],[[[],[[[]]]],[],[[],[]]],[]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[[[],[]]],[[]],[[[],[]],[],[]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[[],[]]],[[]],[[],[],[[],[]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[],[]]],[[[[]],[[[]]],[]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[[[],[]]],[[[[]],[]],[],[]],[]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[[],[]]],[[[]],[],[[],[]]],[]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[],[[[],[]],[],[[]]],[[[],[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[],[[[],[]],[],[[[[]]],[]]],[]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[],[[],[],[[],[[]]]],[[[],[]]]]
[1,0,1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[],[[],[],[[],[[[[]]]],[]]],[]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[[[[],[[[]]],[[]]]],[[[],[]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[],[[[]]],[[[[]]]],[]]],[]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[[],[]],[],[]],[[]],[[[],[]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[],[]],[],[]],[[[[]],[]]],[]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[],[],[[],[]]],[[]],[[[],[]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[],[],[[],[]]],[[[[]],[]]],[]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[],[[[],[[[]],[],[[]]]]],[],[]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[],[[[[[],[]],[]]],[[]]],[],[]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[],[[],[],[[],[]],[],[[]]],[],[]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[[],[[],[[[],[[],[[]]]]]],[],[]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[[],[[[[],[],[[]]],[[]]]],[],[]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[[],[[[]]],[]],[],[[]]],[],[]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[[]]],[],[[],[[]]]],[],[]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[],[]],[],[[[]],[[]]]],[],[]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[],[],[[],[[[]]],[[]]]],[],[]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[],[[[]],[],[]]]],[[]],[],[]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[[[],[]],[]]],[]],[[]],[],[]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[],[],[[],[]],[],[]],[[]],[],[]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[],[[[],[[],[]]]]],[[]],[],[]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[[],[],[[]]],[]]],[[]],[],[]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[],[[[],[[[]],[],[]],[],[[]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[],[[[],[[]],[],[[],[],[[]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0,0,0]=>[[],[[[[[],[[[]],[]]],[[]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[],[[[[[],[]],[]],[],[]],[[]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[],[[[[],[]],[[],[],[]]],[[]]]]
[1,0,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[],[[],[],[[],[[[]],[],[[]]]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[],[[],[],[[[[],[]],[]]],[[]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[[],[[],[[[],[[],[]]]],[],[[]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[],[[[[],[],[[]]],[]],[],[[]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[],[[],[[[],[],[]],[[],[[]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[],[[],[[],[],[[],[[],[[]]]]]]]
[1,0,1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[[],[[[[],[[[],[[]]],[[]]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[],[[[[],[],[]],[],[[]],[[]]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[],[[[],[],[[],[],[[]]],[[]]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[],[[[]]],[[[]],[],[[]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[],[[[[[]]],[]],[]]],[[]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[[]]],[],[[],[]],[],[[]]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[],[[]]],[[[],[[],[[]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[],[[[[]]],[],[[]]],[[]]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[],[]],[],[[[]],[]],[],[[]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[],[]],[],[[]],[],[[],[[]]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[],[],[[],[[[]]],[]],[],[[]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[],[],[[],[[]]],[],[[],[[]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[],[[[]],[],[[[]]]],[[]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[[[[],[]],[]]],[[[]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[],[],[[],[]],[],[[[]],[[]]]]]
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[[[],[[[],[[],[[[]]]]],[[]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[],[],[[]]],[[[]]],[[]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[[[],[[[]],[],[]],[],[]]],[[]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[],[[]],[],[[],[],[]]]],[[]]]
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[[],[[[]],[]]],[]]]],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[[[[],[]],[]],[],[]],[]],[[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[[[],[]],[[],[],[]]],[]],[[]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[],[],[[],[[[]],[],[]]]],[[]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[[[],[],[[[[],[]],[]]],[]],[[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0,1,1,0,0]=>[[[],[[[],[[],[]]]],[],[]],[[]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[[[],[],[[]]],[]],[],[]],[[]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[],[[[],[],[]],[[],[]]]],[[]]]
[1,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[],[[],[],[[],[[],[]]]]],[[]]]
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[],[[[],[[]]],[]]]]],[[]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[[],[],[]],[],[[]],[]]],[[]]]
[1,1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[],[],[[],[],[[]]],[]]],[[]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[[[]]],[],[[]],[],[[[[]]]],[]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[],[[]]],[[]],[],[],[[[[]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[]],[],[[[]],[]],[[[[]]]],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[],[],[[]]],[[]],[],[[[[]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[],[]],[[[]],[]],[[[[]]]],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[]]],[],[[]],[],[[],[[[]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[[],[[[]]]],[[]]],[[]],[],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[]],[],[[[]],[],[]],[[[[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[]]],[],[[],[]],[[],[[[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[[[]]]],[],[[]],[]],[[]],[]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[],[[]]],[[],[]],[[[[]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[[],[[[]]]],[[]],[]],[[]],[]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[[]]],[[],[],[]],[[[[]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[]],[]],[[],[]],[[],[[[]]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[]],[],[[[],[]]],[],[[[[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[[[]]]],[]],[[[],[]]],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[]],[],[[],[[],[]]],[[[[]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[[]]]],[],[]],[[[],[]]],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[],[]],[[],[[],[]]],[[[[]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[],[[[]]],[]]],[],[[[]]],[]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[],[[],[[[]]],[]]],[[[]]],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[[[[[]]],[]]],[],[[[],[]]],[]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[],[[[[]]],[]]],[[[],[]]],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[]]],[],[[],[[]],[],[[[]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[[[[]]],[]]],[],[[[]],[],[]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[]]],[],[[],[[],[]],[[[]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[[]]],[],[]]],[],[[[]],[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[]]],[],[[[],[]],[[[]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[],[[]],[],[[]],[]],[[[[]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[],[[]]],[[],[[[]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[],[[[[]]],[]],[[]],[]],[[]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[[]]],[[],[],[[[]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[[]]],[]],[[]],[]],[[],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[],[[]],[],[[],[]]],[[[[]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[],[]],[[[],[]],[[[]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[],[[[[]]],[],[]],[[]]],[[]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[],[[],[]],[[],[]]],[[[[]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[]],[[[]],[],[[[]]],[]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[[],[]],[[]]],[[],[],[[[]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[]],[[[],[]],[[[]]],[]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[[[],[],[]],[[]]],[[],[[[]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[[],[]],[[],[]]],[[[[]]],[]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[]],[],[[[[[]],[]]]],[],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[]],[]],[[[[[]],[]]]],[],[]]
[1,1,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[]],[],[[],[[[[]],[]]]],[[]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[]],[],[]],[[[[[]],[]]]],[]]
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[],[]],[[],[[[[]],[]]]],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[],[]]],[],[[[[[]],[]]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[],[[],[]]],[[[[[]],[]]]],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[]]],[],[[],[[[[]],[]]],[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[],[]]],[],[[[[[]],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[],[[]],[],[[[[]],[]]]],[[]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[]],[],[]],[[[[[]],[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[],[[],[]],[[[[]],[]]]],[[]]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[]],[]],[[[[[]],[]]],[],[]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[[[[]],[]]]],[[],[]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[[]],[],[[]]]]],[],[[]],[]]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[],[[[[]],[],[[]]]]],[[]],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[[]],[],[[]]]]],[],[[],[]]]
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[],[[[[]],[],[[]]]],[]],[[]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[[]],[],[[]]]],[]],[[],[]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[[[],[]],[[]]]]],[],[[]],[]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[],[[[[],[]],[[]]]]],[[]],[]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[[[[[[],[]],[[]]]]],[],[[],[]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[],[[[[],[]],[[]]]],[]],[[]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[[[[[[],[]],[[]]]],[]],[[],[]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[]],[],[[[[[]]],[],[[]],[]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[],[]],[[[[[]]],[],[[]],[]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[]],[],[[[[],[[]]],[[]],[]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[],[]],[[[[],[[]]],[[]],[]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[]],[],[[[[[]]],[],[[],[]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[[[[]]],[],[[],[]]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[]],[],[[[[],[[]],[]],[[]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[],[]],[[[[],[[]],[]],[[]]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[]],[],[[[[[]],[]],[[],[]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[],[]],[[[[[]],[]],[[],[]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[[]],[],[[[]]],[],[[]]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[[]],[]],[[[]]],[],[]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[]],[],[[],[[]]],[[]]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[[]],[],[]],[[[]]],[]]],[]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[]],[[],[[]]],[[]]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[[],[]]],[],[[[]]],[]]],[]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[],[[],[]]],[[[]]],[]]],[]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[]]],[],[[],[[]],[]]]],[]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[],[]]],[],[[[]],[]]]],[]]
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[[]],[],[[]]],[[]]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[[]],[],[]],[[[]],[]]]],[]]
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[],[[],[]],[[]]],[[]]]],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[[]],[]],[[[]],[],[]]]],[]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[[[],[]],[[]]],[[],[]]]],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[[]]],[],[[]],[],[[[]]],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[[],[[]]],[[]],[],[],[[[]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[]],[],[[[]],[]],[[[]]],[]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[[],[],[[]]],[[]],[],[[[]]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[]],[[[]],[]],[[[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[[[]]],[],[[]],[],[[],[[]]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[[],[[]]],[[]]],[[]],[],[]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[]],[],[[[]],[],[]],[[[]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[]]],[],[[],[]],[[],[[]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[[]]],[],[[]],[]],[[]],[]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[],[[]]],[[],[]],[[[]]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[[],[[]]],[[]],[]],[[]],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[[]]],[[],[],[]],[[[]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[]],[]],[[],[]],[[],[[]]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[]],[],[[[],[]]],[],[[[]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[[]]],[]],[[[],[]]],[],[]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[]],[],[[],[[],[]]],[[[]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[[]]],[],[]],[[[],[]]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[],[]],[[],[[],[]]],[[[]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[[[],[[]],[]]],[],[[[]]],[]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[],[[],[[]],[]]],[[[]]],[]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[[[]],[]]],[],[[[],[]]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[[],[[[]],[]]],[[[],[]]],[]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[[]]],[],[[],[[]],[],[[]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[[[[]],[]]],[],[[[]],[],[]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[]]],[],[[],[[],[]],[[]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[[[[]],[],[]]],[],[[[]],[]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[],[]]],[],[[[],[]],[[]]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[],[[]],[],[[]],[]],[[[]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[]],[],[],[[]]],[[],[[]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[],[[[]],[]],[[]],[]],[[]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[[[]],[],[[]]],[[],[],[[]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[[[]],[]],[[]],[]],[[],[]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[],[[]],[],[[],[]]],[[[]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[[]],[],[]],[[[],[]],[[]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[],[[[]],[],[]],[[]]],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[],[[],[]],[[],[]]],[[[]]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[[]],[]],[[[]],[],[[]],[]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[[[],[]],[[]]],[[],[],[[]]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[[]],[]],[[[],[]],[[]],[]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[[],[],[]],[[]]],[[],[[]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[[],[]],[[],[]]],[[[]],[]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0]=>[[[[[[[[[[[[]]]]]]]]],[]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[]],[],[],[],[],[],[],[],[],[],[]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[[[]],[],[],[],[],[]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[],[],[],[],[],[],[],[],[[],[]],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[],[],[],[],[],[],[],[],[],[[]],[]]
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[],[],[[],[[],[[[],[[]],[]]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[],[],[[],[[[],[[],[[]]],[]]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[],[],[],[[[[],[[]],[[]],[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[],[[[],[]],[[[],[[]],[]]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[],[],[[[],[[],[[],[[]]]],[]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[],[],[],[[[],[[]],[[[]]],[]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[],[[[[],[]],[[],[[]]],[]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[[],[[],[]]],[[[[]],[]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[],[[],[]],[[]],[[[[]],[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[],[[],[]],[[],[[[],[[]],[]]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[],[[],[]],[[[],[[],[[]]],[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[],[[],[]],[[],[]],[[[[]],[]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[],[[],[]]],[[[],[[]],[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[],[[[],[]],[]],[[[],[[]],[]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[],[],[[],[[],[[],[[[]]]]],[]]]
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[],[],[],[[[],[[[]],[[]]]],[]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[],[],[[[],[]],[[],[[[]]]],[]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[],[],[],[[],[[[]]],[[[]]],[]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[],[],[],[[]],[[[[]],[[]]],[]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[],[[],[]],[[],[[],[[[]]]],[]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[]],[],[[[]],[[[]]],[]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[],[[],[]]],[[],[[[]]],[]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[],[[[],[]],[]],[[],[[[]]],[]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[],[],[],[[],[[[[]]]],[[]],[]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[],[],[],[[[[]],[]]],[[[]],[]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[],[[],[]],[],[[[[]]],[[]],[]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[],[],[],[[[[]]],[]],[[[]],[]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[],[],[[]],[[]],[[]],[[[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[],[]],[],[[],[[[],[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[],[]],[],[[[],[[],[[]]],[]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[],[]],[],[[],[]],[[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[]],[[],[]],[[[],[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[],[]],[],[[],[[],[[[]]]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[],[]],[],[],[[[]],[[[]]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[]],[[],[]],[[],[[[]]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[],[]],[],[],[[[[]]],[[]],[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[]],[],[[]],[[]],[[[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[],[[],[]]],[],[[[],[[]],[]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[],[[],[]]],[],[[],[[[]]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[],[[],[]]],[],[[]],[[[]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[[[],[]],[]],[],[[[],[[]],[]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[[[],[]],[]],[],[[],[[[]]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[[[],[]],[]],[],[[]],[[[]],[]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[],[[],[[],[]]]],[],[[[]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[],[[[],[]],[]]],[],[[[]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[],[]],[[],[]]],[],[[[]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[],[[],[]]],[]],[],[[[]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[[[],[]],[]],[]],[],[[[]],[]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[],[[],[[],[[],[[],[[]]]]]],[]]
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[],[],[[],[[[],[[]],[[]]]]],[]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[],[[[],[]],[[],[[]]]]],[]]
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[],[],[[[],[[],[[]]],[[]]]],[]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[],[],[[],[[]],[]],[[[[]]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[],[[[],[]],[[],[[],[[]]]]],[]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[],[[],[]],[[[],[[]],[[]]]],[]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[],[[],[]]],[[],[[]]]],[]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[],[[[[],[]],[]],[[],[[]]]],[]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[[],[[],[]]]],[[[]]],[]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[],[[[],[[]],[]]],[[[]]],[]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[],[[[],[]],[[],[]]],[[[]]],[]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[[],[]]],[[]],[[[]]],[]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[],[[],[]],[[]],[[]],[[[]]],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[],[]],[[],[[],[[],[[]]]]],[]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[],[]],[],[[[],[[]],[[]]]],[]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[]],[[[],[]],[[],[[]]]],[]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[],[]],[[],[[],[]]],[[[]]],[]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[]],[[],[]],[[]],[[[]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[],[[],[]]],[[],[[],[[]]]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[],[[],[]]],[[],[]],[[[]]],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[[],[]],[]],[[],[[],[[]]]],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[[],[]],[]],[[],[]],[[[]]],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[],[[],[[],[]]]],[[],[[]]],[]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[],[[[],[]],[]]],[[],[[]]],[]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[],[]],[[],[]]],[[],[[]]],[]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[],[[],[]]],[]],[[],[[]]],[]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[[[],[]],[]],[]],[[],[[]]],[]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[[],[[[],[[],[[],[]]]]],[[]],[]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[],[],[[],[[[]],[[]]]],[[]],[]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[],[[[[],[]],[[],[]]]],[[]],[]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[[],[[[]]],[]]],[[]],[]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[],[],[[]],[[[]],[[]]],[[]],[]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[],[]],[[[],[[],[]]]],[[]],[]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[],[]],[],[[[[]],[]]],[[]],[]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[],[[],[]]],[[[],[]]],[[]],[]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[[],[]],[]],[[[],[]]],[[]],[]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0]=>[[],[],[[],[[[[]]]],[]],[[]],[]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[[[]],[]]],[[]],[[]],[]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[],[]],[],[[[[]]],[]],[[]],[]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[],[],[[[[]]],[]],[[]],[[]],[]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[[],[[],[]]]],[[]],[[],[]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[[[],[]],[]]],[[]],[[],[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[],[]],[[],[]]],[[]],[[],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[],[[],[]]],[]],[[]],[[],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[[],[]],[]],[]],[[]],[[],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[],[],[],[],[],[],[],[],[[],[]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[[[],[]],[]],[]],[]],[]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[],[],[],[],[],[],[],[],[],[]],[]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[]],[[]],[[]],[[],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[]],[[]],[[]],[[[],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[]],[[]],[[[],[]]],[[],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[]],[[]],[[[],[[],[]]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[]],[[]],[[[[],[]],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[]],[[[],[]]],[[]],[[],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[]],[[[],[]]],[[[],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[]],[[[],[[],[]]]],[[],[]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[]],[[[[],[]],[]]],[[],[]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[],[[]],[[[],[[],[[],[]]]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[],[[]],[[[],[[[],[]],[]]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[]],[[[[],[]],[[],[]]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[],[[]],[[[[],[[],[]]],[]],[]]]
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[],[[]],[[[[[],[]],[]],[]],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[[],[]]],[[]],[[]],[[],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[]]],[[]],[[[],[]],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[[],[]]],[[[],[]]],[[],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[],[[[],[]]],[[[],[[],[]]],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[],[[[],[]]],[[[[],[]],[]],[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[[],[[],[]]]],[[]],[[],[]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[],[[],[]]]],[[[],[]],[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[],[[[[],[]],[]]],[[]],[[],[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[],[[[[],[]],[]]],[[[],[]],[]]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[[],[[[],[[],[[],[]]]]],[[],[]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[[],[[[],[]],[]]]],[[],[]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[],[[[[],[]],[[],[]]]],[[],[]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[[[],[[],[]]],[]]],[[],[]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[],[[[[[],[]],[]],[]]],[[],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[]],[[]],[[]],[[],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[]],[[]],[[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[]],[[]],[[[],[]]],[[],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[]],[[]],[[[],[[],[]]],[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[],[]],[[]],[[[[],[]],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[]],[[[],[]]],[[]],[[],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[]],[[[],[]]],[[[],[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[[],[]],[[[],[[],[]]]],[[],[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[]],[[[[],[]],[]]],[[],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[]],[[]],[[],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[],[[],[]]],[[]],[[[],[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[],[[],[]]],[[[],[]]],[[],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[[],[]],[]],[[]],[[]],[[],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[[[],[]],[]],[[]],[[[],[]],[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[[],[]],[]],[[[],[]]],[[],[]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[],[[],[[],[[],[[],[]]]]],[]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[[[],[[],[[],[[[],[]],[]]]],[]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[[],[[[],[]],[[],[]]]],[]]]
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[[[],[[],[[[],[[],[]]],[]]],[]]]
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[[[],[[],[[[[],[]],[]],[]]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[],[[[],[]],[[],[[],[]]]],[]]]
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[],[[[],[]],[[[],[]],[]]],[]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[],[[],[]]],[[],[]]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[],[[[[],[]],[]],[[],[]]],[]]]
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[[[],[[[],[[],[[],[]]]],[]],[]]]
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[],[[[],[]],[]]],[]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[],[[[[],[]],[[],[]]],[]],[]]]
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[[[],[[[[],[[],[]]],[]],[]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[],[]],[[],[[],[[],[]]]],[]]]
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[],[]],[[],[[[],[]],[]]],[]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[]],[[[],[]],[[],[]]],[]]]
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[],[]],[[[],[[],[]]],[]],[]]]
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[],[]],[[[[],[]],[]],[]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[],[[],[]]],[[],[[],[]]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[],[[],[]]],[[[],[]],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[[[],[]],[]],[[],[[],[]]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[[],[]],[]],[[[],[]],[]],[]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[],[[],[[],[]]]],[[],[]],[]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[],[[[],[]],[]]],[[],[]],[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[],[]],[[],[]]],[[],[]],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[],[[],[]]],[]],[[],[]],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[[[[],[]],[]],[]],[[],[]],[]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[[[[],[[],[[],[[],[]]]]],[],[]]]
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[[[[],[[],[[[],[]],[]]]],[],[]]]
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[],[[[],[]],[[],[]]]],[],[]]]
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[[[[],[[[],[[],[]]],[]]],[],[]]]
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[],[[[[],[]],[]],[]]],[],[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[],[]],[[],[[],[]]]],[],[]]]
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[]],[[[],[]],[]]],[],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[],[[],[]]],[[],[]]],[],[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[[[],[]],[]],[[],[]]],[],[]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[],[[],[[],[]]]],[]],[],[]]]
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[],[[[],[]],[]]],[]],[],[]]]
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[[],[]],[[],[]]],[]],[],[]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[[],[[],[]]],[]],[]],[],[]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[[[[],[]],[]],[]],[]],[],[]]]
          

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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.

Properties

bijective, graded

Sage code

def mapping(elt):
    levels = [OrderedTree().clone()]
    for u in elt:
        if u == 1:
            levels.append(OrderedTree().clone())
        else:
            tree = levels.pop()
            tree.set_immutable()
            root = levels.pop()
            root.append(tree)
            levels.append(root)
    root = levels[0]
    root.set_immutable()
    return root

Weight

Created

Jan 19, 2020 at 07:29 by FindStatCrew

Updated

Jan 19, 2020 at 07:29 by Martin Rubey