- FindStat

edit this map or download as text // json

Identifier

Mp00051: Ordered trees —to Dyck path⟶ Dyck paths

Images

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

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[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[],[[],[]],[[]],[],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[],[[[]]],[[]],[],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[],[[],[]],[[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[],[[[]]],[[]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[],[[],[[],[]]],[],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[],[[],[[[]]]],[],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[],[[[[],[]]]],[],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[],[[[],[[],[]]]],[]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[],[[[[[],[]]]]],[]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[],[[[[[[]]]]]],[]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[],[[]],[],[[]],[]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[],[[]],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[],[[]],[[],[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[[],[[]],[[[]]],[]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[],[[],[]],[[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[[],[[[]]],[[]],[]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[],[[],[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[[],[[],[[]]],[],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[[],[[[]],[]],[],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[[],[[[],[]]],[],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[[],[[[[]]]],[],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[],[[],[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[[],[[],[],[[]]],[]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[[],[[],[[]],[]],[]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[[],[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[],[[],[[[]]]],[]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[[],[[[]],[],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[[],[[[]],[[]]],[]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[[],[[[],[]],[]],[]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[[],[[[[]]],[]],[]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[[],[[[],[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[[],[[[],[[]]]],[]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[[],[[[[]],[]]],[]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[[],[[[[],[]]]],[]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[[],[[[[[]]]]],[]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[[],[[],[[],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[[],[[],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[[],[[[],[]],[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[],[[],[[[],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[],[[],[[[[],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[],[[[],[]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[],[]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[],[[],[]]],[[],[]]]]=>[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]
[[[],[]],[[],[[[],[]],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[]],[[[],[]],[[],[]]]]=>[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]
[[[],[[],[]]],[[],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[],[[],[]]],[[[],[]],[]]]=>[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]
[[[],[[],[[],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[],[[],[[[],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[],[[[],[]],[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[],[[[],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[],[[[[],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]
[[[[],[]],[[],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[]],[[[],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[],[[],[]]],[[],[]]],[]]=>[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]
[[[[[[],[]],[]],[]],[]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
[[],[[],[[],[[],[[],[[],[]]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]
[[],[[],[[],[[],[[[],[]],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[],[[],[[],[[[],[]],[[],[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]
[[],[[],[[],[[[],[[],[]]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]
[[],[[],[[],[[[[],[]],[]],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]
[[],[[],[[[],[]],[[],[[],[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[[],[[[],[]],[[[],[]],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[[],[[[],[[],[]]],[[],[]]]]]=>[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]
[[],[[],[[[],[[],[[],[]]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]
[[],[[],[[[],[[[],[]],[]]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]
[[],[[],[[[[],[]],[[],[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]
[[],[[],[[[[],[[],[]]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]
[[],[[],[[[[[],[]],[]],[]],[]]]]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]
[[],[[[],[]],[[],[[],[[],[]]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[],[[[],[]],[[],[[[],[]],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[],[[[],[]],[[[],[]],[[],[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[],[[[],[]],[[[],[[],[]]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[],[[[],[]],[[[[],[]],[]],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[],[[[],[[],[]]],[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[],[[],[]]],[[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[[],[]],[]],[[],[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[],[[[[],[]],[]],[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[],[[[],[[],[[],[]]]],[[],[]]]]=>[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]
[[[],[]],[[],[[],[[[],[]],[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[[],[]],[[],[[[],[]],[[],[]]]]]=>[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]
[[[],[[],[]]],[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[],[[],[]]],[[],[[[],[]],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[],[[],[]]],[[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[],[[],[]]],[[[],[[],[]]],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[],[[],[]]],[[[[],[]],[]],[]]]=>[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]
[[[[],[]],[]],[[],[[[],[]],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[[],[]],[]],[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[[],[]],[]],[[[],[[],[]]],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[[[],[]],[]],[[[[],[]],[]],[]]]=>[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]
[[[],[[],[[],[[],[[],[]]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]
[[[],[[],[[],[[[],[]],[]]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]
[[[],[[],[[[],[]],[[],[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]
[[[],[[],[[[],[[],[]]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]
[[[],[[],[[[[],[]],[]],[]]]],[]]=>[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]
[[[],[[[],[]],[[],[[],[]]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[],[[[],[]],[[[],[]],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[],[[[],[[],[]]],[[],[]]]],[]]=>[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]
[[[],[[[],[[],[[],[]]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]
[[[],[[[],[[[],[]],[]]],[]]],[]]=>[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]
[[[],[[[[],[]],[[],[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[],[[[[],[[],[]]],[]],[]]],[]]=>[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]
[[[],[[[[[],[]],[]],[]],[]]],[]]=>[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
[[[[],[]],[[],[[],[[],[]]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[[[],[]],[[],[[[],[]],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[[[],[]],[[[],[]],[[],[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[]],[[[],[[],[]]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[[[],[]],[[[[],[]],[]],[]]],[]]=>[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]
[[[[],[[],[]]],[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[],[[],[]]],[[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[[],[]],[]],[[],[[],[]]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[[[[],[]],[]],[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[[[],[[],[[],[]]]],[[],[]]],[]]=>[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]
[[[[[[[],[]],[]],[]],[]],[]],[]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
          

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.

Properties

bijective, graded

Sage code

def mapping(elt):
    word = []
    for child in elt:
        word.append(1)
        word.extend(child.to_dyck_word())
        word.append(0)
    from sage.combinat.dyck_word import DyckWord
    return DyckWord(word)

Weight

Created

Jan 26, 2020 at 12:31 by FindStatCrew

Updated

Feb 19, 2024 at 15:04 by Martin Rubey