Identifier
Mp00051:
Ordered trees
—to Dyck path⟶
Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Images
=>
Cc0021;cc-rep-0Cc0005;cc-rep-1Cc0010;cc-rep-2
[]=>[]=>.
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[[],[[[[]]],[[]]]]=>[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]=>[.,[[[[[.,.],.],.],[.,.]],.]]
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[[],[[[],[[[]]]]]]=>[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]=>[[.,[[[.,.],.],.]],[[.,.],.]]
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[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
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[[[]],[[[],[[]],[]]]]=>[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]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
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[[[]],[[[[[]]],[]]]]=>[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]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
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[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
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[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
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[[[[]]],[[]],[[[]]]]=>[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]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
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[[[],[]],[[],[],[]],[]]=>[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]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
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[[[],[]],[[],[[],[]]]]=>[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]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
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[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
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[[[],[[]]],[],[[]],[]]=>[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]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
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[[[],[],[]],[],[[[]]]]=>[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]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
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[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
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[[[[],[]],[[],[]]],[[],[[],[]]]]=>[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]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path is the depth of the tree.
This sends the maximal height of the Dyck path is the depth of the tree.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
searching the database
Sorry, this map was not found in the database.