Identifier
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2Cc0021;cc-rep-3
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[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]
[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]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]
[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]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]
[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]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]
[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]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]
[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]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]
[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]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]
[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]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]
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[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]
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[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]
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[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]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]
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[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]
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[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]
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[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]
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[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]
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[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]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]
[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]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]
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[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]
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[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]
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[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]
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[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]
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[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]
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[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]
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[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]
[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]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]
[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]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]
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[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]
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[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]
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[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
- if $x$ is the left child of $y$, $x$ becomes the first child of $y$.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
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