Identifier
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Images
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Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2Cc0021;cc-rep-3
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[1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],.],.],[.,.]]]=>[[],[[[[[],[]],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[[],[]]]]],[]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],.],[.,.]],.]]=>[[],[[[[[],[]],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[[],[]]]]],[]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],[.,.]],.],.]]=>[[],[[[[[],[]],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[[],[]]]]],[]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,[.,.]],.],.],.]]=>[[],[[[[[],[[],[]]],[]],[]],[]]]=>[[[],[[],[[],[[[],[]],[]]]]],[]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],.]]=>[[],[[[[[[],[]],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[[],[]]]]]],[]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[],[]],[[],[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]],[]],[[],[]]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],.]]]]=>[[[],[]],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[[],[]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[.,.]]]]=>[[[],[]],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[[],[]]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,[.,.]],.]]]=>[[[],[]],[[],[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]],[]],[[],[]]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]]=>[[[],[]],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[[],[]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,.]]]]=>[[[],[]],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[[],[]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],.]]]=>[[[],[]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[],[]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[.,.]]]=>[[[],[]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[],[]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,.]]],.]]=>[[[],[]],[[[],[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]],[]]],[[],[]]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],.]],.]]=>[[[],[]],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[[],[]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[[.,.],.],[.,.]]]=>[[[],[]],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[[],[]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[[.,.],[.,.]],.]]=>[[[],[]],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[[],[]]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],.]]=>[[[],[]],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[[],[]]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],.]]=>[[[],[]],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[[],[]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[]]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],.]]]=>[[[],[[],[]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[.,.]]]=>[[[],[[],[]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,.]],[[.,[.,.]],.]]=>[[[],[[],[]]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],.]]=>[[[],[[],[]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[],[]],[]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[],[[],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],.]]=>[[[],[[],[[],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[[[],[[],[[],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[]],[]],[]]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[[[],[[],[[],[[],[[],[]]]]]],[]]=>[[],[[[[[[],[]],[]],[]],[]],[]]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],.]=>[[[],[[],[[],[[[],[]],[]]]]],[]]=>[[],[[[[[],[[],[]]],[]],[]],[]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],.]]],[.,.]]=>[[[],[[],[[[],[]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[],[]]],[]],[]]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],.]=>[[[],[[],[[[],[]],[[],[]]]]],[]]=>[[],[[[[[],[]],[[],[]]],[]],[]]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],.]=>[[[],[[],[[[],[[],[]]],[]]]],[]]=>[[],[[[[],[[[],[]],[]]],[]],[]]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[[[.,.],.],.]]],.]=>[[[],[[],[[[[],[]],[]],[]]]],[]]=>[[],[[[[],[[],[[],[]]]],[]],[]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,.]]]=>[[[],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],.]]=>[[[],[[[],[]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[],[]]],[]]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[.,.]]=>[[[],[[[],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[]]],[]]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],.]=>[[[],[[[],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[]]],[]]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],.]=>[[[],[[[],[]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[],[]]],[]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,.]],.]],[.,.]]=>[[[],[[[],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[]]],[]]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],.]=>[[[],[[[],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,.]]],.]],.]=>[[[],[[[],[[],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[]],[]]],[]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],.]],.]],.]=>[[[],[[[],[[[],[]],[]]],[]]],[]]=>[[],[[[],[[[],[[],[]]],[]]],[]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],.],.]],[.,.]]=>[[[],[[[[],[]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[],[]]]],[]]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],.],[.,.]]],.]=>[[[],[[[[],[]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[],[]]]],[]]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],.]=>[[[],[[[[],[]],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[[],[]]]],[]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[[[.,[.,.]],.],.]],.]=>[[[],[[[[],[[],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[]],[]]]],[]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[[[[.,.],.],.],.]],.]=>[[[],[[[[[],[]],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[[],[]]]]],[]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[]]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],.]]]=>[[[[],[]],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[[],[]]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],.],[[.,.],[.,.]]]=>[[[[],[]],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[[],[]]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,[.,.]],.]]=>[[[[],[]],[]],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[[],[[],[]]]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],.]]=>[[[[],[]],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[[],[]]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[[],[]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[],[]]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],.]]=>[[[[],[]],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[[],[]]]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[[[],[]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[],[]]]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],.]=>[[[[],[]],[[],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[]],[[],[]]]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],.]=>[[[[],[]],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[[],[]]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],.]],[.,.]]=>[[[[],[]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[],[]]]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[.,.]]],.]=>[[[[],[]],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[[],[]]]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],.]=>[[[[],[]],[[[],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[]]],[[],[]]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[[.,.],.],.]],.]=>[[[[],[]],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[[],[]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[[[],[[],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[]],[]]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],.]]=>[[[[],[[],[]]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[[[],[[],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],.]=>[[[[],[[],[]]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],.]=>[[[[],[[],[]]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[[],[]],[]]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],.],[.,.]]=>[[[[],[[],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],.]=>[[[[],[[],[[],[]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],.],.]=>[[[[],[[],[[],[[],[]]]]],[]],[]]=>[[],[[],[[[[[],[]],[]],[]],[]]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],.]]],.],.]=>[[[[],[[],[[[],[]],[]]]],[]],[]]=>[[],[[],[[[[],[[],[]]],[]],[]]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],.]],.],[.,.]]=>[[[[],[[[],[]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[],[]]],[]]]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],.]],[.,.]],.]=>[[[[],[[[],[]],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[[],[]]],[]]]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[.,.]]],.],.]=>[[[[],[[[],[]],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[[],[]]],[]]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,[.,.]],.]],.],.]=>[[[[],[[[],[[],[]]],[]]],[]],[]]=>[[],[[],[[[],[[[],[]],[]]],[]]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,[[[.,.],.],.]],.],.]=>[[[[],[[[[],[]],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[[],[]]]],[]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[[[],[]],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[[],[]]]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[[[[.,.],.],.],[[.,.],.]]=>[[[[[],[]],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[[],[]]]]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[[[[.,.],.],[.,.]],[.,.]]=>[[[[[],[]],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[[],[]]]]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,.]]],.]=>[[[[[],[]],[]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[],[[],[]]]]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],.]=>[[[[[],[]],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[[],[]]]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[.,.]],.],[.,.]]=>[[[[[],[]],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[[],[]]]]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[.,.]],.]=>[[[[[],[]],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[[],[]]]]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,.]]],.],.]=>[[[[[],[]],[[],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[]],[[],[]]]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],.]],.],.]=>[[[[[],[]],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[[],[]]]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,.]],.],.],[.,.]]=>[[[[[],[[],[]]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[[],[]],[]]]]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,.]],.],[.,.]],.]=>[[[[[],[[],[]]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[[],[]],[]]]]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],.]=>[[[[[],[[],[]]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[[],[]],[]]]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,.]]],.],.],.]=>[[[[[],[[],[[],[]]]],[]],[]],[]]=>[[],[[],[[],[[[[],[]],[]],[]]]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],.]],.],.],.]=>[[[[[],[[[],[]],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[[],[]]],[]]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],.],.],.],[.,.]]=>[[[[[[],[]],[]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[],[[],[]]]]]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],.],.],[.,.]],.]=>[[[[[[],[]],[]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[],[[],[]]]]]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],.],[.,.]],.],.]=>[[[[[[],[]],[]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[],[[],[]]]]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[.,.]],.],.],.]=>[[[[[[],[]],[[],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[]],[[],[]]]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,[.,.]],.],.],.],.]=>[[[[[[],[[],[]]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[[],[]],[]]]]]] [1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],.]=>[[[[[[[],[]],[]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[],[[],[]]]]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[[],[]]],[[],[]]],[[],[]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[],[]],[[[],[]],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[[],[]]],[[],[]]] [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[],[]],[[[],[]],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[[],[]]],[[],[]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[],[]],[[[],[[],[]]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[[],[]],[]]],[[],[]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[],[]],[[[],[[],[]]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[[],[]],[]]],[[],[]]] [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[],[]],[[[],[[],[]]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[[],[]],[]]],[[],[]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[],[]],[[[],[[],[[],[]]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[[],[]],[]],[]]],[[],[]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[],[]],[[[],[[],[[],[]]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[[],[]],[]],[]]],[[],[]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[],[]],[[[[],[[],[]]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[[],[]],[]]]],[[],[]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[],[]],[[[[],[[],[]]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[[],[]],[]]]],[[],[]]] [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]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[[],[]],[[[[],[[],[[],[]]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[[],[]],[]],[]]]],[[],[]]] [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[[],[]],[[[[[],[[],[[],[]]]],[]],[]],[]]]=>[[[],[[],[[],[[[[],[]],[]],[]]]]],[[],[]]] [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]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[],[[],[]]],[[],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[]],[[[],[]],[]]] [1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[],[[],[]]],[[],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[]],[[[],[]],[]]] [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]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[],[[],[]]],[[[],[]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[],[]]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[],[[],[]]],[[[],[]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[],[]]],[[[],[]],[]]] [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]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[],[[],[]]],[[[],[[],[]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[],[]],[]]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[],[[],[]]],[[[[],[]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[],[]]]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[],[[],[]]],[[[[],[]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[],[]]]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[],[[],[]]],[[[[],[]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[],[]]]],[[[],[]],[]]] [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]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[],[[],[]]],[[[[],[[],[]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]] [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[],[[],[]]],[[[[[],[[],[]]],[]],[]],[]]]=>[[[],[[],[[],[[[],[]],[]]]]],[[[],[]],[]]] [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[],[[],[[],[]]]],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[],[[],[[],[]]]],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[],[[],[[],[]]]],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[],[[],[[],[]]]],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[],[[],[[],[]]]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[],[[],[[],[]]]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[],[[],[[],[]]]],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[],[[],[[],[]]]],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[],[[],[[],[]]]],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[],[[],[[],[]]]],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[[[[],[]],[]],[]]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[],[[],[[],[[],[]]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[[],[]],[]],[]],[]]] [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[],[[],[[],[[],[]]]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[[[],[]],[]],[]],[]]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[],[[],[[],[[],[]]]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[[[],[]],[]],[]],[]]] [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]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[],[[],[[],[[],[]]]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[[[],[]],[]],[]],[]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[],[[],[[],[[[],[]],[]]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[[],[[],[]]],[]],[]],[]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[],[[],[[],[[[],[]],[]]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[[],[[],[]]],[]],[]],[]]] [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[],[[],[[[],[]],[]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[],[[],[]]],[]],[]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[],[[],[[[],[[],[]]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[[],[]],[]]],[]],[]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[],[[],[[[],[[],[]]],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[[[],[]],[]]],[]],[]]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[],[[],[[[],[[],[]]],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[[[],[]],[]]],[]],[]]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[],[[],[[[],[[[],[]],[]]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[[],[[],[]]],[]]],[]],[]]] [1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[],[[],[[[[],[]],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[[],[]]]],[]],[]]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[],[[],[[[[],[]],[]],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[[],[[],[]]]],[]],[]]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[],[[],[[[[],[[],[]]],[]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[],[[[],[]],[]]]],[]],[]]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[[],[]],[[],[]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[],[]],[[],[]]],[]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[[],[]],[[[],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[]]],[[],[]]],[]]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[],[[[],[[],[]]],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[[[],[]],[]]],[]]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[],[[[],[[],[]]],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[[[],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[],[[[],[[],[[],[]]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[[],[]],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[[],[[[],[[],[[],[]]]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[[[],[]],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[],[[[],[[],[[],[]]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[[],[]],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[[],[[[],[[],[[],[]]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[[],[]],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[[],[[[],[[],[[],[]]]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[[[],[]],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[],[[[],[[],[[[],[]],[]]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[[],[[],[]]],[]],[]]],[]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[[],[[[],[[],[[[],[]],[]]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[[],[[],[]]],[]],[]]],[]]] [1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[],[[[],[[[],[]],[]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[],[[],[]]],[]]],[]]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[],[[[],[[[],[]],[]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[],[[],[]]],[]]],[]]] [1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[[[],[[[],[[[],[]],[]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[],[[],[]]],[]]],[]]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[],[[[],[[[],[[],[]]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]] [1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[],[[[],[[[],[[],[]]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[[],[]],[]]],[]]],[]]] [1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[[],[[[],[[[],[[],[]]],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[[[],[]],[]]],[]]],[]]] [1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]=>[[],[[[],[[[],[[[],[[],[]]],[]]],[]]],[]]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[],[[[],[[[[],[]],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[[],[]]]],[]]],[]]] [1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[[[],[[[],[[[[],[]],[]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[],[[],[]]]],[]]],[]]] [1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[[],[[[],[[[[],[]],[]],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[[],[[],[]]]],[]]],[]]] [1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[],[[[],[[[[],[[],[]]],[]],[]]],[]]],[]]=>[[],[[[],[[[],[[],[[[],[]],[]]]],[]]],[]]] [1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[[[[],[]],[]],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[[],[[],[]]]],[]]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[[[],[]],[[],[]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[],[]],[[],[]]]],[]]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[[[],[]],[[],[]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[],[]],[[],[]]]],[]]] [1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[[],[[[[],[]],[[],[]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[],[]],[[],[]]]],[]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[[[],[]],[[[],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[]]],[[],[]]]],[]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[[],[[[[],[]],[[[],[]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[],[]]],[[],[]]]],[]]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[],[[[[],[[],[]]],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[[[],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[],[[[[],[[],[]]],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[[[],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[[],[[[[],[[],[]]],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[[[],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[[],[[],[]]],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[],[[[[],[[],[]]],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[[[],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[],[[[[],[[],[[],[]]]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[[[],[]],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[[],[[[[],[[],[[],[]]]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[[[],[]],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[[],[[[[],[[],[[],[]]]],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[[[[],[]],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[],[[[[],[[],[[[],[]],[]]]],[]],[]]],[]]=>[[],[[[],[[],[[[[],[[],[]]],[]],[]]]],[]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[],[[[[],[[[],[]],[]]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[[],[[],[]]],[]]]],[]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[[],[[[[],[[[],[]],[]]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[[],[[],[]]],[]]]],[]]] [1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[],[[[[],[[[],[[],[]]],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[[[],[]],[]]],[]]]],[]]] [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[[[[[],[]],[]],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[[],[[],[]]]]],[]]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[[[[[],[]],[]],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[[],[[],[]]]]],[]]] [1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[[],[[[[[],[]],[]],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[[],[[],[]]]]],[]]] [1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[[],[[[[[],[[],[[],[]]]],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[[[[],[]],[]],[]]]]],[]]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[],[]],[[],[[],[]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[],[]],[]],[[],[]]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]],[[],[[[],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[]]],[]],[[],[]]]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[],[]],[[[],[]],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[[],[]]],[[],[]]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[[],[]],[[[],[[],[]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[],[]],[]]],[[],[]]]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[[],[]],[[[],[[],[]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[],[]],[]]],[[],[]]]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[[],[]],[[[],[[[],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[]]],[]]],[[],[]]]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[[],[]],[[[[],[]],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[[],[]]]],[[],[]]]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[[[],[]],[[[[],[]],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[[],[]]]],[[],[]]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[[],[[],[]]],[]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[],[[[],[]],[]]]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[[],[[],[]]],[]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[],[[[],[]],[]]]] [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[[],[[],[]]],[]],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[[],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[],[[],[]]],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[[],[[],[]]],[[],[]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[],[[],[]]],[[],[]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[[],[[],[]]],[[],[]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[],[[],[]]],[[],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[[],[[],[]]],[[],[[],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[]],[]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[[],[[],[]]],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[[],[[],[]]],[[[],[]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[],[]]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[],[[],[]]],[[[],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[]]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[[],[[],[]]],[[[],[]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[],[]]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[[],[]]],[[[],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[],[[],[]]],[[[],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[]]],[[[],[]],[]]]] [1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[[],[[],[]]],[[[[],[[],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[]],[]]]],[[[],[]],[]]]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[],[[],[[],[]]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[],[[],[[],[]]]],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[],[[],[[],[]]]],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[],[[],[[],[]]]],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[],[[],[[],[]]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[],[[],[[],[]]]],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[[],[[],[[],[]]]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[[],[[],[[],[]]]],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[],[[],[[],[]]]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[],[[],[[],[]]]],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[],[[],[[],[]]]],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[[[[],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[],[[],[[],[[],[]]]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[[[],[]],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[[],[[],[[],[[],[]]]]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[[[[],[]],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[[],[[],[[],[[],[]]]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[[[],[]],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[[],[[],[[],[[],[]]]]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[[[[],[]],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[[],[[],[[],[[],[]]]]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[[[[],[]],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[[],[[],[[],[[[],[]],[]]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[[],[[],[]]],[]],[]],[]]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[[],[[],[[],[[[],[]],[]]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[[],[[],[]]],[]],[]],[]]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[[],[[[],[]],[]]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[[],[[],[]]],[]],[]]]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[[],[[],[[[],[]],[]]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[[],[[],[]]],[]],[]]]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[[],[[],[[[],[[],[]]],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[[[],[]],[]]],[]],[]]]] [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[[],[[],[[[],[[],[]]],[]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[],[[[],[]],[]]],[]],[]]]] [1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[[],[[],[[[],[[],[]]],[[],[]]]]],[]],[]]=>[[],[[],[[[[[],[]],[[[],[]],[]]],[]],[]]]] [1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[[],[[],[[[],[[[],[]],[]]],[]]]],[]],[]]=>[[],[[],[[[[],[[[],[[],[]]],[]]],[]],[]]]] [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[[],[[],[[[[],[[],[]]],[]],[]]]],[]],[]]=>[[],[[],[[[[],[[],[[[],[]],[]]]],[]],[]]]] [1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[[],[[[],[]],[]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[],[[],[]]],[]]]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[[],[[[],[]],[]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[],[[],[]]],[]]]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[[],[[[],[]],[]]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[[],[[],[]]],[]]]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[[],[[[],[]],[]]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[[],[[],[]]],[]]]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[],[[[],[[],[]]],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[[[],[]],[]]],[]]]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[],[[[],[[],[]]],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[[],[[[],[[],[]]],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[[[],[]],[]]],[]]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[[],[[[],[[],[[],[]]]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[[[],[]],[]],[]]],[]]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[[],[[[],[[],[[],[]]]],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[[[[],[]],[]],[]]],[]]]] [1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[[],[[[],[[],[[],[]]]],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[[[[],[]],[]],[]]],[]]]] [1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[],[[[],[[],[[[],[]],[]]]],[]]],[]],[]]=>[[],[[],[[[],[[[[],[[],[]]],[]],[]]],[]]]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[[],[[[],[[[],[]],[]]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[[],[[],[]]],[]]],[]]]] [1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[],[[[],[[[],[[],[]]],[]]],[]]],[]],[]]=>[[],[[],[[[],[[[],[[[],[]],[]]],[]]],[]]]] [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[[],[[[[],[]],[]],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[[],[[],[]]]],[]]]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[[],[[[[],[]],[]],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[[],[[],[]]]],[]]]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[[],[[[[],[]],[]],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[[],[[],[]]]],[]]]] [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[[],[[[[],[[],[[],[]]]],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[[[[],[]],[]],[]]]],[]]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[[],[]],[]],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[[],[[],[]]]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[[],[]],[]],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[[],[[],[]]]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[[],[]],[[],[]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[],[]],[[],[]]]]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[[],[]],[[],[]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[],[]],[[],[]]]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[[[],[]],[[[],[]],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[[],[]]],[[],[]]]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[[],[[],[]]],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[[[],[]],[]]]]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[[],[[],[]]],[]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[],[[[],[]],[]]]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[[],[[],[]]],[[],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[]],[[[],[]],[]]]]] [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[[],[[],[[],[]]]],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[[[[],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[[],[[],[[],[]]]],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[[[[],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[[],[[],[[],[]]]],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[[[[],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[[],[[],[[],[]]]],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[[[[],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[[],[[],[[],[]]]],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[[[[],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[[],[[],[[],[]]]],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[[[[],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[[],[[],[[],[[],[]]]]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[[[[],[]],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[[],[[],[[],[[],[]]]]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[[[[],[]],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[[],[[],[[],[[],[]]]]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[[[[],[]],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[[],[[],[[],[[[],[]],[]]]]],[]],[]],[]]=>[[],[[],[[],[[[[[],[[],[]]],[]],[]],[]]]]] [1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[[],[[],[[[],[[],[]]],[]]]],[]],[]],[]]=>[[],[[],[[],[[[[],[[[],[]],[]]],[]],[]]]]] [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[],[[[],[]],[]]],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[[[],[[],[]]],[]]]]] [1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[],[[[],[[],[[],[]]]],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[[[[],[]],[]],[]]],[]]]]] [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[],[]],[]],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[[],[[],[]]]]]] [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[[],[[],[[],[[],[]]]]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[[[[],[]],[]],[]],[]]]]]]
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.
Map
to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.