Identifier
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ 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]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[[],[[],[[],[[],[[],[[],[]]]]]]]=>[[[[[[[],[]],[]],[]],[]],[]],[]] [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[],[]],[]],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[[],[[],[]]]]]] [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[[],[]],[]],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[[],[[],[]]]]] [1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[[],[]],[]],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[[],[[],[]]]]] [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[[],[]],[[],[]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[],[]],[[],[]]]]] [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[[],[]],[[],[]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[],[]],[[],[]]]]] [1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[[[],[]],[[[],[]],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[[],[]]],[[],[]]]]] [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[],[]],[[[],[]],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[[],[]]],[[],[]]]] [1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[[],[]],[[[[],[]],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[[],[]]]],[[],[]]]] [1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[[[],[]],[[[[],[]],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[[],[]]]],[[],[]]]] [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[[],[]]],[[],[]]],[[],[]]] [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[],[]],[[[],[]],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[[],[]]],[[],[]]] [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[],[]],[[[],[]],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[[],[]]],[[],[]]] [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[],[]],[[],[[],[]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[],[]],[]],[[],[]]]] [1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[[],[]],[[[],[[],[]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[],[]],[]]],[[],[]]]] [1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[],[]],[[[[],[[],[]]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[[],[]],[]]]],[[],[]]] [1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[[],[]],[[[],[[],[]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[],[]],[]]],[[],[]]]] [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[],[]],[[[[],[[],[]]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[[],[]],[]]]],[[],[]]] [1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[[],[]],[[[[],[[],[]]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[[],[]],[]]]],[[],[]]] [1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[],[]],[[[],[[],[]]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[[],[]],[]]],[[],[]]] [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[],[]],[[[],[[],[]]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[[],[]],[]]],[[],[]]] [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[],[]],[[[],[[],[]]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[[],[]],[]]],[[],[]]] [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]],[[],[[[],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[]]],[]],[[],[]]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[[],[]],[[[],[[[],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[]]],[]]],[[],[]]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[[],[]],[[[[[],[[],[[],[]]]],[]],[]],[]]]=>[[[],[[],[[],[[[[],[]],[]],[]]]]],[[],[]]] [1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[],[]],[[[[],[[],[[],[]]]],[]],[[],[]]]]=>[[[[],[]],[[],[[[[],[]],[]],[]]]],[[],[]]] [1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[[],[]],[[[[],[[],[[],[]]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[[],[]],[]],[]]]],[[],[]]] [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[],[]],[[[],[[],[[],[]]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[[],[]],[]],[]]],[[],[]]] [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[],[]],[[[],[[],[[],[]]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[[],[]],[]],[]]],[[],[]]] [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[[],[[],[]]],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[[[],[]],[]]]]] [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[[],[[],[]]],[]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[],[[[],[]],[]]]]] [1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[[],[[],[]]],[]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[],[[[],[]],[]]]] [1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[[],[[],[]]],[]],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[[],[[[],[]],[]]]] [1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[[],[[],[]]],[]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[],[[[],[]],[]]]] [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[[],[[],[]]],[[],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[]],[[[],[]],[]]]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[[],[[],[]]],[[],[]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[],[]],[[[],[]],[]]]] [1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[],[[],[]]],[[],[]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[],[]],[[[],[]],[]]]] [1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[[],[[],[]]],[[],[]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[],[]],[[[],[]],[]]]] [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[],[[],[]]],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[[[],[]],[]]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[[],[[],[]]],[[[],[]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[],[]]],[[[],[]],[]]]] [1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[[],[[],[]]],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[[[],[]],[]]]] [1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[],[[],[]]],[[[[],[]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[],[]]]],[[[],[]],[]]] [1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[],[[],[]]],[[[],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[]]],[[[],[]],[]]]] [1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[],[[],[]]],[[[[],[]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[],[]]]],[[[],[]],[]]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[[],[[],[]]],[[[],[]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[],[]]],[[[],[]],[]]]] [1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[],[[],[]]],[[[[],[]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[],[]]]],[[[],[]],[]]] [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]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[],[[],[]]],[[[],[]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[],[]]],[[[],[]],[]]] [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[],[[],[]]],[[[],[]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[],[]]],[[[],[]],[]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[[],[[],[]]],[[],[[],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[]],[]],[[[],[]],[]]]] [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[],[[],[]]],[[],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[]],[[[],[]],[]]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[[],[]]],[[[],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]] [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]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[],[[],[]]],[[[[],[[],[]]],[]],[[],[]]]]=>[[[[],[]],[[],[[[],[]],[]]]],[[[],[]],[]]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[],[[],[]]],[[[],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[]]],[[[],[]],[]]]] [1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[],[[],[]]],[[[[],[[],[]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]] [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]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[],[[],[]]],[[[],[[],[]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[],[]],[]]],[[[],[]],[]]] [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[],[[],[]]],[[],[[[],[]],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[[],[]]],[]],[[[],[]],[]]] [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[],[[],[]]],[[],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[]],[[[],[]],[]]] [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[],[[],[]]],[[],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[]],[[[],[]],[]]] [1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[],[[[],[]],[]]],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[[[],[[],[]]],[]]]]] [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[[],[[[],[]],[]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[],[[],[]]],[]]]] [1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[[],[[[],[]],[]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[],[[],[]]],[]]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[[],[[[],[]],[]]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[[],[[],[]]],[]]]] [1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[[],[[[],[]],[]]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[[],[[],[]]],[]]]] [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[[],[[[[],[]],[]],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[[],[[],[]]]],[]]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[[],[[[[],[]],[]],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[[],[[],[]]]],[]]]] [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[[[[],[]],[]],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[[],[[],[]]]],[]]] [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[[[[[],[]],[]],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[[],[[],[]]]]],[]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[[[[[],[]],[]],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[[],[[],[]]]]],[]]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[[],[[[[[],[]],[]],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[[],[[],[]]]]],[]]] [1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[[],[[[[],[]],[]],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[[],[[],[]]]],[]]]] [1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[[],[]],[[],[]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[],[]],[[],[]]],[]]] [1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[[[],[]],[[],[]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[],[]],[[],[]]]],[]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[[[],[]],[[],[]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[],[]],[[],[]]]],[]]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[[],[[[[],[]],[[],[]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[],[]],[[],[]]]],[]]] [1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[[],[]],[[[],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[]]],[[],[]]],[]]] [1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[[[],[]],[[[],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[]]],[[],[]]]],[]]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[[],[[[[],[]],[[[],[]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[],[]]],[[],[]]]],[]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[[],[[],[[],[]]]],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[[[[],[]],[]],[]]]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[[],[[],[[],[]]]],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[[[[],[]],[]],[]]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[[],[[],[[],[]]]],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[[[[],[]],[]],[]]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[],[[],[[],[]]]],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[],[[],[[],[]]]],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[],[[],[[],[]]]],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[],[[],[[],[]]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[[],[[],[[],[]]]],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[[[[],[]],[]],[]]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[[],[[],[[],[]]]],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[[[[],[]],[]],[]]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[],[[],[[],[]]]],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[],[[],[[],[]]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[[],[[],[[],[]]]],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[[[[],[]],[]],[]]]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[],[[],[[],[]]]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[],[[],[[],[]]]],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[],[[],[[],[]]]],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[],[[],[[],[]]]],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[],[[],[[],[]]]],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[],[[],[[],[]]]],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[],[[],[[],[]]]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[],[[],[[],[]]]],[[[],[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[],[]]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[[],[[],[[],[]]]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[],[[],[[],[]]]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[[],[[],[[],[]]]],[[],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[]],[[[[],[]],[]],[]]]] [1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[],[[],[[],[]]]],[[[],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[]]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[],[[],[[],[]]]],[[],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[],[[],[[],[]]]],[[],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[]],[[[[],[]],[]],[]]] [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[],[[],[[],[]]]],[[],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[]],[[[[],[]],[]],[]]] [1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[],[[[],[[],[]]],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[[[],[]],[]]],[]]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[],[[[],[[],[]]],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]] [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[],[[[],[[],[]]],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[[[],[]],[]]],[]]] [1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[],[[[[],[[],[]]],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[[[],[]],[]]]],[]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[],[[[[],[[],[]]],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[[[],[]],[]]]],[]]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[[],[[[[],[[],[]]],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[[[],[]],[]]]],[]]] [1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[[],[[[],[[],[]]],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[[[],[]],[]]],[]]]] [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[],[[[],[[],[]]],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[[[],[]],[]]],[]]] [1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[[],[[],[]]],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[],[[[[],[[],[]]],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[[[],[]],[]]]],[]]] [1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[[],[[[],[]],[]]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[[],[[],[]]],[]],[]]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[[],[[],[[[],[]],[]]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[[],[[],[]]],[]],[]]]] [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[],[[],[[[],[]],[]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[],[[],[]]],[]],[]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[[],[[[],[[[],[]],[]]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[[],[[],[]]],[]]],[]]]] [1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[],[[[],[[[],[]],[]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[],[[],[]]],[]]],[]]] [1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[],[[[[],[[[],[]],[]]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[[],[[],[]]],[]]]],[]]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[[],[[[[],[[[],[]],[]]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[[],[[],[]]],[]]]],[]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[],[[[],[[[],[]],[]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[],[[],[]]],[]]],[]]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[[[],[[[],[[[],[]],[]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[],[[],[]]],[]]],[]]] [1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[],[[],[[[[],[]],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[[],[]]]],[]],[]]] [1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[],[[[],[[[[],[]],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[[],[]]]],[]]],[]]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[[[],[[[],[[[[],[]],[]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[],[[],[]]]],[]]],[]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[],[[],[[[[],[]],[]],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[[],[[],[]]]],[]],[]]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[[],[[[],[[[[],[]],[]],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[[],[[],[]]]],[]]],[]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[[],[[],[[],[[],[]]]]],[]],[]],[]],[]]=>[[],[[],[[],[[],[[[[[],[]],[]],[]],[]]]]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[[],[[],[[],[[],[]]]]],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[[[[[],[]],[]],[]],[]]]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[[],[[],[[],[[],[]]]]],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[[[[[],[]],[]],[]],[]]]]] [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]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[],[[],[[],[[],[]]]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[[[],[]],[]],[]],[]]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[[],[[],[[],[[],[]]]]],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[[[[[],[]],[]],[]],[]]]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[[],[[],[[],[[],[]]]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[[[],[]],[]],[]],[]]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[[],[[],[[],[[],[]]]]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[[[[],[]],[]],[]],[]]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[],[[],[[],[[],[]]]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[[[],[]],[]],[]],[]]] [1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[],[[],[[],[[],[]]]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[[[],[]],[]],[]],[]]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[[],[[],[[],[[],[]]]]],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[[[[[],[]],[]],[]],[]]]] [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]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[],[[],[[],[[],[]]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[[],[]],[]],[]],[]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[],[[[],[[],[[],[]]]],[]]],[]],[]],[]]=>[[],[[],[[],[[[],[[[[],[]],[]],[]]],[]]]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[[],[[[],[[],[[],[]]]],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[[[[],[]],[]],[]]],[]]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[[],[[[],[[],[[],[]]]],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[[[[],[]],[]],[]]],[]]]] [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]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[],[[[],[[],[[],[]]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[[],[]],[]],[]]],[]]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[[],[[[[],[[],[[],[]]]],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[[[[],[]],[]],[]]]],[]]]] [1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[],[[[[],[[],[[],[]]]],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[[[[],[]],[]],[]]]],[]]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[[],[[[[[],[[],[[],[]]]],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[[[[],[]],[]],[]]]]],[]]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[[],[[[[],[[],[[],[]]]],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[[[[],[]],[]],[]]]],[]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[[],[[[],[[],[[],[]]]],[[],[]]]],[]],[]]=>[[],[[],[[[[],[]],[[[[],[]],[]],[]]],[]]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[],[[[],[[],[[],[]]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[[],[]],[]],[]]],[]]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[[],[[[[],[[],[[],[]]]],[[],[]]],[]]],[]]=>[[],[[[],[[[],[]],[[[[],[]],[]],[]]]],[]]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[[],[[[],[[],[[],[]]]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[[[],[]],[]],[]]],[]]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[[],[[[],[[],[[],[]]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[[],[]],[]],[]]],[]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[[],[[],[[[],[[],[]]],[]]]],[]],[]],[]]=>[[],[[],[[],[[[[],[[[],[]],[]]],[]],[]]]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[[],[[],[[[],[[],[]]],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[[[],[]],[]]],[]],[]]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[[],[[],[[[],[[],[]]],[]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[],[[[],[]],[]]],[]],[]]]] [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]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[],[[],[[[],[[],[]]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[[],[]],[]]],[]],[]]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[],[[[],[[[],[[],[]]],[]]],[]]],[]],[]]=>[[],[[],[[[],[[[],[[[],[]],[]]],[]]],[]]]] [1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[],[[[],[[[],[[],[]]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[],[[[[],[[[],[[],[]]],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[[[],[]],[]]],[]]]],[]]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[],[[[],[[[],[[],[]]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[[],[]],[]]],[]]],[]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[[],[[],[[[[],[[],[]]],[]],[]]]],[]],[]]=>[[],[[],[[[[],[[],[[[],[]],[]]]],[]],[]]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[],[[],[[[[],[[],[]]],[]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[],[[[],[]],[]]]],[]],[]]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[],[[[],[[[[],[[],[]]],[]],[]]],[]]],[]]=>[[],[[[],[[[],[[],[[[],[]],[]]]],[]]],[]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[[],[[],[[[],[[],[]]],[[],[]]]]],[]],[]]=>[[],[[],[[[[[],[]],[[[],[]],[]]],[]],[]]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[],[[],[[[],[[],[]]],[[],[]]]]],[[],[]]]=>[[[],[]],[[[[[],[]],[[[],[]],[]]],[]],[]]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[[],[[[],[[[],[[],[]]],[[],[]]]],[]]],[]]=>[[],[[[],[[[[],[]],[[[],[]],[]]],[]]],[]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[[],[[],[[],[[[],[]],[]]]]],[]],[]],[]]=>[[],[[],[[],[[[[[],[[],[]]],[]],[]],[]]]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[[],[[],[[],[[[],[]],[]]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[[],[[],[]]],[]],[]],[]]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[[],[[],[[],[[[],[]],[]]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[[],[[],[]]],[]],[]],[]]]] [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]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[],[[],[[],[[[],[]],[]]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[[],[[],[]]],[]],[]],[]]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[],[[[],[[],[[[],[]],[]]]],[]]],[]],[]]=>[[],[[],[[[],[[[[],[[],[]]],[]],[]]],[]]]] [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[],[[[],[[],[[[],[]],[]]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[[],[[],[]]],[]],[]]],[]]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[],[[[[],[[],[[[],[]],[]]]],[]],[]]],[]]=>[[],[[[],[[],[[[[],[[],[]]],[]],[]]]],[]]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[[],[[[],[[],[[[],[]],[]]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[[],[[],[]]],[]],[]]],[]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[[],[[],[[[],[[[],[]],[]]],[]]]],[]],[]]=>[[],[[],[[[[],[[[],[[],[]]],[]]],[]],[]]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[],[[],[[[],[[[],[]],[]]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[[],[[],[]]],[]]],[]],[]]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]=>[[],[[[],[[[],[[[],[[],[]]],[]]],[]]],[]]]
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.
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.