Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00010: Binary trees —to ordered tree: left child = left 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
[1,0]=>[.,.]=>[[]]=>[[]]
[1,0,1,0]=>[.,[.,.]]=>[[[]]]=>[[[]]]
[1,1,0,0]=>[[.,.],.]=>[[],[]]=>[[],[]]
[1,0,1,0,1,0]=>[.,[.,[.,.]]]=>[[[[]]]]=>[[[[]]]]
[1,0,1,1,0,0]=>[.,[[.,.],.]]=>[[[],[]]]=>[[[],[]]]
[1,1,0,0,1,0]=>[[.,.],[.,.]]=>[[],[[]]]=>[[[]],[]]
[1,1,0,1,0,0]=>[[.,[.,.]],.]=>[[[]],[]]=>[[],[[]]]
[1,1,1,0,0,0]=>[[[.,.],.],.]=>[[],[],[]]=>[[],[],[]]
[1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,.]]]]=>[[[[[]]]]]=>[[[[[]]]]]
[1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],.]]]=>[[[[],[]]]]=>[[[[],[]]]]
[1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,.]]]=>[[[],[[]]]]=>[[[[]],[]]]
[1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],.]]=>[[[[]],[]]]=>[[[],[[]]]]
[1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],.]]=>[[[],[],[]]]=>[[[],[],[]]]
[1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,.]]]=>[[],[[[]]]]=>[[[[]]],[]]
[1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],.]]=>[[],[[],[]]]=>[[[],[]],[]]
[1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,.]]=>[[[]],[[]]]=>[[[]],[[]]]
[1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],.]=>[[[[]]],[]]=>[[],[[[]]]]
[1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],.]=>[[[],[]],[]]=>[[],[[],[]]]
[1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,.]]=>[[],[],[[]]]=>[[[]],[],[]]
[1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],.]=>[[],[[]],[]]=>[[],[[]],[]]
[1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],.]=>[[[]],[],[]]=>[[],[],[[]]]
[1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],.]=>[[],[],[],[]]=>[[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,.]]]]]=>[[[[[[]]]]]]=>[[[[[[]]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],.]]]]=>[[[[[],[]]]]]=>[[[[[],[]]]]]
[1,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,.]]]]=>[[[[],[[]]]]]=>[[[[[]],[]]]]
[1,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],.]]]=>[[[[[]],[]]]]=>[[[[],[[]]]]]
[1,0,1,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],.]]]=>[[[[],[],[]]]]=>[[[[],[],[]]]]
[1,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[.,.]]]]=>[[[],[[[]]]]]=>[[[[[]]],[]]]
[1,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],.]]]=>[[[],[[],[]]]]=>[[[[],[]],[]]]
[1,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[.,.]]]=>[[[[]],[[]]]]=>[[[[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],.]]=>[[[[[]]],[]]]=>[[[],[[[]]]]]
[1,0,1,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],.]],.]]=>[[[[],[]],[]]]=>[[[],[[],[]]]]
[1,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[.,.]]]=>[[[],[],[[]]]]=>[[[[]],[],[]]]
[1,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,.]],.]]=>[[[],[[]],[]]]=>[[[],[[]],[]]]
[1,0,1,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],.],.]]=>[[[[]],[],[]]]=>[[[],[],[[]]]]
[1,0,1,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],.]]=>[[[],[],[],[]]]=>[[[],[],[],[]]]
[1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,.]]]]=>[[],[[[[]]]]]=>[[[[[]]]],[]]
[1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],.]]]=>[[],[[[],[]]]]=>[[[[],[]]],[]]
[1,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,.]]]=>[[],[[],[[]]]]=>[[[[]],[]],[]]
[1,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],.]]=>[[],[[[]],[]]]=>[[[],[[]]],[]]
[1,1,0,0,1,1,1,0,0,0]=>[[.,.],[[[.,.],.],.]]=>[[],[[],[],[]]]=>[[[],[],[]],[]]
[1,1,0,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[.,.]]]=>[[[]],[[[]]]]=>[[[[]]],[[]]]
[1,1,0,1,0,0,1,1,0,0]=>[[.,[.,.]],[[.,.],.]]=>[[[]],[[],[]]]=>[[[],[]],[[]]]
[1,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,.]]=>[[[[]]],[[]]]=>[[[]],[[[]]]]
[1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,.]]]],.]=>[[[[[]]]],[]]=>[[],[[[[]]]]]
[1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],.]=>[[[[],[]]],[]]=>[[],[[[],[]]]]
[1,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[.,.]]=>[[[],[]],[[]]]=>[[[]],[[],[]]]
[1,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,.]]],.]=>[[[],[[]]],[]]=>[[],[[[]],[]]]
[1,1,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],.]],.]=>[[[[]],[]],[]]=>[[],[[],[[]]]]
[1,1,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],.]=>[[[],[],[]],[]]=>[[],[[],[],[]]]
[1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[.,[.,.]]]=>[[],[],[[[]]]]=>[[[[]]],[],[]]
[1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],.]]=>[[],[],[[],[]]]=>[[[],[]],[],[]]
[1,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,.]],[.,.]]=>[[],[[]],[[]]]=>[[[]],[[]],[]]
[1,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],.]=>[[],[[[]]],[]]=>[[],[[[]]],[]]
[1,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],.]],.]=>[[],[[],[]],[]]=>[[],[[],[]],[]]
[1,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],.],[.,.]]=>[[[]],[],[[]]]=>[[[]],[],[[]]]
[1,1,1,0,1,0,0,1,0,0]=>[[[.,[.,.]],[.,.]],.]=>[[[]],[[]],[]]=>[[],[[]],[[]]]
[1,1,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],.]=>[[[[]]],[],[]]=>[[],[],[[[]]]]
[1,1,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],.]=>[[[],[]],[],[]]=>[[],[],[[],[]]]
[1,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],.],[.,.]]=>[[],[],[],[[]]]=>[[[]],[],[],[]]
[1,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[.,.]],.]=>[[],[],[[]],[]]=>[[],[[]],[],[]]
[1,1,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,.]],.],.]=>[[],[[]],[],[]]=>[[],[],[[]],[]]
[1,1,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],.],.],.]=>[[[]],[],[],[]]=>[[],[],[],[[]]]
[1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],.]=>[[],[],[],[],[]]=>[[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[[]]]]]]]=>[[[[[[[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]]=>[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],.]]]]=>[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,[[.,.],.]],.]]]=>[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],.],[.,.]]]]=>[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[.,.]],.]]]=>[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[[[.,[.,.]],.],.]]]=>[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]]=>[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],.]]]]=>[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[.,.]]]]=>[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,[.,.]],.]]]=>[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]]=>[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,.],.]]]=>[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],.]]],.]]=>[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],.]],[.,.]]]=>[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[.,.]]],.]]=>[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,[.,.]],.]],.]]=>[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,[[[.,.],.],.]],.]]=>[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,.]]]]=>[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],.]]]=>[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[.,.]]]=>[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[.,[.,.]]],.]]=>[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],.]],.]]=>[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,.]],.],[.,.]]]=>[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[.,.]],.]]=>[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,.]]],.],.]]=>[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],.]],.],.]]=>[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]
[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]=>[[[[[[.,.],.],.],.],.],.]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]
[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]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]
[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]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]
[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]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[[[[[[[]]]]]],[]]]=>[[[],[[[[[[]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[[[[[[[]]],[]]],[]]]=>[[[],[[[],[[[]]]]]]]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]
[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]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[[[],[[[[],[]]]],[]]]=>[[[],[[[[],[]]]],[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[[[],[[[],[[]]]],[]]]=>[[[],[[[[]],[]]],[]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[[[],[[[[]],[]]],[]]]=>[[[],[[[],[[]]]],[]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[[[],[[[],[],[]]],[]]]=>[[[],[[[],[],[]]],[]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]
[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]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[[[],[[],[[[]]]],[]]]=>[[[],[[[[]]],[]],[]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[[[],[[],[[],[]]],[]]]=>[[[],[[[],[]],[]],[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[[[],[[[]],[[]]],[]]]=>[[[],[[[]],[[]]],[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[[[],[[[[]]],[]],[]]]=>[[[],[[],[[[]]]],[]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[[[],[[[],[]],[]],[]]]=>[[[],[[],[[],[]]],[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[[[],[[],[],[[]]],[]]]=>[[[],[[[]],[],[]],[]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[[[],[[],[[]],[]],[]]]=>[[[],[[],[[]],[]],[]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[[[],[[[]],[],[]],[]]]=>[[[],[[],[],[[]]],[]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[[[],[[],[],[],[]],[]]]=>[[[],[[],[],[],[]],[]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]
[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]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]
[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]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]
[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]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[[[],[],[[[[]]]],[]]]=>[[[],[[[[]]]],[],[]]]
[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]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[[[],[],[[],[[]]],[]]]=>[[[],[[[]],[]],[],[]]]
[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]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[[[],[[]],[[[]]],[]]]=>[[[],[[[]]],[[]],[]]]
[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]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[[[],[[[]]],[[]],[]]]=>[[[],[[]],[[[]]],[]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[[[],[[],[]],[[]],[]]]=>[[[],[[]],[[],[]],[]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]
[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]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[[[],[],[[]],[[]],[]]]=>[[[],[[]],[[]],[],[]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[[[],[[]],[],[[]],[]]]=>[[[],[[]],[],[[]],[]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]
[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]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]
[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]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]
[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]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]
[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]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]
[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]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]
[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]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]
[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]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]
[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]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]
[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]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]
[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]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]
[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]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]
[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]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]
[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]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]
[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]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]
[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]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]
[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]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]
[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]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]
[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]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]
[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]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]
[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]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]
[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]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]
[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]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]
[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]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]
[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]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]
[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]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]
[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]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[[],[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]
[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]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]
[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]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]
[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]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]
[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]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]
[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]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]
[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]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]
[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]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]
[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]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[[[[],[]]],[[[]]],[]]=>[[],[[[]]],[[[],[]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]
[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]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[[]],[]],[[[]]],[]]=>[[],[[[]]],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]
[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]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[],[],[]],[[[]]],[]]=>[[],[[[]]],[[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]
[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]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]
[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]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[[],[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[],[]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]
[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]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]
[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]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]
[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]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]
[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]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]
[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]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]
[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]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]]
[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]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]
[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]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[],[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]
[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: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
- if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
searching the database
Sorry, this map was not found in the database.