Identifier
Mp00015:
Binary trees
—to ordered tree: right child = right brother⟶
Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0021;cc-rep-1Cc0021;cc-rep-2Cc0005;cc-rep-3
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[[[.,.],[.,[.,.]]],[.,.]]=>[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,.]]=>[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,.]]=>[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,.]],[.,.]]=>[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,.]]=>[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],.],[.,.]]=>[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],.],[.,.]]=>[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,.]]=>[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,.]]=>[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],.]=>[[[],[],[],[],[]]]=>[[[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],.]]]],.]=>[[[],[],[],[[]]]]=>[[[[]],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[[.,.],[.,.]]]],.]=>[[[],[],[[]],[]]]=>[[[],[[]],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,.]],.]]],.]=>[[[],[],[[],[]]]]=>[[[[],[]],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],.],.]]],.]=>[[[],[],[[[]]]]]=>[[[[[]]],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0]
[[.,[[.,.],[.,[.,.]]]],.]=>[[[],[[]],[],[]]]=>[[[],[],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],.]=>[[[],[[]],[[]]]]=>[[[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],.]=>[[[],[[],[]],[]]]=>[[[],[[],[]],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],[.,.]]],.]=>[[[],[[[]]],[]]]=>[[[],[[[]]],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],.]=>[[[],[[],[],[]]]]=>[[[[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],.]=>[[[],[[],[[]]]]]=>[[[[[]],[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],.]=>[[[],[[[]],[]]]]=>[[[[],[[]]],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],.]=>[[[],[[[],[]]]]]=>[[[[[],[]]],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],.],.]],.]=>[[[],[[[[]]]]]]=>[[[[[[]]]],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],.]=>[[[[]],[],[],[]]]=>[[[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],.]=>[[[[]],[],[[]]]]=>[[[[]],[],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],.]=>[[[[]],[[]],[]]]=>[[[],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],.]=>[[[[]],[[],[]]]]=>[[[[],[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],.]=>[[[[]],[[[]]]]]=>[[[[[]]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],.]=>[[[[],[]],[],[]]]=>[[[],[],[[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],.]=>[[[[],[]],[[]]]]=>[[[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],.]=>[[[[[]]],[],[]]]=>[[[],[],[[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],.]=>[[[[[]]],[[]]]]=>[[[[]],[[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],.]=>[[[[],[],[]],[]]]=>[[[],[[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],.]=>[[[[],[[]]],[]]]=>[[[],[[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],.]=>[[[[[]],[]],[]]]=>[[[],[[],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],.]=>[[[[[],[]]],[]]]=>[[[],[[[],[]]]]]=>[1,1,0,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],.]=>[[[[[[]]]],[]]]=>[[[],[[[[]]]]]]=>[1,1,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],.]=>[[[[],[],[],[]]]]=>[[[[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],.]=>[[[[],[],[[]]]]]=>[[[[[]],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],.]=>[[[[],[[]],[]]]]=>[[[[],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],.]=>[[[[],[[],[]]]]]=>[[[[[],[]],[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],.],.]=>[[[[],[[[]]]]]]=>[[[[[[]]],[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],.]=>[[[[[]],[],[]]]]=>[[[[],[],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],.]=>[[[[[]],[[]]]]]=>[[[[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],.]=>[[[[[],[]],[]]]]=>[[[[],[[],[]]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],.]=>[[[[[[]]],[]]]]=>[[[[],[[[]]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],.]=>[[[[[],[],[]]]]]=>[[[[[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],.]=>[[[[[],[[]]]]]]=>[[[[[[]],[]]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],.]=>[[[[[[]],[]]]]]=>[[[[[],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],.]=>[[[[[[],[]]]]]]=>[[[[[[],[]]]]]]=>[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]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[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]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],.],.],.],.]]=>[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[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]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[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]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[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]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,.]]=>[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],.]=>[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[[.,.],.],.],.]],.]=>[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],.]],.]=>[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],.]],.]=>[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],[.,.]],.]=>[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],.]=>[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],.]],.],.]=>[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],.],.]=>[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],.],.]=>[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],.]=>[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],.],.]=>[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],.],.],.]=>[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],.]=>[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],.],.]=>[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],.],.]=>[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],.],.],.],.]=>[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[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]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[],[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[],[]]=>[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]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[],[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[],[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[],[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[],[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[],[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[],[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[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]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[],[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]]=>[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]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[[],[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[[],[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[[],[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[[],[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[[],[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[[],[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[[],[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[[],[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[[],[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[[],[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[],[]]=>[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]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[[],[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[[],[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[[],[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[],[]]=>[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]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[],[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[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]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[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]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[],[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[[],[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]],[]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[[],[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]],[]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[],[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[[],[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[],[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[],[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[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]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[],[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[[],[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]],[]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[[],[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]],[]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[[],[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[[],[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[],[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]],[]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[[],[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[[],[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]],[]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[[],[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[[],[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[[],[[],[[[[]]]]],[]]=>[[],[[[[[]]]],[]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[],[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]],[]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[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]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[[],[[[],[],[],[]]],[]]=>[[],[[[],[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[],[[[],[[]],[]]],[]]=>[[],[[[],[[]],[]]],[]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[[],[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]],[]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[[],[[[[]],[],[]]],[]]=>[[],[[[],[],[[]]]],[]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[[],[[[[],[]],[]]],[]]=>[[],[[[],[[],[]]]],[]]=>[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]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[[],[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[[],[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]],[]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[[],[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]],[]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[[],[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]],[]]=>[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]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[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]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[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]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[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]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[]],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[]],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[[]],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[[]],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[[]]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[[]],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[]],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[[[]],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[[[]],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[[]],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[[[]],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[]],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]]=>[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]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[]],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[[]],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[[]]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[[]],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[]],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[[]]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[],[]],[],[],[[]],[]]=>[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[],[]],[],[[],[]],[]]=>[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[],[]],[],[[[]]],[]]=>[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[],[]],[[]],[[]],[]]=>[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[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]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[]]],[],[],[[]],[]]=>[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[[]]],[],[[],[]],[]]=>[[],[[],[]],[],[[[]]]]=>[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]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[[]]],[[]],[[]],[]]=>[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[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]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[],[],[]],[],[[]],[]]=>[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[],[],[]],[[],[]],[]]=>[[],[[],[]],[[],[],[]]]=>[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]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[],[[]]],[],[[]],[]]=>[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[[]]],[[],[]],[]]=>[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[[]]],[[[]]],[]]=>[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[]],[]],[],[[]],[]]=>[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[[]],[]],[[],[]],[]]=>[[],[[],[]],[[],[[]]]]=>[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]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[[[]],[]],[[[]],[]]]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[[],[]]],[],[[]],[]]=>[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[[],[]]],[[],[]],[]]=>[[],[[],[]],[[[],[]]]]=>[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]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[[[[]]]],[],[[]],[]]=>[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[[[]]]],[[],[]],[]]=>[[],[[],[]],[[[[]]]]]=>[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]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[],[],[],[]],[[]],[]]=>[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[],[],[[]]],[[]],[]]=>[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[],[[]],[]],[[]],[]]=>[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[],[[],[]]],[[]],[]]=>[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[],[[[]]]],[[]],[]]=>[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[[]],[],[]],[[]],[]]=>[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[[]],[[]]],[[]],[]]=>[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[],[]],[]],[[]],[]]=>[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[],[],[]]],[[]],[]]=>[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[[],[[]]]],[[]],[]]=>[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[[[]],[]]],[[]],[]]=>[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[[[],[]]]],[[]],[]]=>[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[[[[]]]]],[[]],[]]=>[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[],[],[[[]]]],[],[]]=>[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[],[[],[],[]]],[],[]]=>[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[],[[],[[]]]],[],[]]=>[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[[]],[]]],[],[]]=>[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[],[[[],[]]]],[],[]]=>[[],[],[[[[],[]]],[]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[[[[]]]]],[],[]]=>[[],[],[[[[[]]]],[]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[[]],[[],[]]],[],[]]=>[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[[]],[[[]]]],[],[]]=>[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[],[],[],[]]],[],[]]=>[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[],[[]]]],[],[]]=>[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[[],[[]],[]]],[],[]]=>[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[],[[],[]]]],[],[]]=>[[],[],[[[[],[]],[]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[[],[[[]]]]],[],[]]=>[[],[],[[[[[]]],[]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[[[]],[],[]]],[],[]]=>[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[[[]],[[]]]],[],[]]=>[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[[],[]],[]]],[],[]]=>[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[[[[]]],[]]],[],[]]=>[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[[],[],[]]]],[],[]]=>[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[],[[]]]]],[],[]]=>[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[[[[]],[]]]],[],[]]=>[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[[[[],[]]]]],[],[]]=>[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[[[[[]]]]]],[],[]]=>[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[],[],[],[],[],[]],[]]=>[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[],[],[],[[]],[]],[]]=>[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[],[],[[]],[],[]],[]]=>[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[[],[[]],[],[],[]],[]]=>[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[],[[],[]],[],[]],[]]=>[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[[],[[[]]],[],[]],[]]=>[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[[[]],[],[],[],[]],[]]=>[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[[[]],[],[[]],[]],[]]=>[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[[[]],[[]],[],[]],[]]=>[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[[],[]],[],[],[]],[]]=>[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[[[[]]],[],[],[]],[]]=>[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[[],[],[]],[],[]],[]]=>[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[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]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[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]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[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]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[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]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[[],[],[],[],[[]],[]]]=>[[[],[[]],[],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[[[],[],[],[[],[]],[]]]=>[[[],[[],[]],[],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[[[],[],[],[[[]]],[]]]=>[[[],[[[]]],[],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
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[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
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[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
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[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[[[[]],[],[],[[]],[]]]=>[[[],[[]],[],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[[[[]],[],[[],[]],[]]]=>[[[],[[],[]],[],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[[[[]],[],[[[]]],[]]]=>[[[],[[[]]],[],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[[[[]],[[]],[[]],[]]]=>[[[],[[]],[[]],[[]]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[[[[]],[[],[],[]],[]]]=>[[[],[[],[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[[[[]],[[],[[]]],[]]]=>[[[],[[[]],[]],[[]]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[[[]],[[[]],[]],[]]]=>[[[],[[],[[]]],[[]]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[[[]],[[[],[]]],[]]]=>[[[],[[[],[]]],[[]]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[[[[]],[[[[]]]],[]]]=>[[[],[[[[]]]],[[]]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[[[]],[[[[]],[]]]]]=>[[[[[],[[]]]],[[]]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[[],[]],[],[[]],[]]]=>[[[],[[]],[],[[],[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[],[]],[[],[]],[]]]=>[[[],[[],[]],[[],[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[[[],[]],[[[]]],[]]]=>[[[],[[[]]],[[],[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[[[[[]]],[],[[]],[]]]=>[[[],[[]],[],[[[]]]]]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[[[[[]]],[[],[]],[]]]=>[[[],[[],[]],[[[]]]]]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[[[[[]]],[[[]]],[]]]=>[[[],[[[]]],[[[]]]]]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[],[],[]],[[]],[]]]=>[[[],[[]],[[],[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[[],[[]]],[[]],[]]]=>[[[],[[]],[[[]],[]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[[[[[]],[]],[[]],[]]]=>[[[],[[]],[[],[[]]]]]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[[[[[],[]]],[[]],[]]]=>[[[],[[]],[[[],[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[[[[[[]]]],[[]],[]]]=>[[[],[[]],[[[[]]]]]]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[[[[],[],[[]]],[],[]]]=>[[[],[],[[[]],[],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[[],[[],[]]],[],[]]]=>[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[[],[[[]]]],[],[]]]=>[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[[[[]],[[]]],[],[]]]=>[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[[[[[]]],[]],[],[]]]=>[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[[],[],[]]],[],[]]]=>[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[[[],[[]]]],[],[]]]=>[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[[[]],[]]],[],[]]]=>[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[[[],[]]]],[],[]]]=>[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[[[]]]]],[],[]]]=>[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[[],[],[],[],[]],[]]]=>[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[[],[],[],[[]]],[]]]=>[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[[[[],[],[[]],[]],[]]]=>[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[[],[],[[],[]]],[]]]=>[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[[[[],[],[[[]]]],[]]]=>[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[[[],[[]],[],[]],[]]]=>[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[[[[],[[]],[[]]],[]]]=>[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[[],[[],[]],[]],[]]]=>[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[[[],[[[]]],[]],[]]]=>[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[[],[[],[],[]]],[]]]=>[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[[[],[[],[[]]]],[]]]=>[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[[[],[[[]],[]]],[]]]=>[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[[[[],[[[],[]]]],[]]]=>[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[[[[],[[[[]]]]],[]]]=>[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[[[[]],[],[],[]],[]]]=>[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[[[[]],[],[[]]],[]]]=>[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[[[[]],[[]],[]],[]]]=>[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[[[[]],[[],[]]],[]]]=>[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[[[[]],[[[]]]],[]]]=>[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[[[],[]],[],[]],[]]]=>[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[[[],[]],[[]]],[]]]=>[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[[[[[]]],[],[]],[]]]=>[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[[[[[]]],[[]]],[]]]=>[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[[],[],[]],[]],[]]]=>[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[[],[[]]],[]],[]]]=>[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[[[]],[]],[]],[]]]=>[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[[[[],[]]],[]],[]]]=>[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[[[]]]],[]],[]]]=>[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[[],[],[],[]]],[]]]=>[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[[[[[],[],[[]]]],[]]]=>[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[[[],[[]],[]]],[]]]=>[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[[],[[],[]]]],[]]]=>[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[[[],[[[]]]]],[]]]=>[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[[[]],[],[]]],[]]]=>[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[[[[[]],[[]]]],[]]]=>[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]]]]]=>[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]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[[[],[],[]]]],[]]]=>[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[[[],[[]]]]],[]]]=>[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[[]],[]]]],[]]]=>[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[[[[[],[]]]]],[]]]=>[[[],[[[[[],[]]]]]]]=>[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]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[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]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[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]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[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 ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
- if $x$ is the left child of $y$, $x$ becomes the first child of $y$.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path is the depth of the tree.
This sends the maximal height of the Dyck path is the depth of the tree.
searching the database
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