Identifier
Mp00010:
Binary trees
—to ordered tree: left child = left 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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[[[.,.],[.,[.,.]]],[.,.]]=>[[],[[[]]],[[]]]=>[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[[.,.],.]],[.,.]]=>[[],[[],[]],[[]]]=>[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]]]=>[[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],[.,.]]=>[[],[],[[]],[[]]]=>[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],.],[.,.]]=>[[[[]]],[],[[]]]=>[[[]],[],[[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,.]]=>[[[],[]],[],[[]]]=>[[[]],[],[[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,.]]=>[[],[[]],[],[[]]]=>[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],.],[.,.]]=>[[[]],[],[],[[]]]=>[[[]],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],.],.],.],[.,.]]=>[[],[],[],[],[[]]]=>[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,.]]]]],.]=>[[[[[[]]]]],[]]=>[[],[[[[[]]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[[.,.],.]]]],.]=>[[[[[],[]]]],[]]=>[[],[[[[],[]]]]]=>[1,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,[[.,.],[.,.]]]],.]=>[[[[],[[]]]],[]]=>[[],[[[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,[[.,[.,.]],.]]],.]=>[[[[[]],[]]],[]]=>[[],[[[],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],.],.]]],.]=>[[[[],[],[]]],[]]=>[[],[[[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]
[[.,[[.,.],[.,[.,.]]]],.]=>[[[],[[[]]]],[]]=>[[],[[[[]]],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],.]=>[[[],[[],[]]],[]]=>[[],[[[],[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],.]=>[[[[]],[[]]],[]]=>[[],[[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,0]
[[.,[[[.,.],.],[.,.]]],.]=>[[[],[],[[]]],[]]=>[[],[[[]],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],.]=>[[[[[]]],[]],[]]=>[[],[[],[[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,0,0]
[[.,[[.,[[.,.],.]],.]],.]=>[[[[],[]],[]],[]]=>[[],[[],[[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,0]
[[.,[[[.,.],[.,.]],.]],.]=>[[[],[[]],[]],[]]=>[[],[[],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],.]=>[[[[]],[],[]],[]]=>[[],[[],[],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,0]
[[.,[[[[.,.],.],.],.]],.]=>[[[],[],[],[]],[]]=>[[],[[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],.]=>[[],[[[[]]]],[]]=>[[],[[[[]]]],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],.]]],.]=>[[],[[[],[]]],[]]=>[[],[[[],[]]],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[.,.]]],.]=>[[],[[],[[]]],[]]=>[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],.]=>[[],[[[]],[]],[]]=>[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],.]],.]=>[[],[[],[],[]],[]]=>[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],.]=>[[[]],[[[]]],[]]=>[[],[[[]]],[[]]]=>[1,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],.]],.]=>[[[]],[[],[]],[]]=>[[],[[],[]],[[]]]=>[1,0,1,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,.]]],.]=>[[],[],[[[]]],[]]=>[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,.],.],[[.,.],.]],.]=>[[],[],[[],[]],[]]=>[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],[.,.]],.]=>[[[[]]],[[]],[]]=>[[],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],.]=>[[[],[]],[[]],[]]=>[[],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],[.,.]],.]=>[[],[[]],[[]],[]]=>[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,.]],.]=>[[[]],[],[[]],[]]=>[[],[[]],[],[[]]]=>[1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[.,.],.],.],[.,.]],.]=>[[],[],[],[[]],[]]=>[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,.]]]],.],.]=>[[[[[]]]],[],[]]=>[[],[],[[[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[[.,.],.]]],.],.]=>[[[[],[]]],[],[]]=>[[],[],[[[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],.]=>[[[],[[]]],[],[]]=>[[],[],[[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[[.,[.,.]],.]],.],.]=>[[[[]],[]],[],[]]=>[[],[],[[],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],.]=>[[[],[],[]],[],[]]=>[[],[],[[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,.]]],.],.]=>[[],[[[]]],[],[]]=>[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],.]],.],.]=>[[],[[],[]],[],[]]=>[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],.],.]=>[[[]],[[]],[],[]]=>[[],[],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],.],.]=>[[],[],[[]],[],[]]=>[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],.]=>[[[[]]],[],[],[]]=>[[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],.],.]=>[[[],[]],[],[],[]]=>[[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],.],.],.]=>[[],[[]],[],[],[]]=>[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],.],.]=>[[[]],[],[],[],[]]=>[[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],.],.]=>[[],[],[],[],[],[]]=>[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[.,[[[[[[.,.],.],.],.],.],.]]=>[[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]]]=>[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]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],[[.,.],.]]=>[[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[[[[[[[]]]]]],[]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[[[[[[],[]]]]],[]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[[[[[],[[]]]]],[]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[[[[[[]],[]]]],[]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[[[[[],[],[]]]],[]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
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[[.,[.,[[.,.],[[.,.],.]]]],.]=>[[[[],[[],[]]]],[]]=>[[],[[[[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
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[[.,[[.,.],[.,[[.,.],.]]]],.]=>[[[],[[[],[]]]],[]]=>[[],[[[[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[[[],[[],[[]]]],[]]=>[[],[[[[]],[]],[]]]=>[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]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
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[[.,[[[.,.],.],[[.,.],.]]],.]=>[[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
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[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[[[[[]],[]],[]],[]]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
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[[.,[[[[.,[.,.]],.],.],.]],.]=>[[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
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[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[[],[[[[],[]]]],[]]=>[[],[[[[],[]]]],[]]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[[],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[[],[[[[]],[]]],[]]=>[[],[[[],[[]]]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[[],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[[],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[[],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[[],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[[],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[[.,.],.],.],.]],.]=>[[],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[[[]],[[],[[]]],[]]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[[[]],[[[]],[]],[]]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[[[]],[[],[],[]],[]]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[[],[],[[[[]]]],[]]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[[],[],[[[],[]]],[]]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[[],[],[[],[[]]],[]]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[[],[],[[[]],[]],[]]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[.,.],.],[[[.,.],.],.]],.]=>[[],[],[[],[],[]],[]]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[[[[]]],[[[]]],[]]=>[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[[[]],[],[[[]]],[]]=>[[],[[[]]],[],[[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[[[]],[],[[],[]],[]]=>[[],[[],[]],[],[[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[[],[],[],[[[]]],[]]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,.],.],.],[[.,.],.]],.]=>[[],[],[],[[],[]],[]]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[[[[[]]]],[[]],[]]=>[[],[[]],[[[[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[[[[],[]]],[[]],[]]=>[[],[[]],[[[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[[[],[[]]],[[]],[]]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[[[[]],[]],[[]],[]]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[[[],[],[]],[[]],[]]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[[],[[[]]],[[]],[]]=>[[],[[]],[[[]]],[]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[[],[[],[]],[[]],[]]=>[[],[[]],[[],[]],[]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[[[]],[[]],[[]],[]]=>[[],[[]],[[]],[[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[[],[],[[]],[[]],[]]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[[[[]]],[],[[]],[]]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[[[],[]],[],[[]],[]]=>[[],[[]],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[[],[[]],[],[[]],[]]=>[[],[[]],[],[[]],[]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[[[]],[],[],[[]],[]]=>[[],[[]],[],[],[[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],[.,.]],.]=>[[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],.]=>[[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[.,.],[[[.,.],.],.]],.],.]=>[[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],.]],.],.]=>[[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],[.,.]],.],.]=>[[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],.]=>[[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[.,.],[[.,.],.]],.],.],.]=>[[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[.,.],.],[.,.]],.],.],.]=>[[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],.]=>[[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[.,.],[.,.]],.],.],.],.]=>[[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[]]=>[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]
[[[[[[[.,.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[[[[[],[],[]]]]]]]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[[[[[],[[[]]]]]]]]=>[[[[[[[[]]],[]]]]]]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[[[[[],[[],[]]]]]]]=>[[[[[[[],[]],[]]]]]]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[[[[[[]],[[]]]]]]]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[[[[[],[],[[]]]]]]]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[[[[[[[]]],[]]]]]]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[[[[[[],[]],[]]]]]]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[[[[[],[[]],[]]]]]]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[[[[[[]],[],[]]]]]]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[[],[],[],[]]]]]]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[[[[],[[[[]]]]]]]]=>[[[[[[[[]]]],[]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[[[[],[[[],[]]]]]]]=>[[[[[[[],[]]],[]]]]]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[[[[],[[],[[]]]]]]]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[[[[],[[[]],[]]]]]]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[[[[],[[],[],[]]]]]]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[[[[[]],[[[]]]]]]]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[[[[[]],[[],[]]]]]]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[[[[],[],[[[]]]]]]]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[[[[],[],[[],[]]]]]]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[[[[[[]]],[[]]]]]]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[[[[[],[]],[[]]]]]]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[[[[],[[]],[[]]]]]]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[[[[[]],[],[[]]]]]]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[[[[],[],[],[[]]]]]]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[[[[[[[]]]],[]]]]]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[[[[[[[],[]]],[]]]]]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[[[[[],[[]]],[]]]]]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[[[[[[]],[]],[]]]]]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[[[[[],[],[]],[]]]]]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[[[[],[[[]]],[]]]]]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[[[[],[[],[]],[]]]]]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[[[[[]],[[]],[]]]]]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[[[[[],[],[[]],[]]]]]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[[[[[[]]],[],[]]]]]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[[[[[],[]],[],[]]]]]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[[[[[],[[]],[],[]]]]]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[[[[[]],[],[],[]]]]]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[[[[],[],[],[],[]]]]]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[[],[[[[[]]]]]]]]=>[[[[[[[[]]]]],[]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[[[[],[[[[],[]]]]]]]=>[[[[[[[],[]]]],[]]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[[[],[[[],[[]]]]]]]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[[[[],[[[[]],[]]]]]]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[[[[],[[[],[],[]]]]]]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[[[],[[],[[[]]]]]]]=>[[[[[[[]]],[]],[]]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[],[[],[[],[]]]]]]=>[[[[[[],[]],[]],[]]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[[[],[[[]],[[]]]]]]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[[[[],[[],[],[[]]]]]]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[[[[],[[[[]]],[]]]]]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[[[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[[[[],[[],[[]],[]]]]]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[[[[],[[[]],[],[]]]]]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[[[[],[[],[],[],[]]]]]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[[[[]],[[[[]]]]]]]=>[[[[[[[]]]],[[]]]]]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[[[[]],[[[],[]]]]]]=>[[[[[[],[]]],[[]]]]]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[[[[[]],[[],[[]]]]]]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[[[[[]],[[[]],[]]]]]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[[[[[]],[[],[],[]]]]]=>[[[[[],[],[]],[[]]]]]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[[[[],[],[[[[]]]]]]]=>[[[[[[[]]]],[],[]]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[[[[],[],[[[],[]]]]]]=>[[[[[[],[]]],[],[]]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[[[[],[],[[],[[]]]]]]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[[[[],[],[[[]],[]]]]]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[[[[],[],[[],[],[]]]]]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[[[[[]]],[[[]]]]]]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[[[[[[]]],[[],[]]]]]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[[[[],[]],[[[]]]]]]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[[[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[[[[],[[]],[[[]]]]]]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[[[[],[[]],[[],[]]]]]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[[[[]],[],[[[]]]]]]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[[[[[]],[],[[],[]]]]]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[[[],[],[],[[[]]]]]]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[[[[],[],[],[[],[]]]]]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[[[[[[[]]]],[[]]]]]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[[[[[[],[]]],[[]]]]]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[[[[],[[]]],[[]]]]]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[[[[[[]],[]],[[]]]]]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[[[[[],[],[]],[[]]]]]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[[[[],[[[]]],[[]]]]]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[[[[],[[],[]],[[]]]]]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[[[[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[[[[],[],[[]],[[]]]]]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[[[[[[]]],[],[[]]]]]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[[[[[],[]],[],[[]]]]]=>[[[[[]],[],[[],[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[[[[],[[]],[],[[]]]]]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[[[[[]],[],[],[[]]]]]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[[[[],[],[],[],[[]]]]]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[[[[[[[]]]]],[]]]]=>[[[[],[[[[[]]]]]]]]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[[[[[[[],[]]]],[]]]]=>[[[[],[[[[],[]]]]]]]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[[[[[],[[]]]],[]]]]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[[[[[[]],[]]],[]]]]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[[[[[],[],[]]],[]]]]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[[[[],[[[]]]],[]]]]=>[[[[],[[[[]]],[]]]]]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[[[[],[[],[]]],[]]]]=>[[[[],[[[],[]],[]]]]]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[[[[[[]],[[]]],[]]]]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[[[[],[],[[]]],[]]]]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[[[[[[]]],[]],[]]]]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[[[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[[[[],[[]],[]],[]]]]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[[[[[]],[],[]],[]]]]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[[[[],[],[],[]],[]]]]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[[[],[[[[]]]],[]]]]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[[[[],[[[],[]]],[]]]]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[[[[],[[],[[]]],[]]]]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[[[[],[[[]],[]],[]]]]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[[[[],[[],[],[]],[]]]]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[[[[[]],[[[]]],[]]]]=>[[[[],[[[]]],[[]]]]]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[[[[]],[[],[]],[]]]]=>[[[[],[[],[]],[[]]]]]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[[[],[],[[[]]],[]]]]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[[[],[],[[],[]],[]]]]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[[[[[[]]],[[]],[]]]]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[[[[],[]],[[]],[]]]]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[[[],[[]],[[]],[]]]]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[[[[[]],[],[[]],[]]]]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[[[[],[],[],[[]],[]]]]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[[[[[[[]]]],[],[]]]]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[[[[[[],[]]],[],[]]]]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[[[[],[[]]],[],[]]]]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[[[[[[]],[]],[],[]]]]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[[[[],[],[]],[],[]]]]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[[[],[[[]]],[],[]]]]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[[[],[[],[]],[],[]]]]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[[[[]],[[]],[],[]]]]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[[[[],[],[[]],[],[]]]]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[[[[[]]],[],[],[]]]]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[[[[],[]],[],[],[]]]]=>[[[[],[],[],[[],[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[[[],[[]],[],[],[]]]]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[[[[]],[],[],[],[]]]]=>[[[[],[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[[],[[[[[],[]]]]]]]=>[[[[[[[],[]]]]],[]]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[[],[[[[],[[]]]]]]]=>[[[[[[[]],[]]]],[]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[[[],[[[[[]],[]]]]]]=>[[[[[[],[[]]]]],[]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[[[],[[[[],[],[]]]]]]=>[[[[[[],[],[]]]],[]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[[],[[[],[[[]]]]]]]=>[[[[[[[]]],[]]],[]]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[[],[[[],[[],[]]]]]]=>[[[[[[],[]],[]]],[]]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[[[],[[[[]],[[]]]]]]=>[[[[[[]],[[]]]],[]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[[[],[[[],[],[[]]]]]]=>[[[[[[]],[],[]]],[]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[[[],[[[[[]]],[]]]]]=>[[[[[],[[[]]]]],[]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[[[],[[[[],[]],[]]]]]=>[[[[[],[[],[]]]],[]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[[[],[[[],[[]],[]]]]]=>[[[[[],[[]],[]]],[]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[[[],[[[[]],[],[]]]]]=>[[[[[],[],[[]]]],[]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[[[],[[[],[],[],[]]]]]=>[[[[[],[],[],[]]],[]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[[],[[],[[[[]]]]]]]=>[[[[[[[]]]],[]],[]]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[[],[[],[[[],[]]]]]]=>[[[[[[],[]]],[]],[]]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[],[[],[[],[[]]]]]]=>[[[[[[]],[]],[]],[]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[],[[],[[[]],[]]]]]=>[[[[[],[[]]],[]],[]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[[],[[],[[],[],[]]]]]=>[[[[[],[],[]],[]],[]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[[],[[[]],[[[]]]]]]=>[[[[[[]]],[[]]],[]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[[[],[[[]],[[],[]]]]]=>[[[[[],[]],[[]]],[]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[[[],[[],[],[[[]]]]]]=>[[[[[[]]],[],[]],[]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[[[],[[],[],[[],[]]]]]=>[[[[[],[]],[],[]],[]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[[[],[[[[]]],[[]]]]]=>[[[[[]],[[[]]]],[]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[[],[[[],[]],[[]]]]]=>[[[[[]],[[],[]]],[]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[[],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[[[],[[[]],[],[[]]]]]=>[[[[[]],[],[[]]],[]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[[[],[[],[],[],[[]]]]]=>[[[[[]],[],[],[]],[]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[[[],[[[[[]]]],[]]]]=>[[[[],[[[[]]]]],[]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[[[],[[[[],[]]],[]]]]=>[[[[],[[[],[]]]],[]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[[],[[[],[[]]],[]]]]=>[[[[],[[[]],[]]],[]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[[],[[[[]],[]],[]]]]=>[[[[],[[],[[]]]],[]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[[],[[[],[],[]],[]]]]=>[[[[],[[],[],[]]],[]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[[],[[],[[[]]],[]]]]=>[[[[],[[[]]],[]],[]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[[],[[],[[],[]],[]]]]=>[[[[],[[],[]],[]],[]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[],[[[]],[[]],[]]]]=>[[[[],[[]],[[]]],[]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[[],[[],[],[[]],[]]]]=>[[[[],[[]],[],[]],[]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[[],[[[[]]],[],[]]]]=>[[[[],[],[[[]]]],[]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[[],[[[],[]],[],[]]]]=>[[[[],[],[[],[]]],[]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[[],[[],[[]],[],[]]]]=>[[[[],[],[[]],[]],[]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[[],[[[]],[],[],[]]]]=>[[[[],[],[],[[]]],[]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[],[[],[],[],[],[]]]]=>[[[[],[],[],[],[]],[]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[]],[[[[[]]]]]]]=>[[[[[[[]]]]],[[]]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[[[[]],[[[[],[]]]]]]=>[[[[[[],[]]]],[[]]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[[]],[[[],[[]]]]]]=>[[[[[[]],[]]],[[]]]]=>[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]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[[[[]],[[[],[],[]]]]]=>[[[[[],[],[]]],[[]]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[[[]],[[],[[[]]]]]]=>[[[[[[]]],[]],[[]]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[[[[]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[]]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[]],[[[]],[[]]]]]=>[[[[[]],[[]]],[[]]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[[[]],[[],[],[[]]]]]=>[[[[[]],[],[]],[[]]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[[[]],[[[[]]],[]]]]=>[[[[],[[[]]]],[[]]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[[[[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[]]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[[[]],[[],[[]],[]]]]=>[[[[],[[]],[]],[[]]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[[[]],[[[]],[],[]]]]=>[[[[],[],[[]]],[[]]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[[[]],[[],[],[],[]]]]=>[[[[],[],[],[]],[[]]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[[],[],[[[[[]]]]]]]=>[[[[[[[]]]]],[],[]]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[[[],[],[[[[],[]]]]]]=>[[[[[[],[]]]],[],[]]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[[[],[],[[[],[[]]]]]]=>[[[[[[]],[]]],[],[]]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[[[],[],[[[[]],[]]]]]=>[[[[[],[[]]]],[],[]]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[[[],[],[[[],[],[]]]]]=>[[[[[],[],[]]],[],[]]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[[[],[],[[],[[[]]]]]]=>[[[[[[]]],[]],[],[]]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[[[],[],[[],[[],[]]]]]=>[[[[[],[]],[]],[],[]]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[[[],[],[[[]],[[]]]]]=>[[[[[]],[[]]],[],[]]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[[[],[],[[],[],[[]]]]]=>[[[[[]],[],[]],[],[]]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[[[],[],[[[[]]],[]]]]=>[[[[],[[[]]]],[],[]]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[[[],[],[[[],[]],[]]]]=>[[[[],[[],[]]],[],[]]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[[[],[],[[],[[]],[]]]]=>[[[[],[[]],[]],[],[]]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[[[],[],[[[]],[],[]]]]=>[[[[],[],[[]]],[],[]]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[[[],[],[[],[],[],[]]]]=>[[[[],[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[[[[[]]],[[[[]]]]]]=>[[[[[[]]]],[[[]]]]]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[[[[[]]],[[[],[]]]]]=>[[[[[],[]]],[[[]]]]]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[[[[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[[[[[]]],[[[]],[]]]]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[[[[[]]],[[],[],[]]]]=>[[[[],[],[]],[[[]]]]]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[[[[],[]],[[[[]]]]]]=>[[[[[[]]]],[[],[]]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[[[[],[]],[[[],[]]]]]=>[[[[[],[]]],[[],[]]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[[[[],[]],[[],[[]]]]]=>[[[[[]],[]],[[],[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[[[],[]],[[[]],[]]]]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[[[[],[]],[[],[],[]]]]=>[[[[],[],[]],[[],[]]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[[[],[[]],[[[[]]]]]]=>[[[[[[]]]],[[]],[]]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[[[],[[]],[[[],[]]]]]=>[[[[[],[]]],[[]],[]]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[[[],[[]],[[[]],[]]]]=>[[[[],[[]]],[[]],[]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[[[],[[]],[[],[],[]]]]=>[[[[],[],[]],[[]],[]]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[[[[]],[],[[[[]]]]]]=>[[[[[[]]]],[],[[]]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[[[[]],[],[[[],[]]]]]=>[[[[[],[]]],[],[[]]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[[[[]],[],[[],[[]]]]]=>[[[[[]],[]],[],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[[[[]],[],[[[]],[]]]]=>[[[[],[[]]],[],[[]]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[[[]],[],[[],[],[]]]]=>[[[[],[],[]],[],[[]]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[[[],[],[],[[[[]]]]]]=>[[[[[[]]]],[],[],[]]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[[[],[],[],[[[],[]]]]]=>[[[[[],[]]],[],[],[]]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[[[],[],[],[[],[[]]]]]=>[[[[[]],[]],[],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[[[],[],[],[[[]],[]]]]=>[[[[],[[]]],[],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[[[],[],[],[[],[],[]]]]=>[[[[],[],[]],[],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[[[[[[]]]],[[[]]]]]=>[[[[[]]],[[[[]]]]]]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[[[[[[]]]],[[],[]]]]=>[[[[],[]],[[[[]]]]]]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[[[[[],[]]],[[[]]]]]=>[[[[[]]],[[[],[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[[[[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[[[[],[[]]],[[[]]]]]=>[[[[[]]],[[[]],[]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[[[[],[[]]],[[],[]]]]=>[[[[],[]],[[[]],[]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[[[[[]],[]],[[[]]]]]=>[[[[[]]],[[],[[]]]]]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[[[[[]],[]],[[],[]]]]=>[[[[],[]],[[],[[]]]]]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]
[.,[[.,[[[.,.],.],.]],[.,[.,.]]]]=>[[[[],[],[]],[[[]]]]]=>[[[[[]]],[[],[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]
[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[[[[],[],[]],[[],[]]]]=>[[[[],[]],[[],[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[[[],[[[]]],[[[]]]]]=>[[[[[]]],[[[]]],[]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[[[],[[[]]],[[],[]]]]=>[[[[],[]],[[[]]],[]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[[[],[[],[]],[[[]]]]]=>[[[[[]]],[[],[]],[]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[[[],[[],[]],[[],[]]]]=>[[[[],[]],[[],[]],[]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[[[]],[[]],[[[]]]]]=>[[[[[]]],[[]],[[]]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[[[]],[[]],[[],[]]]]=>[[[[],[]],[[]],[[]]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[[[],[],[[]],[[[]]]]]=>[[[[[]]],[[]],[],[]]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[[[],[],[[]],[[],[]]]]=>[[[[],[]],[[]],[],[]]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[[[[[]]],[],[[[]]]]]=>[[[[[]]],[],[[[]]]]]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[[[[[]]],[],[[],[]]]]=>[[[[],[]],[],[[[]]]]]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]
[.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[[[[],[]],[],[[[]]]]]=>[[[[[]]],[],[[],[]]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[[[[],[]],[],[[],[]]]]=>[[[[],[]],[],[[],[]]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[[[],[[]],[],[[[]]]]]=>[[[[[]]],[],[[]],[]]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[[[],[[]],[],[[],[]]]]=>[[[[],[]],[],[[]],[]]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[[[[]],[],[],[[[]]]]]=>[[[[[]]],[],[],[[]]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[[[[]],[],[],[[],[]]]]=>[[[[],[]],[],[],[[]]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[[[],[],[],[],[[[]]]]]=>[[[[[]]],[],[],[],[]]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[[[],[],[],[],[[],[]]]]=>[[[[],[]],[],[],[],[]]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[[[[[[[]]]]],[[]]]]=>[[[[]],[[[[[]]]]]]]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[[[[[[],[]]]],[[]]]]=>[[[[]],[[[[],[]]]]]]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[[[[[],[[]]]],[[]]]]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[[[[[[]],[]]],[[]]]]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[[[[[],[],[]]],[[]]]]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[[[],[[[]]]],[[]]]]=>[[[[]],[[[[]]],[]]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[[[],[[],[]]],[[]]]]=>[[[[]],[[[],[]],[]]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[[[[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[[[[],[],[[]]],[[]]]]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[[[[[[]]],[]],[[]]]]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[[[[[],[]],[]],[[]]]]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[[[[],[[]],[]],[[]]]]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[[[[[]],[],[]],[[]]]]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[[[[],[],[],[]],[[]]]]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[[[],[[[[]]]],[[]]]]=>[[[[]],[[[[]]]],[]]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[[[],[[[],[]]],[[]]]]=>[[[[]],[[[],[]]],[]]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[[],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]
[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[[[],[[[]],[]],[[]]]]=>[[[[]],[[],[[]]],[]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]
[.,[[[.,.],[[[.,.],.],.]],[.,.]]]=>[[[],[[],[],[]],[[]]]]=>[[[[]],[[],[],[]],[]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[[[[]],[[[]]],[[]]]]=>[[[[]],[[[]]],[[]]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]
[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]=>[[[[]],[[],[]],[[]]]]=>[[[[]],[[],[]],[[]]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[[[],[],[[[]]],[[]]]]=>[[[[]],[[[]]],[],[]]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[[.,.],.],[[.,.],.]],[.,.]]]=>[[[],[],[[],[]],[[]]]]=>[[[[]],[[],[]],[],[]]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[[[[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[[[[],[]],[[]],[[]]]]=>[[[[]],[[]],[[],[]]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[[[],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[]]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[[[[]],[],[[]],[[]]]]=>[[[[]],[[]],[],[[]]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[[[],[],[],[[]],[[]]]]=>[[[[]],[[]],[],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[[[[[[]]]],[],[[]]]]=>[[[[]],[],[[[[]]]]]]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[[[[[],[]]],[],[[]]]]=>[[[[]],[],[[[],[]]]]]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[[[[],[[]]],[],[[]]]]=>[[[[]],[],[[[]],[]]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[[[[[]],[]],[],[[]]]]=>[[[[]],[],[[],[[]]]]]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[[[[],[],[]],[],[[]]]]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[[[],[[[]]],[],[[]]]]=>[[[[]],[],[[[]]],[]]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[[[],[[],[]],[],[[]]]]=>[[[[]],[],[[],[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[[[[]],[[]],[],[[]]]]=>[[[[]],[],[[]],[[]]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[[[],[],[[]],[],[[]]]]=>[[[[]],[],[[]],[],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[[[[[]]],[],[],[[]]]]=>[[[[]],[],[],[[[]]]]]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[[[[],[]],[],[],[[]]]]=>[[[[]],[],[],[[],[]]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[[[],[[]],[],[],[[]]]]=>[[[[]],[],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[[[[]],[],[],[],[[]]]]=>[[[[]],[],[],[],[[]]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[[[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
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[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[[[[[],[]],[]],[],[]]]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[[[[],[[]],[]],[],[]]]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[[[[[]],[],[]],[],[]]]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[[[[],[],[],[]],[],[]]]=>[[[],[],[[],[],[],[]]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[[[],[[[[]]]],[],[]]]=>[[[],[],[[[[]]]],[]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[[[],[[[],[]]],[],[]]]=>[[[],[],[[[],[]]],[]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[[[],[[],[[]]],[],[]]]=>[[[],[],[[[]],[]],[]]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[[[],[[[]],[]],[],[]]]=>[[[],[],[[],[[]]],[]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[[[],[[],[],[]],[],[]]]=>[[[],[],[[],[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[[[[]],[[[]]],[],[]]]=>[[[],[],[[[]]],[[]]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[[[[]],[[],[]],[],[]]]=>[[[],[],[[],[]],[[]]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[[[],[],[[[]]],[],[]]]=>[[[],[],[[[]]],[],[]]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[[[],[],[[],[]],[],[]]]=>[[[],[],[[],[]],[],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[[[[[]]],[[]],[],[]]]=>[[[],[],[[]],[[[]]]]]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[[[[],[]],[[]],[],[]]]=>[[[],[],[[]],[[],[]]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[[[],[[]],[[]],[],[]]]=>[[[],[],[[]],[[]],[]]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[[.,[.,.]],.],[.,.]],.],.]]=>[[[[]],[],[[]],[],[]]]=>[[[],[],[[]],[],[[]]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[[[],[],[],[[]],[],[]]]=>[[[],[],[[]],[],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[[[[[[]]]],[],[],[]]]=>[[[],[],[],[[[[]]]]]]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[[[[[],[]]],[],[],[]]]=>[[[],[],[],[[[],[]]]]]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[[[[],[[]]],[],[],[]]]=>[[[],[],[],[[[]],[]]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[[[[[]],[]],[],[],[]]]=>[[[],[],[],[[],[[]]]]]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[[[[],[],[]],[],[],[]]]=>[[[],[],[],[[],[],[]]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[[[],[[[]]],[],[],[]]]=>[[[],[],[],[[[]]],[]]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[[[],[[],[]],[],[],[]]]=>[[[],[],[],[[],[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[[[[]],[[]],[],[],[]]]=>[[[],[],[],[[]],[[]]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[[[],[],[[]],[],[],[]]]=>[[[],[],[],[[]],[],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[[[[[]]],[],[],[],[]]]=>[[[],[],[],[],[[[]]]]]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[[[[],[]],[],[],[],[]]]=>[[[],[],[],[],[[],[]]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[[[],[[]],[],[],[],[]]]=>[[[],[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[[[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[],[[[[[[],[]]]]]]]=>[[[[[[[],[]]]]]],[]]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[[],[[[[[],[[]]]]]]]=>[[[[[[[]],[]]]]],[]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[[],[[[[[[]],[]]]]]]=>[[[[[[],[[]]]]]],[]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[[],[[[[[],[],[]]]]]]=>[[[[[[],[],[]]]]],[]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[],[[[[],[[[]]]]]]]=>[[[[[[[]]],[]]]],[]]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[[],[[[[],[[],[]]]]]]=>[[[[[[],[]],[]]]],[]]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[[],[[[[[]],[[]]]]]]=>[[[[[[]],[[]]]]],[]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[],[[[[],[],[[]]]]]]=>[[[[[[]],[],[]]]],[]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[[],[[[[[[]]],[]]]]]=>[[[[[],[[[]]]]]],[]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[[],[[[[[],[]],[]]]]]=>[[[[[],[[],[]]]]],[]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[[],[[[[],[[]],[]]]]]=>[[[[[],[[]],[]]]],[]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[[],[[[[[]],[],[]]]]]=>[[[[[],[],[[]]]]],[]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[],[[[[],[],[],[]]]]]=>[[[[[],[],[],[]]]],[]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[[[],[[[[]]]]]]]=>[[[[[[[]]]],[]]],[]]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[[[],[[[],[]]]]]]=>[[[[[[],[]]],[]]],[]]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[[[],[[],[[]]]]]]=>[[[[[[]],[]],[]]],[]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[[],[[[],[[[]],[]]]]]=>[[[[[],[[]]],[]]],[]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[[],[[[],[[],[],[]]]]]=>[[[[[],[],[]],[]]],[]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[],[[[[]],[[[]]]]]]=>[[[[[[]]],[[]]]],[]]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[],[[[[]],[[],[]]]]]=>[[[[[],[]],[[]]]],[]]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[[[],[],[[[]]]]]]=>[[[[[[]]],[],[]]],[]]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[[],[[[],[],[[],[]]]]]=>[[[[[],[]],[],[]]],[]]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[],[[[[[]]],[[]]]]]=>[[[[[]],[[[]]]]],[]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[[],[[[[],[]],[[]]]]]=>[[[[[]],[[],[]]]],[]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[[],[[[],[[]],[[]]]]]=>[[[[[]],[[]],[]]],[]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[],[[[[]],[],[[]]]]]=>[[[[[]],[],[[]]]],[]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[[],[[[],[],[],[[]]]]]=>[[[[[]],[],[],[]]],[]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[],[[[[[[]]]],[]]]]=>[[[[],[[[[]]]]]],[]]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[[],[[[[[],[]]],[]]]]=>[[[[],[[[],[]]]]],[]]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[],[[[[],[[]]],[]]]]=>[[[[],[[[]],[]]]],[]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[],[[[[[]],[]],[]]]]=>[[[[],[[],[[]]]]],[]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[],[[[[],[],[]],[]]]]=>[[[[],[[],[],[]]]],[]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[[],[[[],[[[]]],[]]]]=>[[[[],[[[]]],[]]],[]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[],[[[],[[],[]],[]]]]=>[[[[],[[],[]],[]]],[]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[],[[[[]],[[]],[]]]]=>[[[[],[[]],[[]]]],[]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[],[[[],[],[[]],[]]]]=>[[[[],[[]],[],[]]],[]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[],[[[[[]]],[],[]]]]=>[[[[],[],[[[]]]]],[]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[],[[[[],[]],[],[]]]]=>[[[[],[],[[],[]]]],[]]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[],[[[],[[]],[],[]]]]=>[[[[],[],[[]],[]]],[]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[],[[[[]],[],[],[]]]]=>[[[[],[],[],[[]]]],[]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[],[[[],[],[],[],[]]]]=>[[[[],[],[],[],[]]],[]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[],[[[[[]]]]]]]=>[[[[[[[]]]]],[]],[]]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[[],[[],[[[[],[]]]]]]=>[[[[[[],[]]]],[]],[]]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[],[[[],[[]]]]]]=>[[[[[[]],[]]],[]],[]]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[],[[],[[[[]],[]]]]]=>[[[[[],[[]]]],[]],[]]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[],[[[],[],[]]]]]=>[[[[[],[],[]]],[]],[]]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[],[[],[[[]]]]]]=>[[[[[[]]],[]],[]],[]]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[]]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[],[[],[[[]],[[]]]]]=>[[[[[]],[[]]],[]],[]]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[],[[],[],[[]]]]]=>[[[[[]],[],[]],[]],[]]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[],[[],[[[[]]],[]]]]=>[[[[],[[[]]]],[]],[]]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[[],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[]]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[],[[],[[],[[]],[]]]]=>[[[[],[[]],[]],[]],[]]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[],[[],[[[]],[],[]]]]=>[[[[],[],[[]]],[]],[]]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[],[[],[[],[],[],[]]]]=>[[[[],[],[],[]],[]],[]]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[],[[[]],[[[[]]]]]]=>[[[[[[]]]],[[]]],[]]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[],[[[]],[[[],[]]]]]=>[[[[[],[]]],[[]]],[]]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[],[[[]],[[],[[]]]]]=>[[[[[]],[]],[[]]],[]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[],[[[]],[[[]],[]]]]=>[[[[],[[]]],[[]]],[]]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[],[[[]],[[],[],[]]]]=>[[[[],[],[]],[[]]],[]]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[],[],[[[[]]]]]]=>[[[[[[]]]],[],[]],[]]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[],[],[[[],[]]]]]=>[[[[[],[]]],[],[]],[]]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[],[],[[],[[]]]]]=>[[[[[]],[]],[],[]],[]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[],[[],[],[[[]],[]]]]=>[[[[],[[]]],[],[]],[]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[],[[],[],[[],[],[]]]]=>[[[[],[],[]],[],[]],[]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[],[[[[]]],[[[]]]]]=>[[[[[]]],[[[]]]],[]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[],[[[[]]],[[],[]]]]=>[[[[],[]],[[[]]]],[]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[],[[[],[]],[[[]]]]]=>[[[[[]]],[[],[]]],[]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[],[[],[[]],[[[]]]]]=>[[[[[]]],[[]],[]],[]]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[],[[],[[]],[[],[]]]]=>[[[[],[]],[[]],[]],[]]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[],[[[]],[],[[[]]]]]=>[[[[[]]],[],[[]]],[]]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[],[[[]],[],[[],[]]]]=>[[[[],[]],[],[[]]],[]]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[],[],[],[[[]]]]]=>[[[[[]]],[],[],[]],[]]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[],[[],[],[],[[],[]]]]=>[[[[],[]],[],[],[]],[]]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[],[[[[[]]]],[[]]]]=>[[[[]],[[[[]]]]],[]]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[[],[[[[],[]]],[[]]]]=>[[[[]],[[[],[]]]],[]]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[],[[[],[[]]],[[]]]]=>[[[[]],[[[]],[]]],[]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[],[[[[]],[]],[[]]]]=>[[[[]],[[],[[]]]],[]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[],[[[],[],[]],[[]]]]=>[[[[]],[[],[],[]]],[]]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[],[[],[[[]]],[[]]]]=>[[[[]],[[[]]],[]],[]]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[],[[],[[],[]],[[]]]]=>[[[[]],[[],[]],[]],[]]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[],[[[]],[[]],[[]]]]=>[[[[]],[[]],[[]]],[]]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[],[[],[],[[]],[[]]]]=>[[[[]],[[]],[],[]],[]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[],[[[[]]],[],[[]]]]=>[[[[]],[],[[[]]]],[]]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[],[[[],[]],[],[[]]]]=>[[[[]],[],[[],[]]],[]]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[],[[],[[]],[],[[]]]]=>[[[[]],[],[[]],[]],[]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[],[[[]],[],[],[[]]]]=>[[[[]],[],[],[[]]],[]]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[],[[],[],[],[],[[]]]]=>[[[[]],[],[],[],[]],[]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[],[[[[[[]]]]],[]]]=>[[[],[[[[[]]]]]],[]]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[[],[[[[[],[]]]],[]]]=>[[[],[[[[],[]]]]],[]]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[],[[[[],[[]]]],[]]]=>[[[],[[[[]],[]]]],[]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[],[[[[[]],[]]],[]]]=>[[[],[[[],[[]]]]],[]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[],[[[[],[],[]]],[]]]=>[[[],[[[],[],[]]]],[]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[],[[[],[[[]]]],[]]]=>[[[],[[[[]]],[]]],[]]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[],[[[],[[],[]]],[]]]=>[[[],[[[],[]],[]]],[]]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[],[[[[]],[[]]],[]]]=>[[[],[[[]],[[]]]],[]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[],[[[],[],[[]]],[]]]=>[[[],[[[]],[],[]]],[]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[],[[[[[]]],[]],[]]]=>[[[],[[],[[[]]]]],[]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[[],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[],[[[],[[]],[]],[]]]=>[[[],[[],[[]],[]]],[]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[],[[[[]],[],[]],[]]]=>[[[],[[],[],[[]]]],[]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[],[[[],[],[],[]],[]]]=>[[[],[[],[],[],[]]],[]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[],[[],[[[[]]]],[]]]=>[[[],[[[[]]]],[]],[]]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[],[[],[[[],[]]],[]]]=>[[[],[[[],[]]],[]],[]]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[],[[],[[],[[]]],[]]]=>[[[],[[[]],[]],[]],[]]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[],[[],[[[]],[]],[]]]=>[[[],[[],[[]]],[]],[]]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[],[[],[[],[],[]],[]]]=>[[[],[[],[],[]],[]],[]]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[],[[[]],[[[]]],[]]]=>[[[],[[[]]],[[]]],[]]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[],[[[]],[[],[]],[]]]=>[[[],[[],[]],[[]]],[]]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[],[[],[],[[[]]],[]]]=>[[[],[[[]]],[],[]],[]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[],[[],[],[[],[]],[]]]=>[[[],[[],[]],[],[]],[]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[],[[[[]]],[[]],[]]]=>[[[],[[]],[[[]]]],[]]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[],[[[],[]],[[]],[]]]=>[[[],[[]],[[],[]]],[]]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[],[[],[[]],[[]],[]]]=>[[[],[[]],[[]],[]],[]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[],[[[]],[],[[]],[]]]=>[[[],[[]],[],[[]]],[]]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[],[[],[],[],[[]],[]]]=>[[[],[[]],[],[],[]],[]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[],[[[[[]]]],[],[]]]=>[[[],[],[[[[]]]]],[]]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[[],[[[[],[]]],[],[]]]=>[[[],[],[[[],[]]]],[]]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[],[[[],[[]]],[],[]]]=>[[[],[],[[[]],[]]],[]]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[],[[[[]],[]],[],[]]]=>[[[],[],[[],[[]]]],[]]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[],[[[],[],[]],[],[]]]=>[[[],[],[[],[],[]]],[]]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[],[[],[[[]]],[],[]]]=>[[[],[],[[[]]],[]],[]]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[],[[],[[],[]],[],[]]]=>[[[],[],[[],[]],[]],[]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[],[[[]],[[]],[],[]]]=>[[[],[],[[]],[[]]],[]]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[],[[],[],[[]],[],[]]]=>[[[],[],[[]],[],[]],[]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[],[[[[]]],[],[],[]]]=>[[[],[],[],[[[]]]],[]]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[],[[[],[]],[],[],[]]]=>[[[],[],[],[[],[]]],[]]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[[],[[],[[]],[],[],[]]]=>[[[],[],[],[[]],[]],[]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[],[[[]],[],[],[],[]]]=>[[[],[],[],[],[[]]],[]]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[],[[],[],[],[],[],[]]]=>[[[],[],[],[],[],[]],[]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[]]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[[]]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[]],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[]],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[[]]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[]],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[[]]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[]],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[]],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[]],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[[[]],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[]],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[]],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[]],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[[]]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[[]]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[]],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[]],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[]],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[]],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[]],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[]],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[]],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[]],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[]],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[]],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[]],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[[[]],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[]],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[]],[[[[]],[]],[]]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[]],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[]],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[]],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[]],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[]],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[]],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[]],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[[]],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[]],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[]],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[]]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[],[],[[[[[],[]]]]]]=>[[[[[[],[]]]]],[],[]]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[],[],[[[[],[[]]]]]]=>[[[[[[]],[]]]],[],[]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[],[],[[[[[]],[]]]]]=>[[[[[],[[]]]]],[],[]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[],[],[[[[],[],[]]]]]=>[[[[[],[],[]]]],[],[]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[],[],[[[],[[[]]]]]]=>[[[[[[]]],[]]],[],[]]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[],[],[[[],[[],[]]]]]=>[[[[[],[]],[]]],[],[]]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[],[],[[[[]],[[]]]]]=>[[[[[]],[[]]]],[],[]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[],[],[[[],[],[[]]]]]=>[[[[[]],[],[]]],[],[]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[],[],[[[[[]]],[]]]]=>[[[[],[[[]]]]],[],[]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[],[],[[[[],[]],[]]]]=>[[[[],[[],[]]]],[],[]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[],[],[[[],[[]],[]]]]=>[[[[],[[]],[]]],[],[]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[],[],[[[[]],[],[]]]]=>[[[[],[],[[]]]],[],[]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[],[],[[[],[],[],[]]]]=>[[[[],[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[],[],[[],[[[[]]]]]]=>[[[[[[]]]],[]],[],[]]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[],[],[[],[[[],[]]]]]=>[[[[[],[]]],[]],[],[]]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[],[],[[],[[],[[]]]]]=>[[[[[]],[]],[]],[],[]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[],[],[[],[[[]],[]]]]=>[[[[],[[]]],[]],[],[]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[],[],[[],[[],[],[]]]]=>[[[[],[],[]],[]],[],[]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[],[],[[[]],[[[]]]]]=>[[[[[]]],[[]]],[],[]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[],[],[[[]],[[],[]]]]=>[[[[],[]],[[]]],[],[]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[],[],[[],[],[[[]]]]]=>[[[[[]]],[],[]],[],[]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[],[],[[],[],[[],[]]]]=>[[[[],[]],[],[]],[],[]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[],[],[[[[]]],[[]]]]=>[[[[]],[[[]]]],[],[]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[],[],[[[],[]],[[]]]]=>[[[[]],[[],[]]],[],[]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[],[],[[],[[]],[[]]]]=>[[[[]],[[]],[]],[],[]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[],[],[[[]],[],[[]]]]=>[[[[]],[],[[]]],[],[]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[],[],[[],[],[],[[]]]]=>[[[[]],[],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[],[],[[[[[]]]],[]]]=>[[[],[[[[]]]]],[],[]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[],[],[[[[],[]]],[]]]=>[[[],[[[],[]]]],[],[]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[],[],[[[],[[]]],[]]]=>[[[],[[[]],[]]],[],[]]=>[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]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[],[],[[[],[],[]],[]]]=>[[[],[[],[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[],[],[[],[[[]]],[]]]=>[[[],[[[]]],[]],[],[]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[],[],[[],[[],[]],[]]]=>[[[],[[],[]],[]],[],[]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[],[],[[[]],[[]],[]]]=>[[[],[[]],[[]]],[],[]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[],[],[[],[],[[]],[]]]=>[[[],[[]],[],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[],[],[[[[]]],[],[]]]=>[[[],[],[[[]]]],[],[]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[],[],[[[],[]],[],[]]]=>[[[],[],[[],[]]],[],[]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[],[],[[],[[]],[],[]]]=>[[[],[],[[]],[]],[],[]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[],[],[[[]],[],[],[]]]=>[[[],[],[],[[]]],[],[]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[],[],[[],[],[],[],[]]]=>[[[],[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[[]]],[[[[],[]]]]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[[]]],[[[],[[]]]]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[[]]],[[[[]],[]]]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[[]]],[[[],[],[]]]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[[]]],[[],[[[]]]]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[[]]],[[[]],[[]]]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[[]]],[[],[],[[]]]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[[[]]],[[[[]]],[]]]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[[]]],[[],[[]],[]]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[[[]]],[[[]],[],[]]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[[]]],[[],[],[],[]]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[],[]],[[[[[]]]]]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[],[]],[[[[],[]]]]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[],[]],[[[],[[]]]]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[]],[[[[]],[]]]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[],[]],[[[],[],[]]]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[]],[[],[[[]]]]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[]],[[[]],[[]]]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[]],[[],[],[[]]]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[[],[]],[[[[]]],[]]]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[[],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[]],[[],[[]],[]]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[[],[]],[[[]],[],[]]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[]],[[],[],[],[]]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[],[[]],[[[[[]]]]]]=>[[[[[[]]]]],[[]],[]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[],[[]],[[[[],[]]]]]=>[[[[[],[]]]],[[]],[]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[],[[]],[[[[]],[]]]]=>[[[[],[[]]]],[[]],[]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[],[[]],[[[],[],[]]]]=>[[[[],[],[]]],[[]],[]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[],[[]],[[],[[[]]]]]=>[[[[[]]],[]],[[]],[]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[],[[]],[[],[[],[]]]]=>[[[[],[]],[]],[[]],[]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[],[[]],[[[]],[[]]]]=>[[[[]],[[]]],[[]],[]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[],[[]],[[],[],[[]]]]=>[[[[]],[],[]],[[]],[]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[],[[]],[[[[]]],[]]]=>[[[],[[[]]]],[[]],[]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[],[[]],[[[],[]],[]]]=>[[[],[[],[]]],[[]],[]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[],[[]],[[],[[]],[]]]=>[[[],[[]],[]],[[]],[]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[],[[]],[[[]],[],[]]]=>[[[],[],[[]]],[[]],[]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[],[[]],[[],[],[],[]]]=>[[[],[],[],[]],[[]],[]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[[]]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[]],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[[]]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[[]]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[]],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[[]]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[]],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[[]]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[]],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[[]]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[]],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[[]]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[]],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[[]]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[]],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[[]]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[]],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[[]]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[]],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[[]]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[]],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[[]]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[]],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[[]]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[]],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[[]]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[]]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[],[],[],[[[[],[]]]]]=>[[[[[],[]]]],[],[],[]]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[],[],[],[[[],[[]]]]]=>[[[[[]],[]]],[],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[],[],[],[[[[]],[]]]]=>[[[[],[[]]]],[],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[],[],[],[[[],[],[]]]]=>[[[[],[],[]]],[],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[],[],[],[[],[[[]]]]]=>[[[[[]]],[]],[],[],[]]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[],[],[],[[],[[],[]]]]=>[[[[],[]],[]],[],[],[]]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[],[],[],[[[]],[[]]]]=>[[[[]],[[]]],[],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[],[],[],[[],[],[[]]]]=>[[[[]],[],[]],[],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[],[],[],[[[[]]],[]]]=>[[[],[[[]]]],[],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[],[],[],[[[],[]],[]]]=>[[[],[[],[]]],[],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[],[],[],[[],[[]],[]]]=>[[[],[[]],[]],[],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[],[],[],[[[]],[],[]]]=>[[[],[],[[]]],[],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[[]]]],[[[[]]]]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[[[]]]],[[[],[]]]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[[[]]]],[[],[[]]]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[[[[]]]],[[[]],[]]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[[[]]]],[[],[],[]]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[[],[]]],[[[[]]]]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[[],[]]],[[[],[]]]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[[],[]]],[[],[[]]]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[[[],[]]],[[[]],[]]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[[],[]]],[[],[],[]]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[]]],[[[[]]]]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[],[[]]],[[[],[]]]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[],[[]]],[[],[[]]]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[],[[]]],[[[]],[]]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[[],[[]]],[[],[],[]]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[[]],[]],[[[[]]]]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[[]],[]],[[[],[]]]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[[]],[]],[[],[[]]]]=>[[[[]],[]],[[],[[]]]]=>[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]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[[[]],[]],[[],[],[]]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[],[]],[[[[]]]]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[],[],[]],[[[],[]]]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[],[],[]],[[],[[]]]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[],[],[]],[[[]],[]]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[[],[],[]],[[],[],[]]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[],[[[]]],[[[[]]]]]=>[[[[[]]]],[[[]]],[]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[],[[[]]],[[[],[]]]]=>[[[[],[]]],[[[]]],[]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[],[[[]]],[[],[[]]]]=>[[[[]],[]],[[[]]],[]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[],[[[]]],[[[]],[]]]=>[[[],[[]]],[[[]]],[]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[],[[[]]],[[],[],[]]]=>[[[],[],[]],[[[]]],[]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[],[[],[]],[[[[]]]]]=>[[[[[]]]],[[],[]],[]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[],[[],[]],[[[],[]]]]=>[[[[],[]]],[[],[]],[]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[],[[],[]],[[],[[]]]]=>[[[[]],[]],[[],[]],[]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[],[[],[]],[[[]],[]]]=>[[[],[[]]],[[],[]],[]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[],[[],[]],[[],[],[]]]=>[[[],[],[]],[[],[]],[]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[]],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[[]]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[]],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[[]]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[]],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[[]]]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[]],[[]],[[[]],[]]]=>[[[],[[]]],[[]],[[]]]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[]],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[[]]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[],[],[[]],[[[[]]]]]=>[[[[[]]]],[[]],[],[]]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[],[],[[]],[[[],[]]]]=>[[[[],[]]],[[]],[],[]]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[],[],[[]],[[],[[]]]]=>[[[[]],[]],[[]],[],[]]=>[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]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[],[],[[]],[[],[],[]]]=>[[[],[],[]],[[]],[],[]]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[]]],[],[[[[]]]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[]]],[],[[[],[]]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[]]],[],[[],[[]]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[[[]]],[],[[[]],[]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[]]],[],[[],[],[]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[],[]],[],[[[[]]]]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[],[]],[],[[[],[]]]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[],[]],[],[[],[[]]]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[],[]],[],[[[]],[]]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[],[]],[],[[],[],[]]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[],[[]],[],[[[[]]]]]=>[[[[[]]]],[],[[]],[]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[],[[]],[],[[[],[]]]]=>[[[[],[]]],[],[[]],[]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[],[[]],[],[[],[[]]]]=>[[[[]],[]],[],[[]],[]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[],[[]],[],[[[]],[]]]=>[[[],[[]]],[],[[]],[]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[],[[]],[],[[],[],[]]]=>[[[],[],[]],[],[[]],[]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[]],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[[]]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[]],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[[]]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[]],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[[]]]=>[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]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[]],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[[]]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[],[],[],[],[[[],[]]]]=>[[[[],[]]],[],[],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[],[],[],[],[[],[[]]]]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[],[],[],[],[[],[],[]]]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[[[[]]]]],[[[]]]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[[[[]]]]],[[],[]]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[[[],[]]]],[[[]]]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[[],[[]]]],[[[]]]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[[],[[]]]],[[],[]]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[[[]],[]]],[[[]]]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[[[]],[]]],[[],[]]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[[],[],[]]],[[[]]]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[[],[],[]]],[[],[]]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[],[[[]]]],[[[]]]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[[],[[[]]]],[[],[]]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[],[]]],[[[]]]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[[],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[[]],[[]]],[[[]]]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[[]],[[]]],[[],[]]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[[],[],[[]]],[[[]]]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[[],[],[[]]],[[],[]]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[[[]]],[]],[[[]]]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[[[[]]],[]],[[],[]]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[[],[]],[]],[[[]]]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[[],[]],[]],[[],[]]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[]],[]],[[[]]]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[[],[[]],[]],[[],[]]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[[]],[],[]],[[[]]]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[[]],[],[]],[[],[]]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[],[],[]],[[[]]]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[],[],[],[]],[[],[]]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[],[[[[]]]],[[[]]]]=>[[[[]]],[[[[]]]],[]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[],[[[[]]]],[[],[]]]=>[[[],[]],[[[[]]]],[]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[],[[[],[]]],[[[]]]]=>[[[[]]],[[[],[]]],[]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[],[[[],[]]],[[],[]]]=>[[[],[]],[[[],[]]],[]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[],[[],[[]]],[[[]]]]=>[[[[]]],[[[]],[]],[]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[],[[],[[]]],[[],[]]]=>[[[],[]],[[[]],[]],[]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[],[[[]],[]],[[[]]]]=>[[[[]]],[[],[[]]],[]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[],[[[]],[]],[[],[]]]=>[[[],[]],[[],[[]]],[]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[],[[],[],[]],[[[]]]]=>[[[[]]],[[],[],[]],[]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[],[[],[],[]],[[],[]]]=>[[[],[]],[[],[],[]],[]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[]],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[[]]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[]],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[[]]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[]],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[[]]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[]],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[[]]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[],[],[[[]]],[[[]]]]=>[[[[]]],[[[]]],[],[]]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[],[],[[[]]],[[],[]]]=>[[[],[]],[[[]]],[],[]]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[],[],[[],[]],[[[]]]]=>[[[[]]],[[],[]],[],[]]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[],[],[[],[]],[[],[]]]=>[[[],[]],[[],[]],[],[]]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[]]],[[]],[[[]]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[]]],[[]],[[],[]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[],[]],[[]],[[[]]]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[],[]],[[]],[[],[]]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[],[[]],[[]],[[[]]]]=>[[[[]]],[[]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[],[[]],[[]],[[],[]]]=>[[[],[]],[[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[]],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[[]]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[]],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[[]]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[],[],[],[[]],[[[]]]]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[],[],[],[[]],[[],[]]]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[[]]]],[],[[[]]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[[[]]]],[],[[],[]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[]]],[],[[[]]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[[],[]]],[],[[],[]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[],[[]]],[],[[[]]]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[],[[]]],[],[[],[]]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[]],[]],[],[[[]]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[[]],[]],[],[[],[]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[],[],[]],[],[[[]]]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[],[],[]],[],[[],[]]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[],[[[]]],[],[[[]]]]=>[[[[]]],[],[[[]]],[]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[],[[[]]],[],[[],[]]]=>[[[],[]],[],[[[]]],[]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[],[[],[]],[],[[[]]]]=>[[[[]]],[],[[],[]],[]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[],[[],[]],[],[[],[]]]=>[[[],[]],[],[[],[]],[]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[]],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[[]]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[]],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[[]]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[],[],[[]],[],[[[]]]]=>[[[[]]],[],[[]],[],[]]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[],[],[[]],[],[[],[]]]=>[[[],[]],[],[[]],[],[]]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[]]],[],[],[[[]]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[]]],[],[],[[],[]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[],[]],[],[],[[[]]]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[],[]],[],[],[[],[]]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[],[[]],[],[],[[[]]]]=>[[[[]]],[],[],[[]],[]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[],[[]],[],[],[[],[]]]=>[[[],[]],[],[],[[]],[]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[]],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[[]]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[]],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[[]]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[],[[[]]]]=>[[[[]]],[],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[[[[[[],[]]]]],[[]]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[[[],[[]]]]],[[]]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[[[[]],[]]]],[[]]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[[[],[],[]]]],[[]]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[[],[[[]]]]],[[]]]=>[[[]],[[[[[]]],[]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[[],[[],[]]]],[[]]]=>[[[]],[[[[],[]],[]]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[[[]],[[]]]],[[]]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[[],[],[[]]]],[[]]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[[[[]]],[]]],[[]]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[[[],[]],[]]],[[]]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[[],[[]],[]]],[[]]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[[[]],[],[]]],[[]]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[[[],[],[],[]]],[[]]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[[],[[[[]]]]],[[]]]=>[[[]],[[[[[]]]],[]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[[],[[[],[]]]],[[]]]=>[[[]],[[[[],[]]],[]]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[],[[],[[]]]],[[]]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[[],[[[]],[]]],[[]]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[[],[[],[],[]]],[[]]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[[]],[[[]]]],[[]]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[[]],[[],[]]],[[]]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[[],[],[[[]]]],[[]]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[[],[],[[],[]]],[[]]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[[[]]],[[]]],[[]]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[[],[]],[[]]],[[]]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[]],[[]]],[[]]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[[]],[],[[]]],[[]]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[],[],[[]]],[[]]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[[[[]]]],[]],[[]]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[[[],[]]],[]],[[]]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[[],[[]]],[]],[[]]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[[[]],[]],[]],[[]]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[[],[],[]],[]],[[]]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[[],[[[]]],[]],[[]]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[],[]],[]],[[]]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[[]],[[]],[]],[[]]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[[],[],[[]],[]],[[]]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[[[]]],[],[]],[[]]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[[],[]],[],[]],[[]]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[],[[]],[],[]],[[]]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[[[]],[],[],[]],[[]]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[[],[],[],[],[]],[[]]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[],[[[[[]]]]],[[]]]=>[[[]],[[[[[]]]]],[]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[],[[[[],[]]]],[[]]]=>[[[]],[[[[],[]]]],[]]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[],[[[],[[]]]],[[]]]=>[[[]],[[[[]],[]]],[]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[],[[[[]],[]]],[[]]]=>[[[]],[[[],[[]]]],[]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[],[[[],[],[]]],[[]]]=>[[[]],[[[],[],[]]],[]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[],[[],[[[]]]],[[]]]=>[[[]],[[[[]]],[]],[]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[],[[],[[],[]]],[[]]]=>[[[]],[[[],[]],[]],[]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[],[[[]],[[]]],[[]]]=>[[[]],[[[]],[[]]],[]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[],[[],[],[[]]],[[]]]=>[[[]],[[[]],[],[]],[]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[],[[[[]]],[]],[[]]]=>[[[]],[[],[[[]]]],[]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[],[[[],[]],[]],[[]]]=>[[[]],[[],[[],[]]],[]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[],[[],[[]],[]],[[]]]=>[[[]],[[],[[]],[]],[]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[],[[[]],[],[]],[[]]]=>[[[]],[[],[],[[]]],[]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[],[[],[],[],[]],[[]]]=>[[[]],[[],[],[],[]],[]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[]],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[[]]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[]],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[[]]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[]],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[[]]]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[]],[[[]],[]],[[]]]=>[[[]],[[],[[]]],[[]]]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[]],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[[]]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[],[],[[[[]]]],[[]]]=>[[[]],[[[[]]]],[],[]]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[],[],[[[],[]]],[[]]]=>[[[]],[[[],[]]],[],[]]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[],[],[[],[[]]],[[]]]=>[[[]],[[[]],[]],[],[]]=>[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]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[],[],[[],[],[]],[[]]]=>[[[]],[[],[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[[]]],[[[]]],[[]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[]]],[[],[]],[[]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[],[]],[[[]]],[[]]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[],[]],[[],[]],[[]]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[],[[]],[[[]]],[[]]]=>[[[]],[[[]]],[[]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[],[[]],[[],[]],[[]]]=>[[[]],[[],[]],[[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[]],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[[]]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[]],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[[]]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[],[],[],[[[]]],[[]]]=>[[[]],[[[]]],[],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[],[],[],[[],[]],[[]]]=>[[[]],[[],[]],[],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[[[]]]],[[]],[[]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[[],[]]],[[]],[[]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[],[[]]],[[]],[[]]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[]],[]],[[]],[[]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[],[],[]],[[]],[[]]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[],[[[]]],[[]],[[]]]=>[[[]],[[]],[[[]]],[]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[],[[],[]],[[]],[[]]]=>[[[]],[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[]],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[[]]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[],[],[[]],[[]],[[]]]=>[[[]],[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[]]],[],[[]],[[]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[],[]],[],[[]],[[]]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[],[[]],[],[[]],[[]]]=>[[[]],[[]],[],[[]],[]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[]],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[[]]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[[[[]]]]],[],[[]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[[[],[]]]],[],[[]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[[[],[[]]]],[],[[]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[[[]],[]]],[],[[]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[[[[],[],[]]],[],[[]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[[[],[[[]]]],[],[[]]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[[[],[[],[]]],[],[[]]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[[]],[[]]],[],[[]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[],[],[[]]],[],[[]]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[[[]]],[]],[],[[]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[[],[]],[]],[],[[]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[[[],[[]],[]],[],[[]]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[.,[[[.,[.,.]],.],.]],.],[.,.]]=>[[[[]],[],[]],[],[[]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[[[],[],[],[]],[],[[]]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[],[[[[]]]],[],[[]]]=>[[[]],[],[[[[]]]],[]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[[],[[[],[]]],[],[[]]]=>[[[]],[],[[[],[]]],[]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[[],[[],[[]]],[],[[]]]=>[[[]],[],[[[]],[]],[]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[[],[[[]],[]],[],[[]]]=>[[[]],[],[[],[[]]],[]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[[],[[],[],[]],[],[[]]]=>[[[]],[],[[],[],[]],[]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[[]],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[[]]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[[]],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[[]]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[],[],[[[]]],[],[[]]]=>[[[]],[],[[[]]],[],[]]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[[],[],[[],[]],[],[[]]]=>[[[]],[],[[],[]],[],[]]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[]]],[[]],[],[[]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],[.,.]],.],[.,.]]=>[[[],[]],[[]],[],[[]]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[],[[]],[[]],[],[[]]]=>[[[]],[],[[]],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[[]],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[[]]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[],[],[],[[]],[],[[]]]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[[[[]]]],[],[],[[]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[[[[],[]]],[],[],[[]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[[[],[[]]],[],[],[[]]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[[[[]],[]],[],[],[[]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[[[],[],[]],[],[],[[]]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[],[[[]]],[],[],[[]]]=>[[[]],[],[],[[[]]],[]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[[],[[],[]],[],[],[[]]]=>[[[]],[],[],[[],[]],[]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[[]],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[[]]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[],[],[[]],[],[],[[]]]=>[[[]],[],[],[[]],[],[]]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[[[]]],[],[],[],[[]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[[[],[]],[],[],[],[[]]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[],[[]],[],[],[],[[]]]=>[[[]],[],[],[],[[]],[]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[]]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[[[[[[[[]]]]]]],[]]=>[[],[[[[[[[]]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[[[[[[[],[]]]]]],[]]=>[[],[[[[[[],[]]]]]]]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[[[[[[],[[]]]]]],[]]=>[[],[[[[[[]],[]]]]]]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[[[[[[[]],[]]]]],[]]=>[[],[[[[[],[[]]]]]]]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[[[[[[],[],[]]]]],[]]=>[[],[[[[[],[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[[[[[],[[[]]]]]],[]]=>[[],[[[[[[]]],[]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[[[[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[[[[[[]],[[]]]]],[]]=>[[],[[[[[]],[[]]]]]]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[[[[[],[],[[]]]]],[]]=>[[],[[[[[]],[],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[[[[[[[]]],[]]]],[]]=>[[],[[[[],[[[]]]]]]]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[[[[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[[[[[],[[]],[]]]],[]]=>[[],[[[[],[[]],[]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[[[[[[]],[],[]]]],[]]=>[[],[[[[],[],[[]]]]]]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[[[[[],[],[],[]]]],[]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[[[[],[[[[]]]]]],[]]=>[[],[[[[[[]]]],[]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[[[[],[[[],[]]]]],[]]=>[[],[[[[[],[]]],[]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[[[[],[[],[[]]]]],[]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[[[[],[[[]],[]]]],[]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[[[[],[[],[],[]]]],[]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[[[[[]],[[[]]]]],[]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[[[[[]],[[],[]]]],[]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[[[[],[],[[[]]]]],[]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[.,[.,[[[.,.],.],[[.,.],.]]]],.]=>[[[[],[],[[],[]]]],[]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[[[[[[]]],[[]]]],[]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[[[[[],[]],[[]]]],[]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[[[[],[[]],[[]]]],[]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[[[[[]],[],[[]]]],[]]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[[[[],[],[],[[]]]],[]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[[[[[[[]]]],[]]],[]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[[[[[[],[]]],[]]],[]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[[[[[],[[]]],[]]],[]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[[[[[[]],[]],[]]],[]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[[[[[],[],[]],[]]],[]]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[[[[],[[[]]],[]]],[]]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[[[[],[[],[]],[]]],[]]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[[[[[]],[[]],[]]],[]]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[[[[],[],[[]],[]]],[]]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[[[[[[]]],[],[]]],[]]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[[[[[],[]],[],[]]],[]]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[[[[],[[]],[],[]]],[]]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[.,[.,[[[[.,[.,.]],.],.],.]]],.]=>[[[[[]],[],[],[]]],[]]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[[[[],[],[],[],[]]],[]]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[[[],[[[[[]]]]]],[]]=>[[],[[[[[[]]]]],[]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[[[],[[[[],[]]]]],[]]=>[[],[[[[[],[]]]],[]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[[[],[[[],[[]]]]],[]]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[[[],[[[[]],[]]]],[]]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[[[],[[[],[],[]]]],[]]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[[[],[[],[[[]]]]],[]]=>[[],[[[[[]]],[]],[]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[[[],[[],[[],[]]]],[]]=>[[],[[[[],[]],[]],[]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[[[],[[[]],[[]]]],[]]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[[[],[[],[],[[]]]],[]]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[[[],[[[[]]],[]]],[]]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[[[],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[[[],[[],[[]],[]]],[]]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[[[],[[[]],[],[]]],[]]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[[[],[[],[],[],[]]],[]]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[[[[]],[[[[]]]]],[]]=>[[],[[[[[]]]],[[]]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[[[[]],[[[],[]]]],[]]=>[[],[[[[],[]]],[[]]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[[[[]],[[],[[]]]],[]]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[[[[]],[[[]],[]]],[]]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[[[[]],[[],[],[]]],[]]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[[[],[],[[[[]]]]],[]]=>[[],[[[[[]]]],[],[]]]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[[[],[],[[[],[]]]],[]]=>[[],[[[[],[]]],[],[]]]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[[[],[],[[],[[]]]],[]]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[[[],[],[[[]],[]]],[]]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[[[],[],[[],[],[]]],[]]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[[[[]]],[[[]]]],[]]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[[[[]]],[[],[]]],[]]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[[[[],[]],[[[]]]],[]]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[[[[],[]],[[],[]]],[]]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[[],[[]],[[[]]]],[]]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[[[],[[]],[[],[]]],[]]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[[[[]],[],[[[]]]],[]]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[[[[]],[],[[],[]]],[]]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[[],[],[],[[[]]]],[]]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[[[],[],[],[[],[]]],[]]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[[[[[[]]]],[[]]],[]]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[[[[],[]]],[[]]],[]]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[[[[],[[]]],[[]]],[]]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[[[]],[]],[[]]],[]]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[[[[],[],[]],[[]]],[]]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[[[],[[[]]],[[]]],[]]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[[],[[],[]],[[]]],[]]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[[[[]],[[]],[[]]],[]]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,[[[[.,.],.],[.,.]],[.,.]]],.]=>[[[],[],[[]],[[]]],[]]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[[[[[]]],[],[[]]],[]]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[[[[],[]],[],[[]]],[]]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[[[],[[]],[],[[]]],[]]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,[[[[.,[.,.]],.],.],[.,.]]],.]=>[[[[]],[],[],[[]]],[]]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[[[],[],[],[],[[]]],[]]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[[[[[[[]]]]],[]],[]]=>[[],[[],[[[[[]]]]]]]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[[[[[[],[]]]],[]],[]]=>[[],[[],[[[[],[]]]]]]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[[[[[],[[]]]],[]],[]]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[[[[[[]],[]]],[]],[]]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[[[[[],[],[]]],[]],[]]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[[[[],[[[]]]],[]],[]]=>[[],[[],[[[[]]],[]]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[[[[],[[],[]]],[]],[]]=>[[],[[],[[[],[]],[]]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[[[[[]],[[]]],[]],[]]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[[[[],[],[[]]],[]],[]]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[[[[[[]]],[]],[]],[]]=>[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[[[],[]],[]],[]],[]]=>[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[[[[],[[]],[]],[]],[]]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[[[]],[],[]],[]],[]]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[[[[],[],[],[]],[]],[]]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[[[],[[[[]]]],[]],[]]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,[[[.,.],[.,[[.,.],.]]],.]],.]=>[[[],[[[],[]]],[]],[]]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[[[],[[],[[]]],[]],[]]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[[[],[[[]],[]],[]],[]]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[[[],[[],[],[]],[]],[]]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[[[[]],[[[]]],[]],[]]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[[[[]],[[],[]],[]],[]]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[[[],[],[[[]]],[]],[]]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[[[],[],[[],[]],[]],[]]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[[[[[]]],[[]],[]],[]]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[[[[],[]],[[]],[]],[]]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[[[],[[]],[[]],[]],[]]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
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[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[[[[[[]]]],[],[]],[]]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[[[],[]]],[],[]],[]]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[[[[],[[]]],[],[]],[]]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[[[]],[]],[],[]],[]]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
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[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[[],[[[],[[[]]]]],[]]=>[[],[[[[[]]],[]]],[]]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
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[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[[],[[[[]],[[]]]],[]]=>[[],[[[[]],[[]]]],[]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[[],[[[],[],[[]]]],[]]=>[[],[[[[]],[],[]]],[]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]=>[[],[[[[[]]],[]]],[]]=>[[],[[[],[[[]]]]],[]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
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[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[[],[[],[[[]],[]]],[]]=>[[],[[[],[[]]],[]],[]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[[],[[],[[],[],[]]],[]]=>[[],[[[],[],[]],[]],[]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[[],[[[]],[[[]]]],[]]=>[[],[[[[]]],[[]]],[]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
[[[.,.],[[.,[.,.]],[[.,.],.]]],.]=>[[],[[[]],[[],[]]],[]]=>[[],[[[],[]],[[]]],[]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
[[[.,.],[[[.,.],.],[.,[.,.]]]],.]=>[[],[[],[],[[[]]]],[]]=>[[],[[[[]]],[],[]],[]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[[],[[],[],[[],[]]],[]]=>[[],[[[],[]],[],[]],[]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[[],[[[[]]],[[]]],[]]=>[[],[[[]],[[[]]]],[]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[[],[[[],[]],[[]]],[]]=>[[],[[[]],[[],[]]],[]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[[],[[],[[]],[[]]],[]]=>[[],[[[]],[[]],[]],[]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[[],[[[]],[],[[]]],[]]=>[[],[[[]],[],[[]]],[]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[[],[[],[],[],[[]]],[]]=>[[],[[[]],[],[],[]],[]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[[],[[[[[]]]],[]],[]]=>[[],[[],[[[[]]]]],[]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[[],[[[[],[]]],[]],[]]=>[[],[[],[[[],[]]]],[]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[[],[[[],[[]]],[]],[]]=>[[],[[],[[[]],[]]],[]]=>[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]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[[],[[[],[],[]],[]],[]]=>[[],[[],[[],[],[]]],[]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[[],[[],[[[]]],[]],[]]=>[[],[[],[[[]]],[]],[]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[[]],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[[]]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
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[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[[[]],[[[],[[]]]],[]]=>[[],[[[[]],[]]],[[]]]=>[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]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[[[]],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[[[]],[[],[[[]]]],[]]=>[[],[[[[]]],[]],[[]]]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[]],[[],[[],[]]],[]]=>[[],[[[],[]],[]],[[]]]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[]],[[[]],[[]]],[]]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[[[]],[[],[],[[]]],[]]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[[[]],[[[[]]],[]],[]]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[[[]],[[[],[]],[]],[]]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[[[]],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[]],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[[[]],[[],[],[],[]],[]]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[[],[],[[[[[]]]]],[]]=>[[],[[[[[]]]]],[],[]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
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[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[[],[],[[[],[],[]]],[]]=>[[],[[[],[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
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[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[[],[],[[],[[]],[]],[]]=>[[],[[],[[]],[]],[],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[[],[],[[[]],[],[]],[]]=>[[],[[],[],[[]]],[],[]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
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[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[[[]]],[[[[]]]],[]]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[[]]],[[[],[]]],[]]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[]]],[[],[[]]],[]]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[[[[]]],[[[]],[]],[]]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
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[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
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[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[[[]]],[]],[[]],[]]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
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[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[[],[],[[],[]]],[],[]]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[[[]]],[[]]],[],[]]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[[[],[]],[[]]],[],[]]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[[],[[]],[[]]],[],[]]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[[]],[],[[]]],[],[]]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[[],[],[],[[]]],[],[]]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[[[[]]]],[]],[],[]]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[[],[]]],[]],[],[]]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[[[[],[[]]],[]],[],[]]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[[]],[]],[]],[],[]]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[[],[],[]],[]],[],[]]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[],[[[]]],[]],[],[]]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[[],[[],[]],[]],[],[]]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[[]],[[]],[]],[],[]]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[[],[],[[]],[]],[],[]]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[[[]]],[],[]],[],[]]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[[],[]],[],[]],[],[]]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[[[],[[]],[],[]],[],[]]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[[[[]],[],[],[]],[],[]]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[[[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[[],[[[[[]]]]],[],[]]=>[[],[],[[[[[]]]]],[]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[[],[[[[],[]]]],[],[]]=>[[],[],[[[[],[]]]],[]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[[],[[[],[[]]]],[],[]]=>[[],[],[[[[]],[]]],[]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[[],[[[[]],[]]],[],[]]=>[[],[],[[[],[[]]]],[]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[[],[[[],[],[]]],[],[]]=>[[],[],[[[],[],[]]],[]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[[],[[],[[[]]]],[],[]]=>[[],[],[[[[]]],[]],[]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[[],[[],[[],[]]],[],[]]=>[[],[],[[[],[]],[]],[]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[[],[[[]],[[]]],[],[]]=>[[],[],[[[]],[[]]],[]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[[],[[],[],[[]]],[],[]]=>[[],[],[[[]],[],[]],[]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[[],[[[[]]],[]],[],[]]=>[[],[],[[],[[[]]]],[]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
[[[[.,.],[[.,[[.,.],.]],.]],.],.]=>[[],[[[],[]],[]],[],[]]=>[[],[],[[],[[],[]]],[]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
[[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[[],[[],[[]],[]],[],[]]=>[[],[],[[],[[]],[]],[]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[[],[[[]],[],[]],[],[]]=>[[],[],[[],[],[[]]],[]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[[],[[],[],[],[]],[],[]]=>[[],[],[[],[],[],[]],[]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[[[]],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[[]]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[[[]],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[[]]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[[[]],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[[]]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[[[]],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[[]]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[[[]],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[[]]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[[],[],[[[[]]]],[],[]]=>[[],[],[[[[]]]],[],[]]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[[],[],[[[],[]]],[],[]]=>[[],[],[[[],[]]],[],[]]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[[],[],[[],[[]]],[],[]]=>[[],[],[[[]],[]],[],[]]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[[],[],[[[]],[]],[],[]]=>[[],[],[[],[[]]],[],[]]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[[],[],[[],[],[]],[],[]]=>[[],[],[[],[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[[[[]]],[[[]]],[],[]]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[]]],[[],[]],[],[]]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[[[],[]],[[[]]],[],[]]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[[[],[]],[[],[]],[],[]]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[[],[[]],[[[]]],[],[]]=>[[],[],[[[]]],[[]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[[],[[]],[[],[]],[],[]]=>[[],[],[[],[]],[[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[[[]],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[[]]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
[[[[[.,[.,.]],.],[[.,.],.]],.],.]=>[[[]],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[[]]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[[],[],[],[[[]]],[],[]]=>[[],[],[[[]]],[],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[[],[],[],[[],[]],[],[]]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[[[[[]]]],[[]],[],[]]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[[[[],[]]],[[]],[],[]]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[[[],[[]]],[[]],[],[]]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[[[[]],[]],[[]],[],[]]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[[[],[],[]],[[]],[],[]]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[[],[[[]]],[[]],[],[]]=>[[],[],[[]],[[[]]],[]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[[],[[],[]],[[]],[],[]]=>[[],[],[[]],[[],[]],[]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[]],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[[]]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[],[],[[]],[[]],[],[]]=>[[],[],[[]],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[[[[]]],[],[[]],[],[]]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[[[],[]],[],[[]],[],[]]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[],[[]],[],[[]],[],[]]=>[[],[],[[]],[],[[]],[]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[]],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[[]]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[[[[[],[]]]],[],[],[]]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[[[[],[[]]]],[],[],[]]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[[]],[]]],[],[],[]]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[],[],[]]],[],[],[]]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[],[[[]]]],[],[],[]]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[[[],[[],[]]],[],[],[]]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[]],[[]]],[],[],[]]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[],[],[[]]],[],[],[]]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[]]],[]],[],[],[]]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[],[]],[]],[],[],[]]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[],[[]],[]],[],[],[]]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[[[[]],[],[]],[],[],[]]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[[[],[],[],[]],[],[],[]]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[],[[[[]]]],[],[],[]]=>[[],[],[],[[[[]]]],[]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[],[[[],[]]],[],[],[]]=>[[],[],[],[[[],[]]],[]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[],[[],[[]]],[],[],[]]=>[[],[],[],[[[]],[]],[]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[],[[[]],[]],[],[],[]]=>[[],[],[],[[],[[]]],[]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[],[[],[],[]],[],[],[]]=>[[],[],[],[[],[],[]],[]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[]],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[[]]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[]],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[[]]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[],[],[[[]]],[],[],[]]=>[[],[],[],[[[]]],[],[]]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[],[],[[],[]],[],[],[]]=>[[],[],[],[[],[]],[],[]]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[]]],[[]],[],[],[]]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[],[]],[[]],[],[],[]]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[],[[]],[[]],[],[],[]]=>[[],[],[],[[]],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[]],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[[]]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[],[]]],[],[],[],[]]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[],[[]]],[],[],[],[]]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[]],[]],[],[],[],[]]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[],[],[]],[],[],[],[]]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[],[[[]]],[],[],[],[]]=>[[],[],[],[],[[[]]],[]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[],[[],[]],[],[],[],[]]=>[[],[],[],[],[[],[]],[]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[]],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[[]]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[],[],[[]],[],[],[],[]]=>[[],[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[],[]],[],[],[],[],[]]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[]]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
to ordered tree: left child = left brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
- if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
- if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
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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