Identifier
Mp00010:
Binary trees
—to ordered tree: left child = left brother⟶
Ordered trees
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0021;cc-rep-1Cc0005;cc-rep-2
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[[[.,.],[[.,.],[.,.]]],.]=>[[],[[],[[]]],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0]
[[[.,.],[[.,[.,.]],.]],.]=>[[],[[[]],[]],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0]
[[[.,.],[[[.,.],.],.]],.]=>[[],[[],[],[]],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,[.,.]]],.]=>[[[]],[[[]]],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[.,[.,.]],[[.,.],.]],.]=>[[[]],[[],[]],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[[[.,.],.],[.,[.,.]]],.]=>[[],[],[[[]]],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0]
[[[[.,.],.],[[.,.],.]],.]=>[[],[],[[],[]],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0]
[[[.,[.,[.,.]]],[.,.]],.]=>[[[[]]],[[]],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[.,[[.,.],.]],[.,.]],.]=>[[[],[]],[[]],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],[.,.]],.]=>[[],[[]],[[]],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],[.,.]],.]=>[[[]],[],[[]],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],.],.],[.,.]],.]=>[[],[],[],[[]],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0]
[[[.,[.,[.,[.,.]]]],.],.]=>[[[[[]]]],[],[]]=>[1,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,.],.]]],.],.]=>[[[[],[]]],[],[]]=>[1,1,1,0,1,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,.]]],.],.]=>[[[],[[]]],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],.]],.],.]=>[[[[]],[]],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0]
[[[.,[[[.,.],.],.]],.],.]=>[[[],[],[]],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0]
[[[[.,.],[.,[.,.]]],.],.]=>[[],[[[]]],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],.]],.],.]=>[[],[[],[]],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,.]],[.,.]],.],.]=>[[[]],[[]],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,.],.],[.,.]],.],.]=>[[],[],[[]],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],.],.]=>[[[[]]],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,.],.]],.],.],.]=>[[[],[]],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,.],[.,.]],.],.],.]=>[[],[[]],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],.],.],.],.]=>[[[]],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],.],.],.],.],.]=>[[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[[]]]]]]]]=>[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]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[[[[[[],[[]]]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[[[[[[[]],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[[[[[[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[[[[[],[[[]]]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[[[[[],[[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[[[[[[]],[[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[[[[[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[[[[[[[]]],[]]]]]=>[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]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[[[[[],[[]],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[[[[[[]],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[[[[[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[[[[],[[[[]]]]]]]=>[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]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[[[[],[[],[[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[[[[],[[[]],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[[[[],[[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[[[[[]],[[[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[[[[[]],[[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[[[[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
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[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[[[[[[]]],[[]]]]]=>[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]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[[[[],[[]],[[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[[[[[]],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[[[[],[],[],[[]]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[[[[[[[]]]],[]]]]=>[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]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[[[[[],[[]]],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[[[[[[]],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[[[[[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[[[[],[[[]]],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[[[[],[[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[[[[[]],[[]],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[[[[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[[[[[[]]],[],[]]]]=>[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]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[[[],[[]],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[[[[[]],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[[[[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[],[[[[[]]]]]]]=>[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]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[],[[[],[[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[[[],[[[[]],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[[[],[[[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[[[],[[],[[[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[[[],[[],[[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[[[],[[[]],[[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[[[],[[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[[[],[[[[]]],[]]]]=>[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]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[[[],[[],[[]],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[[[],[[[]],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[[[],[[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[]],[[[[]]]]]]=>[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]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[]],[[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[[[[]],[[[]],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
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[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[[[]]],[[[]]]]]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[[[[]]],[[],[]]]]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[[[[],[]],[[[]]]]]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[[[[],[]],[[],[]]]]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
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[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[[[[[]],[]],[[]]]]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
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[.,[[[[.,.],.],[[.,.],.]],.]]=>[[[],[],[[],[]],[]]]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[[[[[]]],[[]],[]]]=>[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]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[[[],[[]],[[]],[]]]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[[[[]],[],[[]],[]]]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[[[],[],[],[[]],[]]]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[[[[[[]]]],[],[]]]=>[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]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[[[[],[[]]],[],[]]]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[[[[[]],[]],[],[]]]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[[[[],[],[]],[],[]]]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[[[],[[[]]],[],[]]]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[[[],[[],[]],[],[]]]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[[[[]],[[]],[],[]]]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[[[],[],[[]],[],[]]]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[[[[[]]],[],[],[]]]=>[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]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[[[],[[]],[],[],[]]]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[[[[]],[],[],[],[]]]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[.,[[[[[[.,.],.],.],.],.],.]]=>[[[],[],[],[],[],[]]]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[[[[[[]]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[[],[[[[[],[]]]]]]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[[],[[[[],[[]]]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[[],[[[[[]],[]]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[[],[[[[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[],[[[],[[[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[[],[[[],[[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[],[[[[]],[[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[[],[[[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[],[[[[[]]],[]]]]=>[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]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[[],[[[],[[]],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[[],[[[[]],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[[],[[[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[],[[],[[[[]]]]]]=>[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]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[[],[[],[[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[[],[[],[[[]],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[[],[[],[[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[],[[[]],[[[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[[],[[[]],[[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[[],[[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[[],[[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[],[[[[]]],[[]]]]=>[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]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[[],[[],[[]],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[[],[[[]],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[[],[[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[],[[[[[]]]],[]]]=>[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]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[[],[[[],[[]]],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[[],[[[[]],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[[],[[[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[],[[],[[[]]],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[[],[[],[[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[[],[[[]],[[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[[],[[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[[],[[[[]]],[],[]]]=>[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]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[[],[[],[[]],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[[],[[[]],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,.],[[[[[.,.],.],.],.],.]]=>[[],[[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[]],[[[[[]]]]]]=>[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]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[]],[[[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[]],[[[[]],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[]],[[[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[]],[[],[[[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[]],[[],[[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[]],[[[]],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[]],[[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[[]],[[[[]]],[]]]=>[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]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[[[]],[[],[[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[[[]],[[[]],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[[[]],[[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[[[[[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[[],[],[[[[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[[],[],[[[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[[],[],[[[[]],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[[],[],[[[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[[],[],[[],[[[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[[],[],[[],[[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[[],[],[[[]],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[[],[],[[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[[],[],[[[[]]],[]]]=>[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]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[[],[],[[],[[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[[],[],[[[]],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[.,.],.],[[[[.,.],.],.],.]]=>[[],[],[[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[]]],[[[[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[[]]],[[[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[[]]],[[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[[[]]],[[[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[[]]],[[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[],[]],[[[[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[],[]],[[[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[],[]],[[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[[[],[]],[[[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[],[]],[[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[],[[]],[[[[]]]]]=>[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]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[[],[[]],[[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[[],[[]],[[[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[[],[[]],[[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[]],[],[[[[]]]]]=>[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]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[]],[],[[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[]],[],[[[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[]],[],[[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,.],.],.],[[[.,.],.],.]]=>[[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[[[]]]],[[[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[[[]]]],[[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]]],[[[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[[],[]]],[[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[],[[]]],[[[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[],[[]]],[[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[[]],[]],[[[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[[]],[]],[[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[],[[[]]],[[[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[],[[[]]],[[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[],[[],[]],[[[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[[],[[],[]],[[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[]],[[]],[[[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[]],[[]],[[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[],[],[[]],[[[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[[],[],[[]],[[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[]]],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[[]]],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[],[]],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[[[],[]],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[],[[]],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
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[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[]],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
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[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[[[[]]],[]],[[]]]=>[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]
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[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[],[[[[]]]],[[]]]=>[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]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[[],[[],[[]]],[[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[[],[[[]],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[[],[[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
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[[[.,.],[[.,[.,[.,.]]],.]],.]=>[[],[[[[]]],[]],[]]=>[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]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[[],[[],[[]],[]],[]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
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[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[[[[[[]]]]],[],[]]=>[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]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[[[[],[[]]]],[],[]]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[[[]],[]]],[],[]]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[[[[],[],[]]],[],[]]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[],[[[]]]],[],[]]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[[[],[[],[]]],[],[]]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[[]],[[]]],[],[]]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[[[],[],[[]]],[],[]]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[[[]]],[]],[],[]]=>[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]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[[[],[[]],[]],[],[]]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[[[[]],[],[]],[],[]]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
[[[.,[[[[.,.],.],.],.]],.],.]=>[[[],[],[],[]],[],[]]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[[],[[[[]]]],[],[]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[[],[[[],[]]],[],[]]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[[],[[],[[]]],[],[]]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[[],[[[]],[]],[],[]]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
[[[[.,.],[[[.,.],.],.]],.],.]=>[[],[[],[],[]],[],[]]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[]],[[[]]],[],[]]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[[[]],[[],[]],[],[]]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[[],[],[[[]]],[],[]]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],.]],.],.]=>[[],[],[[],[]],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[]]],[[]],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[[[],[]],[[]],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[[],[[]],[[]],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[[[]],[],[[]],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[[.,.],.],.],[.,.]],.],.]=>[[],[],[],[[]],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[[]]]],[],[],[]]=>[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]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[[[],[[]]],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[]],[]],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
[[[[.,[[[.,.],.],.]],.],.],.]=>[[[],[],[]],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[[],[[[]]],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
[[[[[.,.],[[.,.],.]],.],.],.]=>[[],[[],[]],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[[[]],[[]],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[.,.],.],[.,.]],.],.],.]=>[[],[],[[]],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[]]],[],[],[],[]]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[.,.],.]],.],.],.],.]=>[[[],[]],[],[],[],[]]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[.,.]],.],.],.],.]=>[[],[[]],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],.],.],.],.],.]=>[[[]],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[[]]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[[[[[[],[]]]]]]]]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[[[[[[[],[[]]]]]]]]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[[[[[[]],[]]]]]]]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[[[[[],[],[]]]]]]]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[[[[[],[[[]]]]]]]]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[[[[[],[[],[]]]]]]]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[[[[[[[]],[[]]]]]]]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[[[[[],[],[[]]]]]]]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[[[[[[[[]]],[]]]]]]=>[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]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[[[[[[],[[]],[]]]]]]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[[[[[[[]],[],[]]]]]]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[[],[],[],[]]]]]]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[[[[[],[[[[]]]]]]]]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[[[[[],[[[],[]]]]]]]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[[[[[],[[],[[]]]]]]]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[[[[[],[[[]],[]]]]]]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[[[[[],[[],[],[]]]]]]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[[[[[[]],[[[]]]]]]]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[[[[[[]],[[],[]]]]]]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[[[[],[],[[[]]]]]]]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[[[[[],[],[[],[]]]]]]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[[[[[[[]]],[[]]]]]]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[[[[[[],[]],[[]]]]]]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[[[[[],[[]],[[]]]]]]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[[[[[[]],[],[[]]]]]]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[[[[[],[],[],[[]]]]]]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[[[[[[[[]]]],[]]]]]=>[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]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[[[[[[],[[]]],[]]]]]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[[[[[[[]],[]],[]]]]]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[[[[[],[],[]],[]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[[[[[],[[[]]],[]]]]]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[[[[[],[[],[]],[]]]]]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[[[[[[]],[[]],[]]]]]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[[[[[],[],[[]],[]]]]]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[[[[[[[]]],[],[]]]]]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[[[[[[],[]],[],[]]]]]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[[[[[],[[]],[],[]]]]]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[[[[[[]],[],[],[]]]]]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[[[[[],[],[],[],[]]]]]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[[[[],[[[[[]]]]]]]]=>[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]
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[[[[],[[[],[[]]]]]]]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[[[[],[[[[]],[]]]]]]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[[[[],[[[],[],[]]]]]]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[[[[],[[],[[[]]]]]]]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[[[[],[[],[[],[]]]]]]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[[[[],[[[]],[[]]]]]]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[[[[],[[],[],[[]]]]]]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[[[[],[[[[]]],[]]]]]=>[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]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[[[[],[[],[[]],[]]]]]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[[[[],[[[]],[],[]]]]]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[[[[],[[],[],[],[]]]]]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[[[[[]],[[[[]]]]]]]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[[[[[]],[[[],[]]]]]]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[[[[[]],[[],[[]]]]]]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[[[[[]],[[[]],[]]]]]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[[[[[]],[[],[],[]]]]]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[[[[],[],[[[[]]]]]]]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[[[[],[],[[[],[]]]]]]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[[[[],[],[[],[[]]]]]]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[[[[],[],[[[]],[]]]]]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[[[[],[],[[],[],[]]]]]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[[[[[[]]],[[[]]]]]]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[[[[[[]]],[[],[]]]]]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[[[[[],[]],[[[]]]]]]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[[[[[],[]],[[],[]]]]]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[[[[],[[]],[[[]]]]]]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[[[[],[[]],[[],[]]]]]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[[[[]],[],[[[]]]]]]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]
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[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[[[],[],[],[[[]]]]]]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
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[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[[[[],[[]]],[[]]]]]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[[[[[[]],[]],[[]]]]]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]
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[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[[[[[]],[[]],[[]]]]]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]=>[[[[],[],[[]],[[]]]]]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[[[[[[]]],[],[[]]]]]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[[[[[],[]],[],[[]]]]]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[[[[],[[]],[],[[]]]]]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[[[[[]],[],[],[[]]]]]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]
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[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[[[[[[[[]]]]],[]]]]=>[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]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[[[[[[],[[]]]],[]]]]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[[[[[[[]],[]]],[]]]]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[[[[[[],[],[]]],[]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[[[[[],[[[]]]],[]]]]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[[[[[],[[],[]]],[]]]]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[[[[[[]],[[]]],[]]]]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[[[[[],[],[[]]],[]]]]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[[[[[[[]]],[]],[]]]]=>[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]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[[[[[],[[]],[]],[]]]]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[[[[[[]],[],[]],[]]]]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[[[[],[],[],[]],[]]]]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[[[[],[[[[]]]],[]]]]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[[[[],[[[],[]]],[]]]]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[[[[],[[],[[]]],[]]]]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[[[[],[[[]],[]],[]]]]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[[[[],[[],[],[]],[]]]]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[[[[[]],[[[]]],[]]]]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],[[.,.],.]],.]]]=>[[[[[]],[[],[]],[]]]]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[[[[],[],[[[]]],[]]]]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[[[[],[],[[],[]],[]]]]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[[[[[[]]],[[]],[]]]]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[[[[[],[]],[[]],[]]]]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[[[[],[[]],[[]],[]]]]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[[[[[]],[],[[]],[]]]]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[[[[],[],[],[[]],[]]]]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[[[[[[[]]]],[],[]]]]=>[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]
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[[[[[],[[]]],[],[]]]]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[.,[[.,[.,.]],.]],.],.]]]=>[[[[[[]],[]],[],[]]]]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[[[[[],[],[]],[],[]]]]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[[[[],[[[]]],[],[]]]]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[[[[],[[],[]],[],[]]]]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[[[[[]],[[]],[],[]]]]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[[[[],[],[[]],[],[]]]]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[[[[[[]]],[],[],[]]]]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[[[[[],[]],[],[],[]]]]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[[[[],[[]],[],[],[]]]]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[[[[[]],[],[],[],[]]]]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[[],[],[],[],[],[]]]]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[],[[[[[[]]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[[[],[[[[[],[]]]]]]]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[[[],[[[[],[[]]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[[[],[[[[[]],[]]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[[[],[[[[],[],[]]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[[[],[[[],[[[]]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[[[],[[[],[[],[]]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[[[],[[[[]],[[]]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[[[],[[[],[],[[]]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[[[],[[[[[]]],[]]]]]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[[[],[[[[],[]],[]]]]]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[[[],[[[],[[]],[]]]]]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]
[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[[[],[[[[]],[],[]]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[[[],[[[],[],[],[]]]]]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[[[],[[],[[[[]]]]]]]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[[[],[[],[[[],[]]]]]]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[],[[],[[],[[]]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[[[],[[],[[[]],[]]]]]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[[],[[],[[],[],[]]]]]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[[[],[[[]],[[[]]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[[[],[[[]],[[],[]]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[[[],[[],[],[[[]]]]]]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[[[],[[],[],[[],[]]]]]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[[[],[[[[]]],[[]]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[[[],[[[],[]],[[]]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[[[],[[],[[]],[[]]]]]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[[[],[[[]],[],[[]]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[[[],[[],[],[],[[]]]]]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[[[],[[[[[]]]],[]]]]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[[[],[[[[],[]]],[]]]]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[[],[[[],[[]]],[]]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[[[],[[[[]],[]],[]]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[[],[[[],[],[]],[]]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[[[],[[],[[[]]],[]]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[[],[[],[[],[]],[]]]]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[],[[[]],[[]],[]]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[[],[[],[],[[]],[]]]]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[[],[[[[]]],[],[]]]]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[[],[[[],[]],[],[]]]]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[[],[[],[[]],[],[]]]]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[[],[[[]],[],[],[]]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[],[[],[],[],[],[]]]]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[[[[]],[[[[[]]]]]]]=>[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]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[[]],[[[],[[]]]]]]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[[[[]],[[[[]],[]]]]]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[[[[]],[[[],[],[]]]]]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[[[[]],[[],[[[]]]]]]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[[[[]],[[],[[],[]]]]]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[]],[[[]],[[]]]]]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[[[]],[[],[],[[]]]]]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[[[[]],[[[[]]],[]]]]=>[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]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[[[[]],[[],[[]],[]]]]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[[[[]],[[[]],[],[]]]]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[[[[]],[[],[],[],[]]]]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[[],[],[[[[[]]]]]]]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]
[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]=>[[[],[],[[[[],[]]]]]]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[[[],[],[[[],[[]]]]]]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[[[],[],[[[[]],[]]]]]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[[[],[],[[[],[],[]]]]]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[[[],[],[[],[[[]]]]]]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[[[],[],[[],[[],[]]]]]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[[[],[],[[[]],[[]]]]]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[[[],[],[[],[],[[]]]]]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[[[],[],[[[[]]],[]]]]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[[[],[],[[[],[]],[]]]]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[[[],[],[[],[[]],[]]]]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]
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[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[[[[]],[],[[],[],[]]]]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]
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[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[[[[],[[]]],[[[]]]]]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[[[[],[[]]],[[],[]]]]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[[[[[]],[]],[[[]]]]]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]
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[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[[[]],[[]],[[[]]]]]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]
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[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[[],[[[[],[],[],[]]]]]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[[],[[[],[[[[]]]]]]]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[[],[[[],[[[],[]]]]]]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[[],[[[],[[],[[]]]]]]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>[[],[[[],[[[]],[]]]]]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[[],[[[],[[],[],[]]]]]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[[],[[[[]],[[[]]]]]]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[[],[[[[]],[[],[]]]]]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[[],[[[],[],[[[]]]]]]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[[],[[[],[],[[],[]]]]]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[[],[[[[[]]],[[]]]]]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[[],[[[[],[]],[[]]]]]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[[],[[[],[[]],[[]]]]]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[[],[[[[]],[],[[]]]]]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
[[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>[[],[[[],[],[],[[]]]]]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[[],[[[[[[]]]],[]]]]=>[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]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[],[[[[],[[]]],[]]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[[],[[[[[]],[]],[]]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[[],[[[[],[],[]],[]]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[[],[[[],[[[]]],[]]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[[],[[[],[[],[]],[]]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[[],[[[[]],[[]],[]]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[[],[[[],[],[[]],[]]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[[],[[[[[]]],[],[]]]]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[[],[[[[],[]],[],[]]]]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[[],[[[],[[]],[],[]]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[[],[[[[]],[],[],[]]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[[],[[[],[],[],[],[]]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[],[[],[[[[[]]]]]]]=>[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]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[[],[[],[[[],[[]]]]]]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[[],[[],[[[[]],[]]]]]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[[],[[],[[[],[],[]]]]]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[[],[[],[[],[[[]]]]]]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[],[[],[[],[[],[]]]]]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[],[[],[[[]],[[]]]]]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[[],[[],[[],[],[[]]]]]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[[],[[],[[[[]]],[]]]]=>[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]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[[],[[],[[],[[]],[]]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[[],[[],[[[]],[],[]]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[],[[],[[],[],[],[]]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[[],[[[]],[[[[]]]]]]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[],[[[]],[[[],[]]]]]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[],[[[]],[[],[[]]]]]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[[],[[[]],[[[]],[]]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[],[[[]],[[],[],[]]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[[],[[],[],[[[[]]]]]]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[[],[[],[],[[[],[]]]]]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[[],[[],[],[[],[[]]]]]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[[],[[],[],[[[]],[]]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[[],[[],[],[[],[],[]]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[],[[[[]]],[[[]]]]]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[],[[[[]]],[[],[]]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[[],[[[],[]],[[[]]]]]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[],[[[],[]],[[],[]]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[[],[[],[[]],[[[]]]]]=>[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[[],[[],[[]],[[],[]]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[[],[[[]],[],[[[]]]]]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[[],[[[]],[],[[],[]]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[[],[[],[],[],[[[]]]]]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[],[[],[],[],[[],[]]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[[],[[[[[]]]],[[]]]]=>[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]
[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[[],[[[],[[]]],[[]]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[[],[[[[]],[]],[[]]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
[[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>[[],[[[],[],[]],[[]]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[[],[[],[[[]]],[[]]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
[[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[[],[[],[[],[]],[[]]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[[],[[[]],[[]],[[]]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[],[[],[],[[]],[[]]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[],[[[[]]],[],[[]]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[[],[[[],[]],[],[[]]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[],[[],[[]],[],[[]]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[],[[[]],[],[],[[]]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[[],[[],[],[],[],[[]]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[],[[[[[[]]]]],[]]]=>[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]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[[],[[[[],[[]]]],[]]]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[[],[[[[[]],[]]],[]]]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[[],[[[[],[],[]]],[]]]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[[],[[[],[[[]]]],[]]]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[[],[[[],[[],[]]],[]]]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[[],[[[[]],[[]]],[]]]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[[],[[[],[],[[]]],[]]]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[[],[[[[[]]],[]],[]]]=>[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]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[[],[[[],[[]],[]],[]]]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[[],[[[[]],[],[]],[]]]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[[],[[[],[],[],[]],[]]]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[[],[[],[[[[]]]],[]]]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[[],[[],[[[],[]]],[]]]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[[],[[],[[],[[]]],[]]]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[[],[[],[[[]],[]],[]]]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[[],[[],[[],[],[]],[]]]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[[],[[[]],[[[]]],[]]]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[],[[[]],[[],[]],[]]]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[[],[[],[],[[[]]],[]]]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[],[[],[],[[],[]],[]]]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[],[[[[]]],[[]],[]]]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[[],[[[],[]],[[]],[]]]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[],[[],[[]],[[]],[]]]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>[[],[[[]],[],[[]],[]]]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[[],[[],[],[],[[]],[]]]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[[],[[[[[]]]],[],[]]]=>[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]
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[[],[[[],[[]]],[],[]]]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[[],[[[[]],[]],[],[]]]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[[],[[[],[],[]],[],[]]]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[[],[[],[[[]]],[],[]]]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[[],[[],[[],[]],[],[]]]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[[],[[[]],[[]],[],[]]]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[[],[[],[],[[]],[],[]]]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[],[[[[]]],[],[],[]]]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[[],[[[],[]],[],[],[]]]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[[],[[],[[]],[],[],[]]]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[[],[[[]],[],[],[],[]]]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[],[[],[],[],[],[],[]]]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[]],[[[[[[]]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[[[]],[[[[[],[]]]]]]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[[[]],[[[[],[[]]]]]]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[[[]],[[[[[]],[]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[[[]],[[[[],[],[]]]]]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[[[]],[[[],[[[]]]]]]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[]],[[[],[[],[]]]]]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[]],[[[[]],[[]]]]]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[[[]],[[[],[],[[]]]]]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[[[]],[[[[[]]],[]]]]=>[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]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[[[]],[[[],[[]],[]]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[]],[[[[]],[],[]]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[]],[[[],[],[],[]]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[]],[[],[[[[]]]]]]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[]],[[],[[[],[]]]]]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[]],[[],[[],[[]]]]]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[]],[[],[[[]],[]]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[]],[[],[[],[],[]]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[]],[[[]],[[[]]]]]=>[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[]],[[[]],[[],[]]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[]],[[],[],[[[]]]]]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[]],[[],[],[[],[]]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[[[]],[[[[]]],[[]]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[[[]],[[[],[]],[[]]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[]],[[],[[]],[[]]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[]],[[[]],[],[[]]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[]],[[],[],[],[[]]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[[[]],[[[[[]]]],[]]]=>[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]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[[[]],[[[],[[]]],[]]]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[]],[[[[]],[]],[]]]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[[[]],[[[],[],[]],[]]]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[[]],[[],[[[]]],[]]]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[]],[[],[[],[]],[]]]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[]],[[[]],[[]],[]]]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[[]],[[],[],[[]],[]]]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[[]],[[[[]]],[],[]]]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[[]],[[[],[]],[],[]]]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[[]],[[],[[]],[],[]]]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[]],[[[]],[],[],[]]]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[[]],[[],[],[],[],[]]]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[],[[[[[[]]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[],[],[[[[[],[]]]]]]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[],[],[[[[],[[]]]]]]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[],[],[[[[[]],[]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[],[],[[[[],[],[]]]]]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[],[],[[[],[[[]]]]]]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[],[],[[[],[[],[]]]]]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[],[],[[[[]],[[]]]]]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[],[],[[[],[],[[]]]]]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[],[],[[[[[]]],[]]]]=>[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]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[],[],[[[],[[]],[]]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[],[],[[[[]],[],[]]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[],[],[[[],[],[],[]]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[],[],[[],[[[[]]]]]]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[],[],[[],[[[],[]]]]]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[],[],[[],[[],[[]]]]]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[],[],[[],[[[]],[]]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[],[],[[],[[],[],[]]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[],[],[[[]],[[[]]]]]=>[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[],[],[[[]],[[],[]]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[],[],[[],[],[[[]]]]]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[],[],[[],[],[[],[]]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[],[],[[[[]]],[[]]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[],[],[[[],[]],[[]]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[],[],[[],[[]],[[]]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[],[],[[[]],[],[[]]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[[],[],[[],[],[],[[]]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[],[],[[[[[]]]],[]]]=>[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]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[],[],[[[],[[]]],[]]]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[],[],[[[[]],[]],[]]]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[],[],[[[],[],[]],[]]]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[],[],[[],[[[]]],[]]]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[],[],[[],[[],[]],[]]]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[],[],[[[]],[[]],[]]]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[],[],[[],[],[[]],[]]]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[],[],[[[[]]],[],[]]]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[],[],[[[],[]],[],[]]]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[],[],[[],[[]],[],[]]]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[],[],[[[]],[],[],[]]]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[[],[],[[],[],[],[],[]]]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[]]],[[[[[]]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[[]]],[[[[],[]]]]]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[[]]],[[[],[[]]]]]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[[[[]]],[[[[]],[]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[[]]],[[[],[],[]]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[[]]],[[],[[[]]]]]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[[]]],[[],[[],[]]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[[[[]]],[[[]],[[]]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[[]]],[[],[],[[]]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[[[[]]],[[[[]]],[]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[[[[]]],[[[],[]],[]]]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[[]]],[[],[[]],[]]]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[[[[]]],[[[]],[],[]]]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[[]]],[[],[],[],[]]]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[[[],[]],[[[[[]]]]]]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[[[],[]],[[[[],[]]]]]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[[[],[]],[[[],[[]]]]]=>[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[[[],[]],[[[[]],[]]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[[[],[]],[[[],[],[]]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[[[],[]],[[],[[[]]]]]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[],[]],[[],[[],[]]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[],[]],[[[]],[[]]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[],[]],[[],[],[[]]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[[[],[]],[[[[]]],[]]]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[[],[]],[[[],[]],[]]]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[],[]],[[],[[]],[]]]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[[[],[]],[[[]],[],[]]]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[[],[]],[[],[],[],[]]]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[],[[]],[[[[[]]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[],[[]],[[[[],[]]]]]=>[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[],[[]],[[[],[[]]]]]=>[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[],[[]],[[[[]],[]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[],[[]],[[[],[],[]]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[],[[]],[[],[[[]]]]]=>[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[],[[]],[[],[[],[]]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[],[[]],[[[]],[[]]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[],[[]],[[],[],[[]]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[],[[]],[[[[]]],[]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[],[[]],[[[],[]],[]]]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[],[[]],[[],[[]],[]]]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[],[[]],[[[]],[],[]]]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[],[[]],[[],[],[],[]]]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[]],[],[[[[[]]]]]]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[]],[],[[[[],[]]]]]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[]],[],[[[],[[]]]]]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[]],[],[[[[]],[]]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[]],[],[[[],[],[]]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[]],[],[[],[[[]]]]]=>[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[]],[],[[],[[],[]]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[]],[],[[[]],[[]]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[[[]],[],[[],[],[[]]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[[]],[],[[[[]]],[]]]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[[]],[],[[[],[]],[]]]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[[[]],[],[[],[[]],[]]]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[]],[],[[[]],[],[]]]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[[[]],[],[[],[],[],[]]]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[],[[[[[]]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[[],[],[],[[[[],[]]]]]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[[],[],[],[[[],[[]]]]]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[[],[],[],[[[[]],[]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[[],[],[],[[[],[],[]]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[[],[],[],[[],[[[]]]]]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[],[],[],[[],[[],[]]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[],[],[],[[[]],[[]]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[[],[],[],[[],[],[[]]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[[],[],[],[[[[]]],[]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[[],[],[],[[[],[]],[]]]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[[],[],[],[[],[[]],[]]]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[[],[],[],[[[]],[],[]]]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[],[],[],[[],[],[],[]]]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[[]]]],[[[[]]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[[[[[]]]],[[[],[]]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[[[[[]]]],[[],[[]]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[[[[[]]]],[[[]],[]]]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[[[[[]]]],[[],[],[]]]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[[[[],[]]],[[[[]]]]]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[[],[]]],[[[],[]]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[[[[],[]]],[[],[[]]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[[[[],[]]],[[[]],[]]]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[[[[],[]]],[[],[],[]]]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[]]],[[[[]]]]]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[[[],[[]]],[[[],[]]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[],[[]]],[[],[[]]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[[],[[]]],[[[]],[]]]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[[[],[[]]],[[],[],[]]]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[[[[]],[]],[[[[]]]]]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[[[[]],[]],[[[],[]]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[[]],[]],[[],[[]]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[[]],[]],[[[]],[]]]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[[[[]],[]],[[],[],[]]]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[],[]],[[[[]]]]]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[[[],[],[]],[[[],[]]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[[[],[],[]],[[],[[]]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[[[],[],[]],[[[]],[]]]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[[],[],[]],[[],[],[]]]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[],[[[]]],[[[[]]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[],[[[]]],[[[],[]]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[],[[[]]],[[],[[]]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[],[[[]]],[[[]],[]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[],[[[]]],[[],[],[]]]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[],[[],[]],[[[[]]]]]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[],[[],[]],[[[],[]]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[],[[],[]],[[],[[]]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[],[[],[]],[[[]],[]]]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[],[[],[]],[[],[],[]]]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[]],[[]],[[[[]]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[]],[[]],[[[],[]]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[]],[[]],[[],[[]]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[]],[[]],[[[]],[]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[]],[[]],[[],[],[]]]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[],[],[[]],[[[[]]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[],[],[[]],[[[],[]]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[],[],[[]],[[],[[]]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[[],[],[[]],[[[]],[]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[],[],[[]],[[],[],[]]]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[]]],[],[[[[]]]]]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[]]],[],[[[],[]]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[]]],[],[[],[[]]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[[[[]]],[],[[[]],[]]]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[]]],[],[[],[],[]]]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[],[]],[],[[[[]]]]]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[[[],[]],[],[[[],[]]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[[[],[]],[],[[],[[]]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[[[],[]],[],[[[]],[]]]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[[[],[]],[],[[],[],[]]]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[],[[]],[],[[[[]]]]]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[],[[]],[],[[[],[]]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[],[[]],[],[[],[[]]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[],[[]],[],[[[]],[]]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[],[[]],[],[[],[],[]]]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[]],[],[],[[[[]]]]]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[]],[],[],[[[],[]]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[]],[],[],[[],[[]]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[[[]],[],[],[[[]],[]]]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[[]],[],[],[[],[],[]]]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[],[[[[]]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[],[],[],[],[[[],[]]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[],[],[],[],[[],[[]]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[],[],[],[],[[[]],[]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[],[],[],[],[[],[],[]]]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[[[[]]]]],[[[]]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[[[[[[]]]]],[[],[]]]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[[[],[]]]],[[[]]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[[[],[]]]],[[],[]]]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[[[[],[[]]]],[[[]]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[[[[],[[]]]],[[],[]]]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[[[]],[]]],[[[]]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[[[]],[]]],[[],[]]]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[[[[],[],[]]],[[[]]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[[[[],[],[]]],[[],[]]]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[[[],[[[]]]],[[[]]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[[[],[[[]]]],[[],[]]]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[],[]]],[[[]]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[[[],[[],[]]],[[],[]]]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[[[[]],[[]]],[[[]]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[[[[]],[[]]],[[],[]]]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[[[],[],[[]]],[[[]]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[[[],[],[[]]],[[],[]]]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[[[[[]]],[]],[[[]]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[[[[[]]],[]],[[],[]]]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[[[[],[]],[]],[[[]]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[[[[],[]],[]],[[],[]]]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[]],[]],[[[]]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[[[],[[]],[]],[[],[]]]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[[[[]],[],[]],[[[]]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[[[[]],[],[]],[[],[]]]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[],[],[]],[[[]]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[[[],[],[],[]],[[],[]]]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[],[[[[]]]],[[[]]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[[],[[[[]]]],[[],[]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[],[[[],[]]],[[[]]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[[],[[[],[]]],[[],[]]]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[[],[[],[[]]],[[[]]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[],[[],[[]]],[[],[]]]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[],[[[]],[]],[[[]]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[],[[[]],[]],[[],[]]]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[],[[],[],[]],[[[]]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[],[[],[],[]],[[],[]]]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[]],[[[]]],[[[]]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[]],[[[]]],[[],[]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[]],[[],[]],[[[]]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[]],[[],[]],[[],[]]]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[],[],[[[]]],[[[]]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[[],[],[[[]]],[[],[]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[[],[],[[],[]],[[[]]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[],[],[[],[]],[[],[]]]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[]]],[[]],[[[]]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[]]],[[]],[[],[]]]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[],[]],[[]],[[[]]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[[[],[]],[[]],[[],[]]]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[],[[]],[[]],[[[]]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[],[[]],[[]],[[],[]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[]],[],[[]],[[[]]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[[]],[],[[]],[[],[]]]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[],[],[],[[]],[[[]]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[],[],[],[[]],[[],[]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[[[]]]],[],[[[]]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[[[[[]]]],[],[[],[]]]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[[[[],[]]],[],[[[]]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[[[[],[]]],[],[[],[]]]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[[[],[[]]],[],[[[]]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[[[],[[]]],[],[[],[]]]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[[[[]],[]],[],[[[]]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[[[[]],[]],[],[[],[]]]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[],[],[]],[],[[[]]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[[[],[],[]],[],[[],[]]]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[],[[[]]],[],[[[]]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[],[[[]]],[],[[],[]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[],[[],[]],[],[[[]]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[],[[],[]],[],[[],[]]]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[]],[[]],[],[[[]]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[[]],[[]],[],[[],[]]]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[],[],[[]],[],[[[]]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[[],[],[[]],[],[[],[]]]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[]]],[],[],[[[]]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[]]],[],[],[[],[]]]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[],[]],[],[],[[[]]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[],[]],[],[],[[],[]]]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[],[[]],[],[],[[[]]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[],[[]],[],[],[[],[]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[]],[],[],[],[[[]]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[[[]],[],[],[],[[],[]]]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[],[],[],[],[],[[[]]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[],[],[],[],[],[[],[]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[[[[[]]]]]],[[]]]=>[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]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[[[[[],[[]]]]],[[]]]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[[[[[[]],[]]]],[[]]]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[[[[[],[],[]]]],[[]]]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[[[[],[[[]]]]],[[]]]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[[[[],[[],[]]]],[[]]]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[[[[[]],[[]]]],[[]]]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[[[[],[],[[]]]],[[]]]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[[[[[[]]],[]]],[[]]]=>[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]
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[[[[],[[]],[]]],[[]]]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[[[]],[],[]]],[[]]]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[[[[],[],[],[]]],[[]]]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[[[],[[[[]]]]],[[]]]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[[[],[[[],[]]]],[[]]]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[[[],[[],[[]]]],[[]]]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]=>[[[],[[[]],[]]],[[]]]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[[[],[[],[],[]]],[[]]]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[[[[]],[[[]]]],[[]]]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[[[[]],[[],[]]],[[]]]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[[],[],[[[]]]],[[]]]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[[],[],[[],[]]],[[]]]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[[[[]]],[[]]],[[]]]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[[[],[]],[[]]],[[]]]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[]],[[]]],[[]]]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[[[]],[],[[]]],[[]]]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[],[],[[]]],[[]]]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[[[[[]]]],[]],[[]]]=>[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]
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[[[],[[]]],[]],[[]]]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[[[]],[]],[]],[[]]]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[[],[],[]],[]],[[]]]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[[],[[[]]],[]],[[]]]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[],[]],[]],[[]]]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[[]],[[]],[]],[[]]]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[[],[],[[]],[]],[[]]]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[[[[]]],[],[]],[[]]]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[[[],[]],[],[]],[[]]]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[[],[[]],[],[]],[[]]]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[[[]],[],[],[]],[[]]]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[[],[],[],[],[]],[[]]]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[],[[[[[]]]]],[[]]]=>[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]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[],[[[],[[]]]],[[]]]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[],[[[[]],[]]],[[]]]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[],[[[],[],[]]],[[]]]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[],[[],[[[]]]],[[]]]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[],[[],[[],[]]],[[]]]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[],[[[]],[[]]],[[]]]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[],[[],[],[[]]],[[]]]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[],[[[[]]],[]],[[]]]=>[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]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[],[[],[[]],[]],[[]]]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[],[[[]],[],[]],[[]]]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[],[[],[],[],[]],[[]]]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
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[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[],[],[[],[]],[],[],[]]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[]]],[[]],[],[],[]]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[],[]],[[]],[],[],[]]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[],[[]],[[]],[],[],[]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[]],[],[[]],[],[],[]]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[],[],[],[[]],[],[],[]]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[]]]],[],[],[],[]]=>[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]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[],[[]]],[],[],[],[]]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[]],[]],[],[],[],[]]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[],[],[]],[],[],[],[]]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[],[[[]]],[],[],[],[]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[],[[],[]],[],[],[],[]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[]],[[]],[],[],[],[]]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[],[],[[]],[],[],[],[]]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[]]],[],[],[],[],[]]=>[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]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[],[[]],[],[],[],[],[]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[]],[],[],[],[],[],[]]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[],[]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
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
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
Sorry, this map was not found in the database.