Identifier
Mp00018:
Binary trees
—left border symmetry⟶
Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0005;cc-rep-2
[.,.]=>[.,.]=>[1,0]
[.,[.,.]]=>[.,[.,.]]=>[1,1,0,0]
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[[.,.],[.,.]]=>[[.,[.,.]],.]=>[1,1,0,0,1,0]
[[.,[.,.]],.]=>[[.,.],[.,.]]=>[1,0,1,1,0,0]
[[[.,.],.],.]=>[[[.,.],.],.]=>[1,0,1,0,1,0]
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[.,[.,[[.,.],.]]]=>[.,[.,[[.,.],.]]]=>[1,1,1,0,1,0,0,0]
[.,[[.,.],[.,.]]]=>[.,[[.,[.,.]],.]]=>[1,1,1,0,0,1,0,0]
[.,[[.,[.,.]],.]]=>[.,[[.,.],[.,.]]]=>[1,1,0,1,1,0,0,0]
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[[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>[1,1,1,0,0,0,1,0]
[[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>[1,1,0,1,0,0,1,0]
[[.,[.,.]],[.,.]]=>[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0]
[[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>[1,1,0,0,1,0,1,0]
[[.,[.,[.,.]]],.]=>[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0]
[[.,[[.,.],.]],.]=>[[.,.],[[.,.],.]]=>[1,0,1,1,0,1,0,0]
[[[.,.],[.,.]],.]=>[[[.,.],[.,.]],.]=>[1,0,1,1,0,0,1,0]
[[[.,[.,.]],.],.]=>[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0]
[[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>[1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,0,0]
[.,[.,[.,[[.,.],.]]]]=>[.,[.,[.,[[.,.],.]]]]=>[1,1,1,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],.]]]=>[1,1,1,1,0,0,1,0,0,0]
[.,[.,[[.,[.,.]],.]]]=>[.,[.,[[.,.],[.,.]]]]=>[1,1,1,0,1,1,0,0,0,0]
[.,[.,[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],.]]]=>[1,1,1,0,1,0,1,0,0,0]
[.,[[.,.],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],.]]=>[1,1,1,1,0,0,0,1,0,0]
[.,[[.,.],[[.,.],.]]]=>[.,[[.,[[.,.],.]],.]]=>[1,1,1,0,1,0,0,1,0,0]
[.,[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[.,.]]]=>[1,1,1,0,0,1,1,0,0,0]
[.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[1,1,1,0,0,1,0,1,0,0]
[.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[1,1,0,1,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[1,1,0,1,1,0,1,0,0,0]
[.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[1,1,0,1,1,0,0,1,0,0]
[.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[1,1,0,1,0,1,1,0,0,0]
[.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[1,1,0,1,0,1,0,1,0,0]
[[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[1,1,1,1,0,0,0,0,1,0]
[[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[1,1,1,0,1,0,0,0,1,0]
[[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[1,1,1,0,0,1,0,0,1,0]
[[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[1,1,0,1,1,0,0,0,1,0]
[[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[1,1,0,1,0,1,0,0,1,0]
[[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[1,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[1,1,0,1,0,0,1,1,0,0]
[[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[1,1,1,0,0,0,1,0,1,0]
[[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[1,1,0,1,0,0,1,0,1,0]
[[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[1,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[1,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[1,1,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[1,1,0,0,1,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[1,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[1,0,1,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[1,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],.],.]],.]=>[[.,.],[[[.,.],.],.]]=>[1,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,0]
[[[.,.],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],.]=>[1,0,1,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],.]=>[[[[.,.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,0]
[[[.,[.,[.,.]]],.],.]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0]
[[[.,[[.,.],.]],.],.]=>[[[.,.],.],[[.,.],.]]=>[1,0,1,0,1,1,0,1,0,0]
[[[[.,.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],.]=>[1,0,1,0,1,1,0,0,1,0]
[[[[.,[.,.]],.],.],.]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0]
[[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0]
[.,[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[1,1,1,1,1,0,1,0,0,0,0,0]
[.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[1,1,1,1,1,0,0,1,0,0,0,0]
[.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[1,1,1,1,0,1,1,0,0,0,0,0]
[.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[1,1,1,1,0,1,0,1,0,0,0,0]
[.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[1,1,1,1,1,0,0,0,1,0,0,0]
[.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[1,1,1,1,0,1,0,0,1,0,0,0]
[.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[1,1,1,1,0,0,1,1,0,0,0,0]
[.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[1,1,1,1,0,0,1,0,1,0,0,0]
[.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[1,1,1,0,1,1,1,0,0,0,0,0]
[.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[1,1,1,0,1,1,0,1,0,0,0,0]
[.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[1,1,1,0,1,1,0,0,1,0,0,0]
[.,[.,[[[.,[.,.]],.],.]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[1,1,1,0,1,0,1,1,0,0,0,0]
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[.,[[.,[.,[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[1,1,1,0,0,1,1,1,0,0,0,0]
[.,[[.,[[.,.],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[1,1,1,0,0,1,1,0,1,0,0,0]
[.,[[[.,.],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[1,1,1,0,0,1,1,0,0,1,0,0]
[.,[[[.,[.,.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[1,1,1,0,0,1,0,1,1,0,0,0]
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[[.,.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[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]
[[.,[.,.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[1,1,1,1,0,0,0,0,1,1,0,0]
[[.,[.,.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[1,1,1,0,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[1,1,1,0,0,1,0,0,1,1,0,0]
[[.,[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[1,1,0,1,1,0,0,0,1,1,0,0]
[[.,[.,.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,.]]=>[1,1,0,1,0,1,0,0,1,1,0,0]
[[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[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]
[[.,[.,[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0]
[[.,[.,[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[1,1,0,1,0,0,1,1,1,0,0,0]
[[.,[[.,.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[1,1,1,0,0,0,1,1,0,1,0,0]
[[.,[[.,.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],.]]=>[1,1,0,1,0,0,1,1,0,1,0,0]
[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[1,1,1,0,0,0,1,1,0,0,1,0]
[[[.,.],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],.]=>[1,1,0,1,0,0,1,1,0,0,1,0]
[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[1,1,1,0,0,0,1,0,1,1,0,0]
[[[.,[.,.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,.]]=>[1,1,0,1,0,0,1,0,1,1,0,0]
[[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[1,1,1,0,0,0,1,0,1,0,1,0]
[[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>[1,1,0,1,0,0,1,0,1,0,1,0]
[[.,[.,[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0]
[[.,[.,[[.,.],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[1,1,0,0,1,1,1,0,1,0,0,0]
[[.,[[.,.],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[1,1,0,0,1,1,1,0,0,1,0,0]
[[.,[[.,[.,.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[1,1,0,0,1,1,0,1,1,0,0,0]
[[.,[[[.,.],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],.]]=>[1,1,0,0,1,1,0,1,0,1,0,0]
[[[.,.],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[1,1,0,0,1,1,1,0,0,0,1,0]
[[[.,.],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],.]=>[1,1,0,0,1,1,0,1,0,0,1,0]
[[[.,[.,.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0]
[[[[.,.],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],.]=>[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]
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[[.,[.,[[.,.],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,0,1,1,1,1,0,0,1,0,0,0]
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[[.,[.,[[[.,.],.],.]]],.]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,0,1,1,1,0,1,0,1,0,0,0]
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[[.,[[.,[.,.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,.]]]=>[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]
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[[[[[.,.],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],.]=>[1,0,1,0,1,0,1,1,0,0,1,0]
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[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
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[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[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]
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[.,[[[.,.],[[.,.],.]],[.,.]]]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[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]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[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]
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[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[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]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]
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[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[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]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]
[.,[[.,[.,[[.,[[.,.],.]],.]]],.]]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]
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[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]
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[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[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]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[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]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[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]
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[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]
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[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]
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[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[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]
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[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[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]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[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]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[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]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[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]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[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]
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[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]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[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]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[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]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[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]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[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]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[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]
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[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]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[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]
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[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]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[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]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
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[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[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
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
The bijection is defined recursively as follows:
- a leaf is associated with an empty Dyck path,
- a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.
searching the database
Sorry, this map was not found in the database.