Identifier
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=>
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[[],[[[[],[]],[[[],[]],[]]],[[[],[]],[[],[]]]]]=>[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[[[[],[]],[[],[]]],[[[[],[]],[[],[[],[]]]],[]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]],[.,.]]]
[[[[],[]],[[[],[]],[]]],[[[],[]],[[],[[],[]]]]]=>[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]
[[[],[]],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]]
[[[],[]],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]]
[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[]],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]]
[[[],[]],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]]=>[[.,[.,.]],[[[.,.],[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]]
[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[]],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]
[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[]],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.],[.,.]]]
[[[],[]],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.],[.,.]]]
[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[]],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]]
[[[],[]],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.],[.,.]]]
[[[],[]],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]
[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[[[],[]],[]]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[]],[]]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]
[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[[[],[]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[]],[]]]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]]
[[[],[[[],[]],[]]],[[[],[[[],[[[],[]],[]]],[]]],[]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],[.,.]]],.]
[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]],.]
[[[],[[[],[]],[[[],[]],[]]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]
[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[[[],[]],[]]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.]],.]
[[[],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]],.]
[[[],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]],.]
[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[[[],[]],[]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]
[[[],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]],.]
[[[],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]],[]]=>[[.,[[[.,.],[.,.]],[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]]],.]
[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[[[],[]],[]]],[]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]
[[[],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]
[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]],[]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.]
[[],[[[],[[[],[[[],[[[],[[],[]]],[]]],[]]],[]]],[]]]=>[.,[[[.,[[[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]
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[[[],[[],[]]],[[[],[[[],[[[],[[],[]]],[]]],[]]],[]]]=>[[.,[[.,[.,.]],[[[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]],.]
[[[],[[],[]]],[[[],[[[[],[[],[]]],[[],[]]],[]]],[]]]=>[[.,[[.,.],[.,.]]],[[[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]],.],[.,.]]]
[[[],[[],[]]],[[[[],[[],[]]],[[[],[[],[]]],[]]],[]]]=>[[.,[[.,.],[.,.]]],[[[[.,[[.,.],[.,.]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]]
[[[],[[],[]]],[[[[],[[[],[[],[]]],[]]],[[],[]]],[]]]=>[[.,[[.,.],[.,.]]],[[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[[[],[[],[]]],[[[[[],[[],[]]],[[],[]]],[[],[]]],[]]]=>[[.,[[.,.],[.,.]]],[[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]]
[[[],[[[],[[],[]]],[]]],[[[],[[[],[[],[]]],[]]],[]]]=>[[.,[[[.,[[.,[.,.]],[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]],.],[.,.]]],.]
[[[],[[[],[[],[]]],[]]],[[[[],[[],[]]],[[],[]]],[]]]=>[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[[[],[[[],[[[],[[],[]]],[]]],[]]],[[[],[[],[]]],[]]]=>[[.,[[[.,[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[[],[]]],[]]],[]]],[]]],[[],[]]]=>[[.,[[[.,[[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[[],[[],[]]],[[],[]]],[]]],[]]],[[],[]]]=>[[.,[[[.,[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[.,.]]],.],[.,.]]],.]
[[[],[[[[],[[],[]]],[[],[]]],[]]],[[[],[[],[]]],[]]]=>[[.,[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]],.]
[[[],[[[[],[[],[]]],[[[],[[],[]]],[]]],[]]],[[],[]]]=>[[.,[[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[.,.],[.,.]]],[.,.]]],.]
[[[],[[[[],[[[],[[],[]]],[]]],[[],[]]],[]]],[[],[]]]=>[[.,[[[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]],.]
[[[],[[[[[],[[],[]]],[[],[]]],[[],[]]],[]]],[[],[]]]=>[[.,[[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]],.]
[[[[],[[],[]]],[[],[]]],[[[],[[[],[[],[]]],[]]],[]]]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]
[[[[],[[],[]]],[[],[]]],[[[[],[[],[]]],[[],[]]],[]]]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[[[[],[[],[]]],[[[],[[],[]]],[]]],[[[],[[],[]]],[]]]=>[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[[[[],[[],[]]],[[[],[[[],[[],[]]],[]]],[]]],[[],[]]]=>[[[.,[[.,[.,.]],[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]],.],[[.,.],[.,.]]]
[[[[],[[],[]]],[[[[],[[],[]]],[[],[]]],[]]],[[],[]]]=>[[[.,[[.,.],[.,.]]],[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[.,.]]],.]
[[[[],[[[],[[],[]]],[]]],[[],[]]],[[[],[[],[]]],[]]]=>[[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[[[[],[[[],[[],[]]],[]]],[[[],[[],[]]],[]]],[[],[]]]=>[[[.,[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[.,.]]],.],[[.,.],[.,.]]]
[[[[],[[[],[[[],[[],[]]],[]]],[]]],[[],[]]],[[],[]]]=>[[[.,[[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.],[.,.]]],.],[[.,.],[.,.]]]
[[[[],[[[[],[[],[]]],[[],[]]],[]]],[[],[]]],[[],[]]]=>[[[.,[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[.,.]]],.],[[.,.],[.,.]]]
[[[[[],[[],[]]],[[],[]]],[[],[]]],[[[],[[],[]]],[]]]=>[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]],[[.,.],[.,.]]]
[[[[[],[[],[]]],[[],[]]],[[[],[[],[]]],[]]],[[],[]]]=>[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[[[[[],[[],[]]],[[[],[[],[]]],[]]],[[],[]]],[[],[]]]=>[[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]]
[[[[[],[[[],[[],[]]],[]]],[[],[]]],[[],[]]],[[],[]]]=>[[[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]]
[[[[[[],[[],[]]],[[],[]]],[[],[]]],[[],[]]],[[],[]]]=>[[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]
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[[[],[[],[]]],[[[[],[[[],[]],[[],[]]]],[]],[[],[]]]]=>[[.,[[.,.],[.,.]]],[[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]],[[.,.],[.,.]]]]
[[[],[[],[]]],[[[[[],[]],[[],[]]],[[],[]]],[[],[]]]]=>[[.,[[.,.],[.,.]]],[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]]
[[[],[[[],[[],[]]],[[[],[[[],[]],[[],[]]]],[]]]],[]]=>[[.,[[[.,[[.,.],[.,.]]],[[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]]],.]],.]
[[[],[[[],[[],[]]],[[[[],[]],[[],[]]],[[],[]]]]],[]]=>[[.,[[[.,[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]]],.]],.]
[[[],[[[],[[[],[[],[]]],[[[],[]],[[],[]]]]],[]]],[]]=>[[.,[[[.,[[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[[],[]]],[[],[]]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[[],[[],[]]],[[],[]]],[[],[]]]],[]]],[]]=>[[.,[[[.,[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]]],.],[.,.]]],.]
[[[],[[[[],[[],[]]],[[[],[]],[[],[]]]],[[],[]]]],[]]=>[[.,[[[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[[.,.],[.,.]]]],.]
[[[],[[[[],[]],[[],[]]],[[],[[[],[]],[[],[]]]]]],[]]=>[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]]],.]
[[[],[[[[],[[[],[[],[]]],[[],[]]]],[]],[[],[]]]],[]]=>[[.,[[[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.],[.,.]],[[.,.],[.,.]]]],.]
[[[],[[[[[],[[],[]]],[[],[]]],[[],[]]],[[],[]]]],[]]=>[[.,[[[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]
[[[[],[[],[]]],[[[],[[[],[]],[[],[]]]],[]]],[[],[]]]=>[[[.,[[.,.],[.,.]]],[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.],[.,.]]],.]
[[[[],[[],[]]],[[[[],[]],[[],[]]],[[],[]]]],[[],[]]]=>[[[.,[[.,.],[.,.]]],[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]
[[[[],[[],[]]],[[[],[]],[[],[]]]],[[[],[]],[[],[]]]]=>[[[.,[[.,.],[.,.]]],[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]],.]
[[[[],[]],[[],[]]],[[],[[[],[[[],[]],[[],[]]]],[]]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.]]
[[[[],[]],[[],[]]],[[],[[[[],[]],[[],[]]],[[],[]]]]]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]]
[[[[],[[[],[[],[]]],[[[],[]],[[],[]]]]],[]],[[],[]]]=>[[[.,[[[.,[[.,.],[.,.]]],[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]],.],[.,.]]
[[[[],[[[],[]],[[],[]]]],[]],[[],[[[],[]],[[],[]]]]]=>[[[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]],.],[.,.]]
[[[[],[[[],[[[],[[],[]]],[[],[]]]],[]]],[]],[[],[]]]=>[[[.,[[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]],.],[.,.]]],.],[.,.]]
[[[[],[[[[],[[],[]]],[[],[]]],[[],[]]]],[]],[[],[]]]=>[[[.,[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]]],.],[.,.]]
[[[[[],[[],[]]],[[[],[]],[[],[]]]],[[],[]]],[[],[]]]=>[[[[.,[[.,.],[.,.]]],[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]
[[[[[],[]],[[],[]]],[[],[]]],[[],[[[],[]],[[],[]]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]],[[.,.],[.,.]]]
[[[[[],[]],[[],[]]],[[],[[[],[]],[[],[]]]]],[[],[]]]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,[.,.]],[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]]]
[[[[[],[[[],[[],[]]],[[],[]]]],[]],[[],[]]],[[],[]]]=>[[[[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]],.],[.,.]],[[.,.],[.,.]]]
[[[],[]],[[],[[],[[],[[],[[],[[],[[],[[],[]]]]]]]]]]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]],.]],.]],.]]
[[[],[[],[[],[[],[[],[[],[[],[[],[[],[]]]]]]]]]],[]]=>[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.]],.]],.]],.]],.]
[[[],[]],[[],[[],[[],[[],[[],[[],[[[],[]],[]]]]]]]]]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]],.]],.]],.]]
[[[],[[],[[],[[],[[],[[],[[],[[[],[]],[]]]]]]]]],[]]=>[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.]],.]],.]],.]],.]
[[],[[[[[[[[[[],[]],[]],[]],[]],[]],[]],[]],[]],[]]]=>[.,[[[[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[[[[[[[[[[],[]],[]],[]],[]],[]],[]],[]],[]],[[],[]]]=>[[[[[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[[],[[[[[[[[[],[[],[]]],[]],[]],[]],[]],[]],[]],[]]]=>[.,[[[[[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[[[[[[[[[],[[],[]]],[]],[]],[]],[]],[]],[]],[[],[]]]=>[[[[[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[[[[[],[]],[[],[]]],[[],[]]],[[[],[]],[[],[[],[]]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],[[.,.],[.,.]]]
[[],[[[[[[],[]],[]],[]],[[],[]]],[[[],[]],[[],[]]]]]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[[[[[[],[]],[]],[]],[[],[]]],[[[],[]],[[],[[],[]]]]]=>[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]]
[[[],[]],[[],[[],[[],[[],[[],[[],[[],[[],[[],[]]]]]]]]]]]=>[[.,[.,.]],[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]],.]],.]],.]],.]]
[[[],[[],[[],[[],[[],[[],[[],[[],[[],[[],[]]]]]]]]]]],[]]=>[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.]],.]],.]],.]],.]],.]
[[],[[[[[[[[[[[],[]],[]],[]],[]],[]],[]],[]],[]],[]],[]]]=>[.,[[[[[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]
[[[[[[[[[[[],[]],[]],[]],[]],[]],[]],[]],[]],[]],[[],[]]]=>[[[[[[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[[],[[[[[],[]],[[],[]]],[[[],[]],[]]],[[[],[]],[[],[]]]]]=>[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]
[[[[[],[]],[[],[]]],[[[],[]],[]]],[[[],[]],[[],[[],[]]]]]=>[[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,[[.,.],[.,.]]],.]]],[[[.,.],[.,.]],[.,.]]]
[[[],[]],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]],.]]
[[[],[[[],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[[[],[]],[]]]],[]]=>[[.,[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[[.,[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[.,.]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[]]],[[[],[[[],[]],[]]],[]]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]
[[[],[[[],[[[],[]],[]]],[]]],[[[],[[[],[[[],[]],[]]],[]]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[]]],[]]],[[[],[[[],[]],[]]],[[[],[]],[]]]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[[[],[]],[]]]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]
[[[],[[[],[[[],[]],[]]],[]]],[[[],[[[],[]],[[[],[]],[]]]],[]]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]]
[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[[[],[[[],[]],[]]],[]]]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]
[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[[[],[]],[[[],[]],[]]]]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[[[],[]],[]]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]
[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]],.]
[[[],[[[],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[[[],[]],[]]],[[[],[[[],[[[],[]],[]]],[]]],[]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]]],.]
[[[],[[[],[]],[]]],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],[.,.]]],.]
[[[],[[[],[]],[]]],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[[[],[]],[]]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]
[[[],[[[],[]],[]]],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]]
[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]
[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.]],.]
[[[],[[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[]],[]]]],[]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]],.]
[[[],[[[],[]],[]]],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.],[.,.]]]
[[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[]],[]]],[]]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]],.]
[[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.],[.,.]]]
[[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]]
[[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[[[],[]],[]]]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]],.]
[[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.],[.,.]]]
[[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]]
[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]]
[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]]
[[[],[[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[]],[]]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]
[[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[[[],[]],[]]],[]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]
[[[],[[[],[]],[[[],[]],[]]]],[[[],[[[],[[[],[]],[]]],[]]],[]]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]],.]
[[[],[[[],[]],[[[],[]],[]]]],[[[],[[[],[]],[]]],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]],.]
[[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[[[],[]],[]]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]]],.]
[[[],[[[],[]],[[[],[]],[]]]],[[[],[[[],[]],[[[],[]],[]]]],[]]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]]],.]
[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[[[],[[[],[]],[]]],[]]]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]
[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[[[],[]],[[[],[]],[]]]]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]],.]
[[[],[[[],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[[[],[]],[]]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]
[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]],.]
[[[],[[[],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]],[]]],[]]=>[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]]],.],[.,.]]],.]
[[[],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]],[[[],[]],[]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[]],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]]],[]]=>[[.,[[[.,.],[.,.]],[.,[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]]],.]
[[[],[]],[[[],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]
[[[],[]],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[[[],[]],[]]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]
[[[],[]],[[[],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]]
[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[[[],[[[],[]],[]]],[]]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]
[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[[[],[]],[]]]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]],[]]],[]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.],[.,.]]],.]
[[[],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]],[[[],[]],[]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]],.]
[[[],[[[],[]],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]],.]
[[[],[]],[[[],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.],[.,.]]]
[[[],[]],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[[[],[]],[]]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[]],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]],.]
[[[],[]],[[[],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.],[.,.]]]
[[[],[]],[[[],[[[],[]],[]]],[[[],[[[],[[[],[]],[]]],[]]],[]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]]
[[[],[]],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[[[],[]],[]]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]],.]
[[[],[]],[[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.],[.,.]]]
[[[],[]],[[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[]],[]]]],[]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]]
[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[]],[]]],[]]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]]
[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[[[],[]],[]]]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]]
[[[],[[[],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.],[.,.]]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]],[[[],[]],[]]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.]],.],[.,.]]],.]
[[[],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[[[],[]],[]]]],[]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.],[[[.,.],[.,.]],[.,.]]]],.]
[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]],.]
[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]],.]],.]
[[[],[[[],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]],[]]],[]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]],.],[.,.]]],.]
[[[],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]],[[[],[]],[]]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]],.]
[[[],[[[],[]],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.],[.,.]]],.]],.]
[[[],[]],[[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]
[[[],[]],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[]],[]]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[[[.,.],[.,.]],[.,.]]]],.]],.]
[[[],[]],[[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]]
[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[[[],[[[],[]],[]]],[]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]
[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[[[],[]],[]]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]]
[[[],[[[],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]],[]]],[]]=>[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]],.],[.,.]]],.]
[[[],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]],[[[],[]],[]]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.]],.]
[[[],[[[],[]],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.],[.,.]]],.]],.]
[[[],[]],[[[],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.],[.,.]]],.],[.,.]]]
[[[],[]],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[[[],[]],[]]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[]],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]]],.]],.]
[[[],[]],[[[],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]],.],[.,.]]]
[[[],[]],[[[],[]],[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]]]=>[[.,[.,.]],[[[.,.],[.,.]],[[[.,[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]]
[[[],[]],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[[[],[]],[]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]],.]
[[[],[]],[[[],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]],.],[.,.]]]
[[[],[]],[[[],[]],[[[],[[[],[[[],[]],[]]],[[[],[]],[]]]],[]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]]
[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[[[],[[[],[]],[]]],[]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]]
[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[]]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]]
[[[],[[[],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]],[]]],[]]=>[[.,[[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]],.],[.,.]]],.]
[[[],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]],[[[],[]],[]]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]],.]],.]],.]
[[[],[[[],[]],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.],[.,.]]],.]],.]
[[[],[]],[[[],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.],[.,.]]],.],[.,.]]]
[[[],[]],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[[[],[]],[]]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.],[[[.,.],[.,.]],[.,.]]]]
[[[],[[[],[]],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.],[.,.]]],.]],.]],.]
[[[],[]],[[[],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]],.],[.,.]]]
[[[],[]],[[[],[]],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.],[.,.]]],.]]
[[[],[]],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[[[.,.],[.,.]],[.,.]]]],.]]
[[[],[[[],[]],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]]],.]],.]],.]
[[[],[]],[[[],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]],.],[.,.]]]
[[[],[]],[[[],[]],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.],[.,.]]],.]]
[[[],[]],[[[],[]],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]]],.]]
[[[],[]],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[[[.,.],[.,.]],[.,.]]]],.]],.]]
[[[],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]]],[]]=>[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]],.]],.]],.]
[[[],[]],[[[],[[[],[]],[[[],[]],[[[],[]],[[[],[]],[]]]]]],[]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.]],.],[.,.]]]
[[[],[]],[[[],[]],[[[],[[[],[]],[[[],[]],[[[],[]],[]]]]],[]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.]],.],[.,.]]],.]]
[[[],[]],[[[],[]],[[[],[]],[[[],[[[],[]],[[[],[]],[]]]],[]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.],[.,.]]],.]],.]]
[[[],[]],[[[],[]],[[[],[]],[[[],[]],[[[],[[[],[]],[]]],[]]]]]]=>[[.,[.,.]],[[[.,[.,.]],[[[.,[.,.]],[[[.,.],[.,.]],[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]],.]],.]]
[[[[[[[],[[],[]]],[[],[]]],[[],[]]],[[],[]]],[[],[]]],[[],[]]]=>[[[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[[[[[[],[[],[]]],[[],[]]],[[],[]]],[[],[]]],[[[],[[],[]]],[]]]=>[[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[[[[[[],[[],[]]],[[],[]]],[[],[]]],[[[],[[],[]]],[]]],[[],[]]]=>[[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[[[[[],[[],[]]],[[],[]]],[[],[]]],[[[[],[[],[]]],[[],[]]],[]]]=>[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]],[[.,.],[.,.]]]
[[[[[],[[],[]]],[[],[]]],[[],[]]],[[[],[[[],[[],[]]],[]]],[]]]=>[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]],[[.,.],[.,.]]]
[[[[[[],[[],[]]],[[],[]]],[[[],[[],[]]],[]]],[[],[]]],[[],[]]]=>[[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[[.,[[.,.],[.,.]]],.],[.,.]]],[[.,.],[.,.]]]
[[[[[],[[],[]]],[[],[]]],[[[],[[],[]]],[]]],[[[],[[],[]]],[]]]=>[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[[[[[],[[],[]]],[[],[]]],[[[[],[[],[]]],[[],[]]],[]]],[[],[]]]=>[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[[.,[.,.]],[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]]
[[[[],[[],[]]],[[],[]]],[[[[[],[[],[]]],[[],[]]],[[],[]]],[]]]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]]
[[[[],[[],[]]],[[],[]]],[[[[],[[],[]]],[[[],[[],[]]],[]]],[]]]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[[.,[[.,.],[.,.]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]]]
[[[[[],[[],[]]],[[],[]]],[[[],[[[],[[],[]]],[]]],[]]],[[],[]]]=>[[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]],[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]
[[[[],[[],[]]],[[],[]]],[[[[],[[[],[[],[]]],[]]],[[],[]]],[]]]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[[[[],[[],[]]],[[],[]]],[[[],[[[[],[[],[]]],[[],[]]],[]]],[]]]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]],.],[.,.]]]
[[[[],[[],[]]],[[],[]]],[[[],[[[],[[[],[[],[]]],[]]],[]]],[]]]=>[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]
[[[[[[],[[],[]]],[[[],[[],[]]],[]]],[[],[]]],[[],[]]],[[],[]]]=>[[[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]
[[[[[],[[],[]]],[[[],[[],[]]],[]]],[[],[]]],[[[],[[],[]]],[]]]=>[[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[[.,[[.,.],[.,.]]],.],[.,.]]],[[.,.],[.,.]]]
[[[[[],[[],[]]],[[[],[[],[]]],[]]],[[[],[[],[]]],[]]],[[],[]]]=>[[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[.,.],[.,.]]],[[[.,[[.,.],[.,.]]],.],[.,.]]]
[[[[],[[],[]]],[[[],[[],[]]],[]]],[[[[],[[],[]]],[[],[]]],[]]]=>[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]],[.,.]]]
[[[[],[[],[]]],[[[],[[],[]]],[]]],[[[],[[[],[[],[]]],[]]],[]]]=>[[[.,[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]],.],[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]]
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[[[],[[[],[[[],[[[],[[[],[[],[]]],[[],[]]]],[]]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.]
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[[],[[[],[[[],[[[],[[[],[[[],[]],[[],[]]]],[]]],[]]],[]]],[]]]=>[.,[[[.,[[[.,[[[.,[[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.],[.,.]]],.],[.,.]]],.],[.,.]]]
Description
Zeilberger's Strahler bijection between ordered and binary trees.
This is a bijection sending the pruning number of the ordered tree to the Strahler number of the binary tree.
This is a bijection sending the pruning number of the ordered tree to the Strahler number of the binary tree.
References
[1] Zeilberger, D. A bijection from ordered trees to binary trees that sends the pruning order to the Strahler number MathSciNet:1058712
Properties
bijective, graded
Sage code
def mapping(t): """ sage: mapping([]) . sage: mapping([[]]) [., .] sage: [mapping(t) for t in OrderedTrees(3)] [[., [., .]], [[., .], .]] """ def prune(t): def is_branch(b): n = len(b) return n == 0 or (n == 1 and is_branch(b[0])) if len(t) == 0: return [] else: return [prune(b) for b in t if not is_branch(b) ] def pruning_order(t): o = 0 while len(t) > 0: t = prune(t) o += 1 return o def below(t): t1 = t[0] t2 = t[1:] k = pruning_order(t) k1 = pruning_order(t1) k2 = pruning_order(t2) if (k1 <= k-1 and k2 == k) or (k1 == k-1 and k2 == k-1): return (t1, t2) elif k1 == k-1 and k2 <= k-2: i = 0 while pruning_order(t1[:i+1]) <= k-2: i += 1 f1 = t1[:i] s1 = t1[i] j = i+1 while pruning_order(t1[i+1:j+1]) <= k-2: j += 1 f2 = t1[i+1:j] return (f1+[s1]+f2, t2+t1[j:]) elif k1 == k: i = 0 while pruning_order(t1[:i+1]) <= k-1: i += 1 f1 = t1[:i] s1 = t1[i] f2 = t1[i+1:] return (f1+[s1]+t2, f2) if len(t) == 0: return BinaryTree() else: u1, u2 = below(t) return BinaryTree([mapping(u1), mapping(u2)])
Created
Jan 29, 2020 at 13:27 by FindStatCrew
Updated
Jan 29, 2020 at 13:27 by Martin Rubey
searching the database
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