Identifier
Mp00018: left border symmetryBinary trees
Mp00016: left-right symmetryBinary trees
Mp00014: to 132-avoiding permutationPermutations
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
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[.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5] [.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5] [.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5] [.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5] [.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5] [.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5] [[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1] [[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1] [[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1] [[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1] [[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1] [[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2] [[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2] [[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1] [[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1] [[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3] [[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3] [[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1] [[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2] [[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1] [[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4] [[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4] [[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4] [[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4] 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[.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6] [.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6] [.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6] [.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6] [.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6] [.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6] [.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6] [.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6] [.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6] [.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6] 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[[[.,.],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1] [[[.,.],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1] [[[[.,.],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3] 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[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1] [[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1] [[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1] [[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1] [[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1] [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2] [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2] [[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2] 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[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6] [[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6] [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6] [[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6] [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6] [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,3,1,2,6] [[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6] [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6] [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6] [[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6] [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6] [[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6] [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6] [[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6] [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6] [[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[7,8,5,3,4,2,1,6] [[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6] [[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6] [[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6] [[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6] [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6] [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1] [[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1] [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1] [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1] [[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1] [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]=>[7,8,3,4,5,2,6,1] [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1] [[[.,.],[[.,[.,.]],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,2,3,6,1] [[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[7,8,4,5,3,2,6,1] [[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1] [[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1] [[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1] [[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,2,3,6,1] [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1] [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2] [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2] [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2] [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2] [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2] [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1] [[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1] [[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[7,8,4,5,3,6,2,1] [[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1] [[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1] [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3] [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3] [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3] [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3] [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1] [[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,2,3,1] [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2] [[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2] [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1] [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4] [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4] [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4] [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4] [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4] [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1] [[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2] [[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1] [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3] [[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3] [[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1] [[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2] [[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1] [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5] [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5] [[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5] [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5] [[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5] [[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5] [[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[7,8,6,3,2,4,1,5] [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5] [[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5] [[[.,[[.,[.,[.,.]]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5] [[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5] 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[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1] [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1] [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4] [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4] [[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4] [[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4] [[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4] [[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4] [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4] [[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4] [[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4] [[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4] [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1] [[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1] [[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1] [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1] [[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2] [[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2] [[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1] [[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1] [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3] [[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3] [[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3] [[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3] [[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1] [[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1] [[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,3,1,2] [[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2] [[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1] [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1] [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5] [[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5] [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5] [[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5] [[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5] [[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[8,6,7,2,3,4,1,5] [[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5] [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5] [[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5] [[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5] [[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5] [[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5] [[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,3,1,2,5] [[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5] [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1] [[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1] [[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1] [[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1] [[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1] [[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2] [[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2] [[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1] [[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1] [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3] [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3] [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1] [[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2] [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1] [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4] [[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4] [[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4] [[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4] [[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4] [[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1] [[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1] [[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,4,1,2] [[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1] [[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3] [[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3] [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1] [[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2] [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1] [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6] [[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6] [[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6] [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6] [[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6] [[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6] [[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6] [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6] [[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6] [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6] [[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6] [[[.,[.,[[[.,.],[.,.]],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]=>[8,7,4,2,3,1,5,6] [[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6] [[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6] [[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6] [[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[8,7,3,2,4,5,1,6] [[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6] [[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6] [[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6] [[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6] [[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6] [[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6] [[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6] [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6] [[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,2,1,3,6] [[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6] [[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,3,1,2,6] [[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6] [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6] [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6] [[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6] [[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6] [[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6] [[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6] [[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6] [[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6] [[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6] [[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6] [[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6] [[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6] 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[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1] [[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3] [[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3] [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1] [[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2] [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1] [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4] [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4] [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4] [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4] [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4] [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1] [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1] [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2] [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1] [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3] [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3] [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1] [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]
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
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.