Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0
[.,[.,.]]=>[2,1]=>0=>[2] [[.,.],.]=>[1,2]=>1=>[1,1] [.,[.,[.,.]]]=>[3,2,1]=>00=>[3] [.,[[.,.],.]]=>[2,3,1]=>00=>[3] [[.,.],[.,.]]=>[1,3,2]=>10=>[1,2] [[.,[.,.]],.]=>[2,1,3]=>01=>[2,1] [[[.,.],.],.]=>[1,2,3]=>11=>[1,1,1] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>000=>[4] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>000=>[4] [.,[[.,.],[.,.]]]=>[2,4,3,1]=>000=>[4] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>000=>[4] [.,[[[.,.],.],.]]=>[2,3,4,1]=>000=>[4] [[.,.],[.,[.,.]]]=>[1,4,3,2]=>100=>[1,3] [[.,.],[[.,.],.]]=>[1,3,4,2]=>100=>[1,3] [[.,[.,.]],[.,.]]=>[2,1,4,3]=>010=>[2,2] [[[.,.],.],[.,.]]=>[1,2,4,3]=>110=>[1,1,2] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>001=>[3,1] [[.,[[.,.],.]],.]=>[2,3,1,4]=>001=>[3,1] [[[.,.],[.,.]],.]=>[1,3,2,4]=>101=>[1,2,1] [[[.,[.,.]],.],.]=>[2,1,3,4]=>011=>[2,1,1] [[[[.,.],.],.],.]=>[1,2,3,4]=>111=>[1,1,1,1] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0000=>[5] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0000=>[5] [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>0000=>[5] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>0000=>[5] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0000=>[5] [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0000=>[5] [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0000=>[5] [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>0000=>[5] [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0000=>[5] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>0000=>[5] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0000=>[5] [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0000=>[5] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0000=>[5] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0000=>[5] [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1000=>[1,4] [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1000=>[1,4] [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1000=>[1,4] [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1000=>[1,4] [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1000=>[1,4] [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>0100=>[2,3] [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>0100=>[2,3] [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>1100=>[1,1,3] [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1100=>[1,1,3] [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>0010=>[3,2] [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>0010=>[3,2] [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>1010=>[1,2,2] [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>0110=>[2,1,2] [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1110=>[1,1,1,2] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>0001=>[4,1] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0001=>[4,1] [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>0001=>[4,1] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>0001=>[4,1] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0001=>[4,1] [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>1001=>[1,3,1] [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1001=>[1,3,1] [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>0101=>[2,2,1] [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1101=>[1,1,2,1] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>0011=>[3,1,1] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0011=>[3,1,1] [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1011=>[1,2,1,1] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>0111=>[2,1,1,1] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>1111=>[1,1,1,1,1] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>00000=>[6] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>00000=>[6] [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>00000=>[6] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>00000=>[6] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00000=>[6] [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>00000=>[6] [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>00000=>[6] [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>00000=>[6] [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>00000=>[6] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>00000=>[6] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>00000=>[6] [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>00000=>[6] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>00000=>[6] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00000=>[6] [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>00000=>[6] [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>00000=>[6] [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>00000=>[6] [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>00000=>[6] [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>00000=>[6] [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>00000=>[6] [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>00000=>[6] [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>00000=>[6] [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>00000=>[6] [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>00000=>[6] [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>00000=>[6] [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>00000=>[6] [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>00000=>[6] [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>00000=>[6] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>00000=>[6] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>00000=>[6] [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>00000=>[6] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>00000=>[6] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00000=>[6] [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>00000=>[6] [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>00000=>[6] [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>00000=>[6] [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>00000=>[6] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>00000=>[6] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>00000=>[6] [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>00000=>[6] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>00000=>[6] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00000=>[6] [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>10000=>[1,5] [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>10000=>[1,5] [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>10000=>[1,5] [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>10000=>[1,5] [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>10000=>[1,5] [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>10000=>[1,5] [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>10000=>[1,5] [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>10000=>[1,5] [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>10000=>[1,5] [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>10000=>[1,5] [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>10000=>[1,5] [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>10000=>[1,5] [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>10000=>[1,5] [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>10000=>[1,5] [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>01000=>[2,4] [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>01000=>[2,4] [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>01000=>[2,4] [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>01000=>[2,4] [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>01000=>[2,4] [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>11000=>[1,1,4] [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>11000=>[1,1,4] [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>11000=>[1,1,4] [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>11000=>[1,1,4] [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>11000=>[1,1,4] [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>00100=>[3,3] [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>00100=>[3,3] [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>00100=>[3,3] [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>00100=>[3,3] [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>10100=>[1,2,3] [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>10100=>[1,2,3] [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>01100=>[2,1,3] [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>01100=>[2,1,3] [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>11100=>[1,1,1,3] [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>11100=>[1,1,1,3] [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>00010=>[4,2] [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>00010=>[4,2] [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>00010=>[4,2] [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>00010=>[4,2] [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>00010=>[4,2] [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>10010=>[1,3,2] [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>10010=>[1,3,2] [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>01010=>[2,2,2] [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>11010=>[1,1,2,2] [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>00110=>[3,1,2] [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>00110=>[3,1,2] [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>10110=>[1,2,1,2] [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>01110=>[2,1,1,2] [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>11110=>[1,1,1,1,2] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>00001=>[5,1] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>00001=>[5,1] [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>00001=>[5,1] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>00001=>[5,1] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00001=>[5,1] [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>00001=>[5,1] [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>00001=>[5,1] [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>00001=>[5,1] [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>00001=>[5,1] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>00001=>[5,1] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>00001=>[5,1] [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>00001=>[5,1] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>00001=>[5,1] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00001=>[5,1] [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>10001=>[1,4,1] [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>10001=>[1,4,1] [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>10001=>[1,4,1] [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>10001=>[1,4,1] [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>10001=>[1,4,1] [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>01001=>[2,3,1] [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>01001=>[2,3,1] [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>11001=>[1,1,3,1] [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>11001=>[1,1,3,1] [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>00101=>[3,2,1] [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>00101=>[3,2,1] [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>10101=>[1,2,2,1] [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>01101=>[2,1,2,1] [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>11101=>[1,1,1,2,1] [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>00011=>[4,1,1] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>00011=>[4,1,1] [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>00011=>[4,1,1] [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>00011=>[4,1,1] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00011=>[4,1,1] [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>10011=>[1,3,1,1] [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>10011=>[1,3,1,1] [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>01011=>[2,2,1,1] [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>11011=>[1,1,2,1,1] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>00111=>[3,1,1,1] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>00111=>[3,1,1,1] [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>10111=>[1,2,1,1,1] [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>01111=>[2,1,1,1,1] [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>11111=>[1,1,1,1,1,1] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>000000=>[7] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>000000=>[7] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>000000=>[7] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>000000=>[7] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>000000=>[7] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>000000=>[7] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>000000=>[7] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>000000=>[7] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>000000=>[7] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>000000=>[7] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>000000=>[7] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>000000=>[7] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>000000=>[7] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>000000=>[7] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>000000=>[7] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>000000=>[7] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>000000=>[7] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>000000=>[7] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>000000=>[7] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>000000=>[7] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>000000=>[7] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>000000=>[7] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>000000=>[7] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>000000=>[7] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>000000=>[7] 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[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>100000=>[1,6] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>100000=>[1,6] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>100000=>[1,6] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>100000=>[1,6] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>100000=>[1,6] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>100000=>[1,6] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>100000=>[1,6] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>100000=>[1,6] [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>100000=>[1,6] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>100000=>[1,6] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>100000=>[1,6] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>100000=>[1,6] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>100000=>[1,6] [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>100000=>[1,6] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>100000=>[1,6] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>100000=>[1,6] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>100000=>[1,6] [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>100000=>[1,6] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>100000=>[1,6] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>100000=>[1,6] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>100000=>[1,6] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>100000=>[1,6] [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>100000=>[1,6] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>100000=>[1,6] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>100000=>[1,6] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>100000=>[1,6] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>100000=>[1,6] [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>100000=>[1,6] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>100000=>[1,6] [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>100000=>[1,6] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>100000=>[1,6] [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>100000=>[1,6] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>100000=>[1,6] [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>100000=>[1,6] [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>100000=>[1,6] [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>100000=>[1,6] [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>100000=>[1,6] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>010000=>[2,5] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>010000=>[2,5] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>010000=>[2,5] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>010000=>[2,5] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>010000=>[2,5] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>010000=>[2,5] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>010000=>[2,5] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>010000=>[2,5] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>010000=>[2,5] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>010000=>[2,5] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>010000=>[2,5] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>010000=>[2,5] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>010000=>[2,5] [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>010000=>[2,5] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>110000=>[1,1,5] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>110000=>[1,1,5] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>110000=>[1,1,5] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>110000=>[1,1,5] [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>110000=>[1,1,5] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>110000=>[1,1,5] [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>110000=>[1,1,5] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>110000=>[1,1,5] [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>110000=>[1,1,5] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>110000=>[1,1,5] [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>110000=>[1,1,5] [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>110000=>[1,1,5] [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>110000=>[1,1,5] [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>110000=>[1,1,5] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>001000=>[3,4] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>001000=>[3,4] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>001000=>[3,4] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>001000=>[3,4] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>001000=>[3,4] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>001000=>[3,4] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>001000=>[3,4] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>001000=>[3,4] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>001000=>[3,4] [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>001000=>[3,4] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>101000=>[1,2,4] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>101000=>[1,2,4] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>101000=>[1,2,4] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>101000=>[1,2,4] [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>101000=>[1,2,4] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>011000=>[2,1,4] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>011000=>[2,1,4] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>011000=>[2,1,4] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>011000=>[2,1,4] [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>011000=>[2,1,4] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>111000=>[1,1,1,4] [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>111000=>[1,1,1,4] [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>111000=>[1,1,1,4] [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>111000=>[1,1,1,4] [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>111000=>[1,1,1,4] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>000100=>[4,3] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>000100=>[4,3] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>000100=>[4,3] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>000100=>[4,3] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>000100=>[4,3] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>000100=>[4,3] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>000100=>[4,3] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>000100=>[4,3] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>000100=>[4,3] [[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>000100=>[4,3] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>100100=>[1,3,3] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>100100=>[1,3,3] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>100100=>[1,3,3] [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>100100=>[1,3,3] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>010100=>[2,2,3] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>010100=>[2,2,3] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>110100=>[1,1,2,3] [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>110100=>[1,1,2,3] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>001100=>[3,1,3] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>001100=>[3,1,3] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>001100=>[3,1,3] [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>001100=>[3,1,3] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>101100=>[1,2,1,3] [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>101100=>[1,2,1,3] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>011100=>[2,1,1,3] [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>011100=>[2,1,1,3] [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>111100=>[1,1,1,1,3] [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>111100=>[1,1,1,1,3] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>000010=>[5,2] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>000010=>[5,2] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>000010=>[5,2] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>000010=>[5,2] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>000010=>[5,2] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>000010=>[5,2] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>000010=>[5,2] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>000010=>[5,2] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>000010=>[5,2] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>000010=>[5,2] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>000010=>[5,2] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>000010=>[5,2] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>000010=>[5,2] [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>000010=>[5,2] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>100010=>[1,4,2] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>100010=>[1,4,2] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>100010=>[1,4,2] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>100010=>[1,4,2] [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>100010=>[1,4,2] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>010010=>[2,3,2] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>010010=>[2,3,2] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>110010=>[1,1,3,2] [[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>110010=>[1,1,3,2] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>001010=>[3,2,2] [[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>001010=>[3,2,2] [[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>101010=>[1,2,2,2] [[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>011010=>[2,1,2,2] [[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>111010=>[1,1,1,2,2] [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>000110=>[4,1,2] [[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>000110=>[4,1,2] [[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>000110=>[4,1,2] [[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>000110=>[4,1,2] [[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>000110=>[4,1,2] [[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>100110=>[1,3,1,2] [[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>100110=>[1,3,1,2] [[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>010110=>[2,2,1,2] [[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>110110=>[1,1,2,1,2] [[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>001110=>[3,1,1,2] [[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>001110=>[3,1,1,2] [[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>101110=>[1,2,1,1,2] [[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>011110=>[2,1,1,1,2] [[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>111110=>[1,1,1,1,1,2] [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>000001=>[6,1] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>000001=>[6,1] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>000001=>[6,1] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>000001=>[6,1] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>000001=>[6,1] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>000001=>[6,1] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>000001=>[6,1] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>000001=>[6,1] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>000001=>[6,1] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>000001=>[6,1] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>000001=>[6,1] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>000001=>[6,1] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>000001=>[6,1] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>000001=>[6,1] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>000001=>[6,1] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>000001=>[6,1] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>000001=>[6,1] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>000001=>[6,1] [[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>000001=>[6,1] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>000001=>[6,1] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>000001=>[6,1] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>000001=>[6,1] [[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>000001=>[6,1] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>000001=>[6,1] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>000001=>[6,1] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>000001=>[6,1] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>000001=>[6,1] [[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>000001=>[6,1] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>000001=>[6,1] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>000001=>[6,1] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>000001=>[6,1] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>000001=>[6,1] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>000001=>[6,1] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>000001=>[6,1] [[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>000001=>[6,1] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>000001=>[6,1] [[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>000001=>[6,1] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>000001=>[6,1] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>000001=>[6,1] [[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>000001=>[6,1] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>000001=>[6,1] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>000001=>[6,1] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>100001=>[1,5,1] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>100001=>[1,5,1] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>100001=>[1,5,1] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>100001=>[1,5,1] [[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>100001=>[1,5,1] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>100001=>[1,5,1] [[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>100001=>[1,5,1] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>100001=>[1,5,1] [[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>100001=>[1,5,1] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>100001=>[1,5,1] [[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>100001=>[1,5,1] [[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>100001=>[1,5,1] [[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>100001=>[1,5,1] [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>100001=>[1,5,1] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>010001=>[2,4,1] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>010001=>[2,4,1] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>010001=>[2,4,1] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>010001=>[2,4,1] [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>010001=>[2,4,1] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>110001=>[1,1,4,1] [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>110001=>[1,1,4,1] [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>110001=>[1,1,4,1] [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>110001=>[1,1,4,1] [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>110001=>[1,1,4,1] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>001001=>[3,3,1] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>001001=>[3,3,1] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>001001=>[3,3,1] [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>001001=>[3,3,1] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>101001=>[1,2,3,1] [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>101001=>[1,2,3,1] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>011001=>[2,1,3,1] [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>011001=>[2,1,3,1] [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>111001=>[1,1,1,3,1] [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>111001=>[1,1,1,3,1] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>000101=>[4,2,1] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>000101=>[4,2,1] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>000101=>[4,2,1] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>000101=>[4,2,1] [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>000101=>[4,2,1] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>100101=>[1,3,2,1] [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>100101=>[1,3,2,1] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>010101=>[2,2,2,1] [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>110101=>[1,1,2,2,1] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>001101=>[3,1,2,1] [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>001101=>[3,1,2,1] [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>101101=>[1,2,1,2,1] [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>011101=>[2,1,1,2,1] [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>111101=>[1,1,1,1,2,1] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>000011=>[5,1,1] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>000011=>[5,1,1] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>000011=>[5,1,1] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>000011=>[5,1,1] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>000011=>[5,1,1] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>000011=>[5,1,1] [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>000011=>[5,1,1] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>000011=>[5,1,1] [[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>000011=>[5,1,1] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>000011=>[5,1,1] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>000011=>[5,1,1] [[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>000011=>[5,1,1] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>000011=>[5,1,1] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>000011=>[5,1,1] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>100011=>[1,4,1,1] [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>100011=>[1,4,1,1] [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>100011=>[1,4,1,1] [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>100011=>[1,4,1,1] [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>100011=>[1,4,1,1] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>010011=>[2,3,1,1] [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>010011=>[2,3,1,1] [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>110011=>[1,1,3,1,1] [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>110011=>[1,1,3,1,1] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>001011=>[3,2,1,1] [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>001011=>[3,2,1,1] [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>101011=>[1,2,2,1,1] [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>011011=>[2,1,2,1,1] [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>111011=>[1,1,1,2,1,1] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>000111=>[4,1,1,1] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>000111=>[4,1,1,1] [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>000111=>[4,1,1,1] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>000111=>[4,1,1,1] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>000111=>[4,1,1,1] [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>100111=>[1,3,1,1,1] [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>100111=>[1,3,1,1,1] [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>010111=>[2,2,1,1,1] [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>110111=>[1,1,2,1,1,1] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>001111=>[3,1,1,1,1] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>001111=>[3,1,1,1,1] [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>101111=>[1,2,1,1,1,1] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>011111=>[2,1,1,1,1,1] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>111111=>[1,1,1,1,1,1,1] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>0000000=>[8] [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>0000000=>[8] [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>0000000=>[8] [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>0000000=>[8] [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>0000000=>[8] [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>0000000=>[8] [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>0000000=>[8] [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>0000000=>[8] [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>0000000=>[8] [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>0000000=>[8] [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>0000000=>[8] [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>0000000=>[8] [.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>0000000=>[8] [.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>0000000=>[8] [.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>0000000=>[8] [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>0000000=>[8] [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[5,4,3,6,8,7,2,1]=>0000000=>[8] [.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[4,5,3,6,8,7,2,1]=>0000000=>[8] [.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[4,3,5,6,8,7,2,1]=>0000000=>[8] [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>0000000=>[8] [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>0000000=>[8] [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[3,4,7,6,5,8,2,1]=>0000000=>[8] [.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[4,5,3,7,6,8,2,1]=>0000000=>[8] [.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[4,3,5,7,6,8,2,1]=>0000000=>[8] [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>0000000=>[8] [.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[3,4,6,5,7,8,2,1]=>0000000=>[8] [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>0000000=>[8] [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>0000000=>[8] [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>0000000=>[8] [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>0000000=>[8] [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>0000000=>[8] [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>0000000=>[8] [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[2,4,7,6,5,8,3,1]=>0000000=>[8] [.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[2,6,5,4,7,8,3,1]=>0000000=>[8] [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[3,2,8,7,6,5,4,1]=>0000000=>[8] [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[3,2,6,8,7,5,4,1]=>0000000=>[8] [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[3,2,5,6,7,8,4,1]=>0000000=>[8] [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>0000000=>[8] [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[2,3,5,8,7,6,4,1]=>0000000=>[8] [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>0000000=>[8] [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>0000000=>[8] [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>0000000=>[8] [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>0000000=>[8] [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>0000000=>[8] [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>0000000=>[8] [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>0000000=>[8] [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>0000000=>[8] [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>0000000=>[8] [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>0000000=>[8] [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>0000000=>[8] [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[4,5,3,2,8,7,6,1]=>0000000=>[8] [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>0000000=>[8] [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>0000000=>[8] [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>0000000=>[8] [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[2,4,5,3,8,7,6,1]=>0000000=>[8] [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[2,3,5,4,8,7,6,1]=>0000000=>[8] [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[4,3,2,5,8,7,6,1]=>0000000=>[8] [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>0000000=>[8] [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>0000000=>[8] [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>0000000=>[8] [.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>0000000=>[8] [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>0000000=>[8] [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>0000000=>[8] [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>0000000=>[8] [.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>0000000=>[8] [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>0000000=>[8] [.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>0000000=>[8] [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>0000000=>[8] [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>0000000=>[8] [.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>0000000=>[8] [.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>0000000=>[8] [.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>0000000=>[8] [.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>0000000=>[8] [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>0000000=>[8] [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>0000000=>[8] [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>0000000=>[8] [.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>0000000=>[8] [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[5,4,3,7,6,2,8,1]=>0000000=>[8] [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>0000000=>[8] [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>0000000=>[8] [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>0000000=>[8] [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>0000000=>[8] [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>0000000=>[8] [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>0000000=>[8] [.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>0000000=>[8] [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>0000000=>[8] [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[2,3,7,6,5,4,8,1]=>0000000=>[8] [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>0000000=>[8] [.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>0000000=>[8] [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>0000000=>[8] [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>0000000=>[8] [.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>0000000=>[8] [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>0000000=>[8] [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>0000000=>[8] [.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[2,4,3,5,7,6,8,1]=>0000000=>[8] [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>0000000=>[8] [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>0000000=>[8] [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>0000000=>[8] [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>0000000=>[8] [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>0000000=>[8] [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[2,3,6,5,4,7,8,1]=>0000000=>[8] [.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[4,3,2,6,5,7,8,1]=>0000000=>[8] [.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>0000000=>[8] [.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[2,3,4,6,5,7,8,1]=>0000000=>[8] [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>0000000=>[8] [.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>0000000=>[8] [.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[2,4,3,5,6,7,8,1]=>0000000=>[8] [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>0000000=>[8] [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[1,6,7,5,8,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[1,5,7,6,8,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[1,6,5,7,8,4,3,2]=>1000000=>[1,7] [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>1000000=>[1,7] [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>1000000=>[1,7] [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>1000000=>[1,7] [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[1,4,6,8,7,5,3,2]=>1000000=>[1,7] [[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[1,4,6,7,8,5,3,2]=>1000000=>[1,7] [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>1000000=>[1,7] [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>1000000=>[1,7] [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[1,6,5,4,7,8,3,2]=>1000000=>[1,7] [[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[1,5,4,6,7,8,3,2]=>1000000=>[1,7] [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[1,3,8,7,6,5,4,2]=>1000000=>[1,7] [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[1,3,6,8,7,5,4,2]=>1000000=>[1,7] [[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[1,3,6,7,8,5,4,2]=>1000000=>[1,7] [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>1000000=>[1,7] [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>1000000=>[1,7] [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>1000000=>[1,7] [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>1000000=>[1,7] [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>1000000=>[1,7] [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>1000000=>[1,7] [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>1000000=>[1,7] [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>1000000=>[1,7] [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>1000000=>[1,7] [[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>1000000=>[1,7] [[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>1000000=>[1,7] [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[1,4,3,5,8,7,6,2]=>1000000=>[1,7] [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[1,4,3,5,7,8,6,2]=>1000000=>[1,7] [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>1000000=>[1,7] [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>1000000=>[1,7] [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>[1,4,6,5,3,8,7,2]=>1000000=>[1,7] [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>[1,3,6,5,4,8,7,2]=>1000000=>[1,7] [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>1000000=>[1,7] [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[1,5,4,3,6,8,7,2]=>1000000=>[1,7] [[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>1000000=>[1,7] [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>1000000=>[1,7] [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>0100000=>[2,6] [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>0100000=>[2,6] [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>0100000=>[2,6] [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>0100000=>[2,6] [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>0100000=>[2,6] [[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>0100000=>[2,6] [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>0100000=>[2,6] [[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[2,1,4,5,6,8,7,3]=>0100000=>[2,6] [[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>0100000=>[2,6] [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[2,1,4,7,6,5,8,3]=>0100000=>[2,6] [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>0100000=>[2,6] [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]=>1100000=>[1,1,6] [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>1100000=>[1,1,6] [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>1100000=>[1,1,6] [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>1100000=>[1,1,6] [[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>1100000=>[1,1,6] [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[1,2,4,6,8,7,5,3]=>1100000=>[1,1,6] [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[1,2,5,4,8,7,6,3]=>1100000=>[1,1,6] [[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[1,2,5,4,7,8,6,3]=>1100000=>[1,1,6] [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[1,2,6,5,4,8,7,3]=>1100000=>[1,1,6] [[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[1,2,4,6,5,8,7,3]=>1100000=>[1,1,6] [[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[1,2,5,4,6,8,7,3]=>1100000=>[1,1,6] [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>1100000=>[1,1,6] [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>0010000=>[3,5] [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>0010000=>[3,5] [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>0010000=>[3,5] [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[2,3,1,6,8,7,5,4]=>0010000=>[3,5] [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>0010000=>[3,5] [[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[2,3,1,6,7,8,5,4]=>0010000=>[3,5] [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[2,3,1,6,5,8,7,4]=>0010000=>[3,5] [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[2,3,1,5,6,7,8,4]=>0010000=>[3,5] [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>1010000=>[1,2,5] [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,6,8,7,5,4]=>1010000=>[1,2,5] [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>1010000=>[1,2,5] [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>0110000=>[2,1,5] [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[2,1,3,7,8,6,5,4]=>0110000=>[2,1,5] [[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[2,1,3,6,8,7,5,4]=>0110000=>[2,1,5] [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>1110000=>[1,1,1,5] [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>1110000=>[1,1,1,5] [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>0001000=>[4,4] [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>0001000=>[4,4] [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>0001000=>[4,4] [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>0001000=>[4,4] [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>0001000=>[4,4] [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>0001000=>[4,4] [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>0001000=>[4,4] [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>0001000=>[4,4] [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>0001000=>[4,4] [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>0001000=>[4,4] [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>0001000=>[4,4] [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>0001000=>[4,4] [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>0001000=>[4,4] [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>0001000=>[4,4] [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>0001000=>[4,4] [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>1001000=>[1,3,4] [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>1001000=>[1,3,4] [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>1001000=>[1,3,4] [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>1001000=>[1,3,4] [[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>1001000=>[1,3,4] [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>0101000=>[2,2,4] [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>0101000=>[2,2,4] [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>0101000=>[2,2,4] [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>1101000=>[1,1,2,4] [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>1101000=>[1,1,2,4] [[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>1101000=>[1,1,2,4] [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>1101000=>[1,1,2,4] [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>0011000=>[3,1,4] [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>0011000=>[3,1,4] [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>0011000=>[3,1,4] [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>0011000=>[3,1,4] [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>0011000=>[3,1,4] [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>1011000=>[1,2,1,4] [[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>1011000=>[1,2,1,4] [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>1011000=>[1,2,1,4] [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>0111000=>[2,1,1,4] [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>0111000=>[2,1,1,4] [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>1111000=>[1,1,1,1,4] [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>1111000=>[1,1,1,1,4] [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>1111000=>[1,1,1,1,4] [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>1111000=>[1,1,1,1,4] [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>1111000=>[1,1,1,1,4] [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>0000100=>[5,3] [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>0000100=>[5,3] [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>0000100=>[5,3] [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>0000100=>[5,3] [[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[3,5,4,2,1,7,8,6]=>0000100=>[5,3] [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>0000100=>[5,3] [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>0000100=>[5,3] [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>0000100=>[5,3] [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>0000100=>[5,3] [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>0000100=>[5,3] [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[3,2,5,4,1,7,8,6]=>0000100=>[5,3] [[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>0000100=>[5,3] [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>0000100=>[5,3] [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>0000100=>[5,3] [[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>0000100=>[5,3] [[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>0000100=>[5,3] [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>0000100=>[5,3] [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>1100100=>[1,1,3,3] [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[1,2,4,5,3,8,7,6]=>1100100=>[1,1,3,3] [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]=>1010100=>[1,2,2,3] [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[1,3,2,5,4,7,8,6]=>1010100=>[1,2,2,3] [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]=>0110100=>[2,1,2,3] [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>1110100=>[1,1,1,2,3] [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>1110100=>[1,1,1,2,3] [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>0001100=>[4,1,3] [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>0001100=>[4,1,3] [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>0001100=>[4,1,3] [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>1001100=>[1,3,1,3] [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>1001100=>[1,3,1,3] [[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[1,2,4,3,5,7,8,6]=>1101100=>[1,1,2,1,3] [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>0011100=>[3,1,1,3] [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>0011100=>[3,1,1,3] [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>0011100=>[3,1,1,3] [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>1111100=>[1,1,1,1,1,3] [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>1111100=>[1,1,1,1,1,3] [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>0000010=>[6,2] [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>0000010=>[6,2] [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>0000010=>[6,2] [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>0000010=>[6,2] [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>0000010=>[6,2] [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[4,5,3,2,6,1,8,7]=>0000010=>[6,2] [[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[3,5,4,2,6,1,8,7]=>0000010=>[6,2] [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[1,5,4,6,3,2,8,7]=>1000010=>[1,5,2] [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[1,3,6,5,4,2,8,7]=>1000010=>[1,5,2] [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>0100010=>[2,4,2] [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>0100010=>[2,4,2] [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>0100010=>[2,4,2] [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>0010010=>[3,3,2] [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>0110010=>[2,1,3,2] [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>1110010=>[1,1,1,3,2] [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>1110010=>[1,1,1,3,2] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>0001010=>[4,2,2] [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>0001010=>[4,2,2] [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>0001010=>[4,2,2] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>0101010=>[2,2,2,2] [[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]=>1101010=>[1,1,2,2,2] [[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]=>1011010=>[1,2,1,2,2] [[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]=>0111010=>[2,1,1,2,2] [[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]=>1111010=>[1,1,1,1,2,2] [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>0000110=>[5,1,2] [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>0000110=>[5,1,2] [[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>0000110=>[5,1,2] [[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>0000110=>[5,1,2] [[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>0000110=>[5,1,2] [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>0000110=>[5,1,2] [[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>1000110=>[1,4,1,2] [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>0100110=>[2,3,1,2] [[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>1100110=>[1,1,3,1,2] [[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]=>0110110=>[2,1,2,1,2] [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>0001110=>[4,1,1,2] [[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]=>1001110=>[1,3,1,1,2] [[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]=>0101110=>[2,2,1,1,2] [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>1101110=>[1,1,2,1,1,2] [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>0111110=>[2,1,1,1,1,2] [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>1111110=>[1,1,1,1,1,1,2] [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>0000001=>[7,1] [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>0000001=>[7,1] [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>0000001=>[7,1] [[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>0000001=>[7,1] [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>0000001=>[7,1] [[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>0000001=>[7,1] [[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>0000001=>[7,1] [[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>0000001=>[7,1] [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>0000001=>[7,1] [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>0000001=>[7,1] [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>0000001=>[7,1] [[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>0000001=>[7,1] [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>0000001=>[7,1] [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>0000001=>[7,1] [[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>0000001=>[7,1] [[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[3,2,5,7,6,4,1,8]=>0000001=>[7,1] [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[2,3,7,6,5,4,1,8]=>0000001=>[7,1] [[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[2,3,6,7,5,4,1,8]=>0000001=>[7,1] [[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[2,3,5,7,6,4,1,8]=>0000001=>[7,1] [[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[2,3,6,5,7,4,1,8]=>0000001=>[7,1] [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[2,3,5,6,7,4,1,8]=>0000001=>[7,1] [[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>0000001=>[7,1] [[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>0000001=>[7,1] [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>0000001=>[7,1] [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>0000001=>[7,1] [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>0000001=>[7,1] [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>0000001=>[7,1] [[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>0000001=>[7,1] [[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>0000001=>[7,1] [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>0000001=>[7,1] [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>0000001=>[7,1] [[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>0000001=>[7,1] [[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>0000001=>[7,1] [[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>0000001=>[7,1] [[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>0000001=>[7,1] [[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[3,4,2,6,5,7,1,8]=>0000001=>[7,1] [[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[2,4,3,6,5,7,1,8]=>0000001=>[7,1] [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>0000001=>[7,1] [[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>0000001=>[7,1] [[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>0000001=>[7,1] [[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[1,5,6,7,4,3,2,8]=>1000001=>[1,6,1] [[[.,.],[.,[[[.,.],[.,.]],.]]],.]=>[1,4,6,5,7,3,2,8]=>1000001=>[1,6,1] [[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>1000001=>[1,6,1] [[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[1,3,5,6,7,4,2,8]=>1000001=>[1,6,1] [[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[1,3,5,4,7,6,2,8]=>1000001=>[1,6,1] [[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[1,4,3,5,7,6,2,8]=>1000001=>[1,6,1] [[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[1,5,4,6,3,7,2,8]=>1000001=>[1,6,1] [[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[1,3,6,5,4,7,2,8]=>1000001=>[1,6,1] [[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[1,4,3,6,5,7,2,8]=>1000001=>[1,6,1] [[[.,.],[[[[[.,.],.],.],.],.]],.]=>[1,3,4,5,6,7,2,8]=>1000001=>[1,6,1] [[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[2,1,5,6,7,4,3,8]=>0100001=>[2,5,1] [[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[1,2,5,7,6,4,3,8]=>1100001=>[1,1,5,1] [[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[1,2,5,6,7,4,3,8]=>1100001=>[1,1,5,1] [[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[1,2,5,6,4,7,3,8]=>1100001=>[1,1,5,1] [[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[1,2,5,4,6,7,3,8]=>1100001=>[1,1,5,1] [[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>0010001=>[3,4,1] [[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>0010001=>[3,4,1] [[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>0010001=>[3,4,1] [[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[1,3,2,6,5,7,4,8]=>1010001=>[1,2,4,1] [[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[2,1,3,6,7,5,4,8]=>0110001=>[2,1,4,1] [[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>1110001=>[1,1,1,4,1] [[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>1110001=>[1,1,1,4,1] [[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>1110001=>[1,1,1,4,1] [[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>1110001=>[1,1,1,4,1] [[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>1110001=>[1,1,1,4,1] [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>0001001=>[4,3,1] [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>0001001=>[4,3,1] [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>1001001=>[1,3,3,1] [[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[1,4,3,2,6,7,5,8]=>1001001=>[1,3,3,1] [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>1001001=>[1,3,3,1] [[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[2,1,4,3,6,7,5,8]=>0101001=>[2,2,3,1] [[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>1101001=>[1,1,2,3,1] [[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>0011001=>[3,1,3,1] [[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]=>1011001=>[1,2,1,3,1] [[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]=>1111001=>[1,1,1,1,3,1] [[[[[[.,.],.],.],.],[[.,.],.]],.]=>[1,2,3,4,6,7,5,8]=>1111001=>[1,1,1,1,3,1] [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>0000101=>[5,2,1] [[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>0000101=>[5,2,1] [[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>0000101=>[5,2,1] [[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>0000101=>[5,2,1] [[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>0000101=>[5,2,1] [[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>0000101=>[5,2,1] [[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>1000101=>[1,4,2,1] [[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>0010101=>[3,2,2,1] [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>0010101=>[3,2,2,1] [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>1010101=>[1,2,2,2,1] [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>1110101=>[1,1,1,2,2,1] [[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>0001101=>[4,1,2,1] [[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]=>1001101=>[1,3,1,2,1] [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>1011101=>[1,2,1,1,2,1] [[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>1111101=>[1,1,1,1,1,2,1] [[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>0000011=>[6,1,1] [[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>0000011=>[6,1,1] [[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[4,3,6,5,2,1,7,8]=>0000011=>[6,1,1] [[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>0000011=>[6,1,1] [[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>0000011=>[6,1,1] [[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[2,4,6,5,3,1,7,8]=>0000011=>[6,1,1] [[[.,[[.,.],[[[.,.],.],.]]],.],.]=>[2,4,5,6,3,1,7,8]=>0000011=>[6,1,1] [[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>0000011=>[6,1,1] [[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>0000011=>[6,1,1] [[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>0000011=>[6,1,1] [[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>0000011=>[6,1,1] [[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[1,5,6,4,3,2,7,8]=>1000011=>[1,5,1,1] [[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[1,4,6,5,3,2,7,8]=>1000011=>[1,5,1,1] [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>1000011=>[1,5,1,1] [[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[1,4,5,6,3,2,7,8]=>1000011=>[1,5,1,1] [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>1000011=>[1,5,1,1] [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>1000011=>[1,5,1,1] [[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>1000011=>[1,5,1,1] [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>0100011=>[2,4,1,1] [[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[2,1,4,6,5,3,7,8]=>0100011=>[2,4,1,1] [[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>1100011=>[1,1,4,1,1] [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>1100011=>[1,1,4,1,1] [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[3,2,1,5,6,4,7,8]=>0010011=>[3,3,1,1] [[[[[[.,.],.],.],[[.,.],.]],.],.]=>[1,2,3,5,6,4,7,8]=>1110011=>[1,1,1,3,1,1] [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>0001011=>[4,2,1,1] [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>0001011=>[4,2,1,1] [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>0101011=>[2,2,2,1,1] [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>1101011=>[1,1,2,2,1,1] [[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]=>1011011=>[1,2,1,2,1,1] [[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]=>0111011=>[2,1,1,2,1,1] [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]=>1111011=>[1,1,1,1,2,1,1] [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>0000111=>[5,1,1,1] [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0000111=>[5,1,1,1] [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>1010111=>[1,2,2,1,1,1] [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>1110111=>[1,1,1,2,1,1,1] [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>0001111=>[4,1,1,1,1] [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>1001111=>[1,3,1,1,1,1] [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>1001111=>[1,3,1,1,1,1] [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>0101111=>[2,2,1,1,1,1] [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>1101111=>[1,1,2,1,1,1,1] [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>0011111=>[3,1,1,1,1,1] [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>0011111=>[3,1,1,1,1,1] [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>1011111=>[1,2,1,1,1,1,1] [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>0111111=>[2,1,1,1,1,1,1] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>1111111=>[1,1,1,1,1,1,1,1]
Map
to 312-avoiding permutation
Description
Return a 312-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 minimal element of this Sylvester class.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.