Identifier
Mp00014: Binary trees to 132-avoiding permutationPermutations
Mp00073: Permutations major-index to inversion-number bijectionPermutations
Mp00109: Permutations descent wordBinary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=> [.,[.,.]]=>[2,1]=>[2,1]=>1 [[.,.],.]=>[1,2]=>[1,2]=>0 [.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>11 [.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>10 [[.,.],[.,.]]=>[3,1,2]=>[1,3,2]=>01 [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>10 [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>00 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>111 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>110 [.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,1,3,2]=>101 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>110 [.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>100 [[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,4,3,2]=>011 [[.,.],[[.,.],.]]=>[3,4,1,2]=>[1,4,2,3]=>010 [[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,4,2]=>101 [[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,2,4,3]=>001 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>110 [[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>100 [[[.,.],[.,.]],.]=>[3,1,2,4]=>[1,3,2,4]=>010 [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>100 [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>000 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>1111 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>1110 [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,4,1,3,2]=>1101 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>1110 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>1100 [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,1,4,3,2]=>1011 [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,1,4,2,3]=>1010 [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,3,1,4,2]=>1101 [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,1,2,4,3]=>1001 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>1110 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>1100 [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,1,3,2,4]=>1010 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>1100 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>1000 [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,5,4,3,2]=>0111 [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[1,5,4,2,3]=>0110 [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,5,2,4,3]=>0101 [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[1,5,3,2,4]=>0110 [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[1,5,2,3,4]=>0100 [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,1,5,3,2]=>1011 [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,1,5,2,3]=>1010 [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011 [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[1,2,5,3,4]=>0010 [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,3,1,5,2]=>1101 [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,2,5,3]=>1001 [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,4,2,5,3]=>0101 [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,2,5,4]=>1001 [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,2,3,5,4]=>0001 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>1100 [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,1,3,2,5]=>1010 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>1100 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>1000 [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[1,4,3,2,5]=>0110 [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[1,4,2,3,5]=>0100 [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,4,2,5]=>1010 [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[1,2,4,3,5]=>0010 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>1000 [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[1,3,2,4,5]=>0100 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>11110 [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>11101 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>11110 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>11100 [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>11011 [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,5,1,4,2,3]=>11010 [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>11101 [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>11001 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>11110 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>11100 [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>11010 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>11100 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>11000 [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>10111 [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,1,5,4,2,3]=>10110 [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,1,5,2,4,3]=>10101 [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,1,5,3,2,4]=>10110 [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,1,5,2,3,4]=>10100 [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>11011 [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,1,5,2,3]=>11010 [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>10011 [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,1,2,5,3,4]=>10010 [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>11101 [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>11001 [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>10101 [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>11001 [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>10001 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>11110 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>11100 [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>11010 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>11100 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>11000 [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>10110 [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,1,4,2,3,5]=>10100 [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>11010 [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>10010 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>11100 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>11000 [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>10100 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>11000 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>10000 [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>01111 [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[1,6,5,4,2,3]=>01110 [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,6,5,2,4,3]=>01101 [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[1,6,5,3,2,4]=>01110 [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[1,6,5,2,3,4]=>01100 [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,6,2,5,4,3]=>01011 [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[1,6,2,5,3,4]=>01010 [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,6,4,2,5,3]=>01101 [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,6,2,3,5,4]=>01001 [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[1,6,4,3,2,5]=>01110 [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[1,6,4,2,3,5]=>01100 [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[1,6,2,4,3,5]=>01010 [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[1,6,3,2,4,5]=>01100 [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[1,6,2,3,4,5]=>01000 [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>10111 [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,1,6,4,2,3]=>10110 [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[5,1,6,2,4,3]=>10101 [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,1,6,3,2,4]=>10110 [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[5,1,6,2,3,4]=>10100 [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>00111 [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[1,2,6,5,3,4]=>00110 [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,2,6,3,5,4]=>00101 [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[1,2,6,4,3,5]=>00110 [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[1,2,6,3,4,5]=>00100 [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>11011 [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,4,1,6,2,3]=>11010 [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>10011 [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,1,2,6,3,4]=>10010 [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>01011 [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[1,5,2,6,3,4]=>01010 [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>10011 [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,1,2,6,3,5]=>10010 [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>00011 [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[1,2,3,6,4,5]=>00010 [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>11101 [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>11001 [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>10101 [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>11001 [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>10001 [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>01101 [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,5,2,3,6,4]=>01001 [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>10101 [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>00101 [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>11001 [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>10001 [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>01001 [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>10001 [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>00001 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>11100 [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>11010 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>11100 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>11000 [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>10110 [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,1,4,2,3,6]=>10100 [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>11010 [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>10010 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>11100 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>11000 [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>10100 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>11000 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>10000 [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>01110 [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[1,5,4,2,3,6]=>01100 [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[1,5,2,4,3,6]=>01010 [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[1,5,3,2,4,6]=>01100 [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[1,5,2,3,4,6]=>01000 [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>10110 [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,1,5,2,3,6]=>10100 [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>00110 [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[1,2,5,3,4,6]=>00100 [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>11010 [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>10010 [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>01010 [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>10010 [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>00010 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>11000 [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>10100 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>11000 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>10000 [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>01100 [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[1,4,2,3,5,6]=>01000 [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>10100 [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>00100 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>10000 [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>01000 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>111110 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>111101 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>111110 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>111100 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>111011 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,6,5,1,4,2,3]=>111010 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>111101 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>111001 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>111110 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>111100 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>111010 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>111100 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>111000 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>110111 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,6,1,5,4,2,3]=>110110 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,6,1,5,2,4,3]=>110101 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,6,1,5,3,2,4]=>110110 [.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,6,1,5,2,3,4]=>110100 [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>111011 [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,6,4,1,5,2,3]=>111010 [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>110011 [.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,6,1,2,5,3,4]=>110010 [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>111101 [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>111001 [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>110101 [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>111001 [.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>110001 [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>111110 [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>111100 [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>111010 [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>111100 [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>111000 [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>110110 [.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,6,1,4,2,3,5]=>110100 [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>111010 [.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>110010 [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>111100 [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>111000 [.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>110100 [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>111000 [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>110000 [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>101111 [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,1,6,5,4,2,3]=>101110 [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,1,6,5,2,4,3]=>101101 [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,1,6,5,3,2,4]=>101110 [.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,1,6,5,2,3,4]=>101100 [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,1,6,2,5,4,3]=>101011 [.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,1,6,2,5,3,4]=>101010 [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,1,6,4,2,5,3]=>101101 [.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,1,6,2,3,5,4]=>101001 [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,1,6,4,3,2,5]=>101110 [.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,1,6,4,2,3,5]=>101100 [.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,1,6,2,4,3,5]=>101010 [.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,1,6,3,2,4,5]=>101100 [.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,1,6,2,3,4,5]=>101000 [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>110111 [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,5,1,6,4,2,3]=>110110 [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,5,1,6,2,4,3]=>110101 [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,5,1,6,3,2,4]=>110110 [.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,5,1,6,2,3,4]=>110100 [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>100111 [.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,1,2,6,5,3,4]=>100110 [.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,1,2,6,3,5,4]=>100101 [.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,1,2,6,4,3,5]=>100110 [.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,1,2,6,3,4,5]=>100100 [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>111011 [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,4,1,6,2,3]=>111010 [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>110011 [.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,1,2,6,3,4]=>110010 [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>101011 [.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,1,5,2,6,3,4]=>101010 [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>110011 [.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,1,2,6,3,5]=>110010 [.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>100011 [.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,1,2,3,6,4,5]=>100010 [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>111101 [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>111001 [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>110101 [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>111001 [.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>110001 [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>101101 [.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,1,5,2,3,6,4]=>101001 [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>110101 [.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>100101 [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>111001 [.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>110001 [.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>101001 [.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>110001 [.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>100001 [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>111110 [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>111100 [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>111010 [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>111100 [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>111000 [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>110110 [.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,5,1,4,2,3,6]=>110100 [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>111010 [.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>110010 [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>111100 [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>111000 [.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>110100 [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>111000 [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>110000 [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>101110 [.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,1,5,4,2,3,6]=>101100 [.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,1,5,2,4,3,6]=>101010 [.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,1,5,3,2,4,6]=>101100 [.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,1,5,2,3,4,6]=>101000 [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>110110 [.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,1,5,2,3,6]=>110100 [.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>100110 [.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,1,2,5,3,4,6]=>100100 [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>111010 [.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>110010 [.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>101010 [.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>110010 [.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>100010 [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>111100 [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>111000 [.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>110100 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>111000 [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>110000 [.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>101100 [.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,1,4,2,3,5,6]=>101000 [.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>110100 [.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>100100 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>111000 [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>110000 [.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>101000 [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>110000 [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>100000 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>011111 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[1,7,6,5,4,2,3]=>011110 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,7,6,5,2,4,3]=>011101 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[1,7,6,5,3,2,4]=>011110 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[1,7,6,5,2,3,4]=>011100 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,7,6,2,5,4,3]=>011011 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[1,7,6,2,5,3,4]=>011010 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,7,6,4,2,5,3]=>011101 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,7,6,2,3,5,4]=>011001 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[1,7,6,4,3,2,5]=>011110 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[1,7,6,4,2,3,5]=>011100 [[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[1,7,6,2,4,3,5]=>011010 [[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[1,7,6,3,2,4,5]=>011100 [[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[1,7,6,2,3,4,5]=>011000 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,7,2,6,5,4,3]=>010111 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[1,7,2,6,5,3,4]=>010110 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,7,2,6,3,5,4]=>010101 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[1,7,2,6,4,3,5]=>010110 [[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[1,7,2,6,3,4,5]=>010100 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,7,5,2,6,4,3]=>011011 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[1,7,5,2,6,3,4]=>011010 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,7,2,3,6,5,4]=>010011 [[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[1,7,2,3,6,4,5]=>010010 [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,7,5,4,2,6,3]=>011101 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,7,5,2,3,6,4]=>011001 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,7,2,5,3,6,4]=>010101 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[1,7,4,2,3,6,5]=>011001 [[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,7,2,3,4,6,5]=>010001 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[1,7,5,4,3,2,6]=>011110 [[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[1,7,5,4,2,3,6]=>011100 [[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[1,7,5,2,4,3,6]=>011010 [[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[1,7,5,3,2,4,6]=>011100 [[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[1,7,5,2,3,4,6]=>011000 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[1,7,2,5,4,3,6]=>010110 [[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[1,7,2,5,3,4,6]=>010100 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[1,7,4,2,5,3,6]=>011010 [[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[1,7,2,3,5,4,6]=>010010 [[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[1,7,4,3,2,5,6]=>011100 [[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[1,7,4,2,3,5,6]=>011000 [[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[1,7,2,4,3,5,6]=>010100 [[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[1,7,3,2,4,5,6]=>011000 [[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[1,7,2,3,4,5,6]=>010000 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>101111 [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,1,7,5,4,2,3]=>101110 [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[6,1,7,5,2,4,3]=>101101 [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,1,7,5,3,2,4]=>101110 [[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[6,1,7,5,2,3,4]=>101100 [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,1,7,2,5,4,3]=>101011 [[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,1,7,2,5,3,4]=>101010 [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[6,1,7,4,2,5,3]=>101101 [[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[6,1,7,2,3,5,4]=>101001 [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,1,7,4,3,2,5]=>101110 [[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[6,1,7,4,2,3,5]=>101100 [[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,1,7,2,4,3,5]=>101010 [[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[6,1,7,3,2,4,5]=>101100 [[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[6,1,7,2,3,4,5]=>101000 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>001111 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[1,2,7,6,5,3,4]=>001110 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,2,7,6,3,5,4]=>001101 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[1,2,7,6,4,3,5]=>001110 [[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[1,2,7,6,3,4,5]=>001100 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,2,7,3,6,5,4]=>001011 [[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[1,2,7,3,6,4,5]=>001010 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,2,7,5,3,6,4]=>001101 [[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,2,7,3,4,6,5]=>001001 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[1,2,7,5,4,3,6]=>001110 [[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[1,2,7,5,3,4,6]=>001100 [[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[1,2,7,3,5,4,6]=>001010 [[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[1,2,7,4,3,5,6]=>001100 [[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[1,2,7,3,4,5,6]=>001000 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>110111 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,1,7,4,2,3]=>110110 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[6,5,1,7,2,4,3]=>110101 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,1,7,3,2,4]=>110110 [[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[6,5,1,7,2,3,4]=>110100 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>100111 [[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,1,2,7,5,3,4]=>100110 [[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[6,1,2,7,3,5,4]=>100101 [[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,1,2,7,4,3,5]=>100110 [[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[6,1,2,7,3,4,5]=>100100 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>010111 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[1,6,2,7,5,3,4]=>010110 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,6,2,7,3,5,4]=>010101 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[1,6,2,7,4,3,5]=>010110 [[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[1,6,2,7,3,4,5]=>010100 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>100111 [[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[5,1,2,7,6,3,4]=>100110 [[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,1,2,7,3,6,4]=>100101 [[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[5,1,2,7,4,3,6]=>100110 [[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,1,2,7,3,4,6]=>100100 [[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111 [[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[1,2,3,7,6,4,5]=>000110 [[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,3,7,4,6,5]=>000101 [[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[1,2,3,7,5,4,6]=>000110 [[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[1,2,3,7,4,5,6]=>000100 [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>111011 [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,5,4,1,7,2,3]=>111010 [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>110011 [[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,5,1,2,7,3,4]=>110010 [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>101011 [[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,1,5,2,7,3,4]=>101010 [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>110011 [[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,4,1,2,7,3,5]=>110010 [[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>100011 [[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,1,2,3,7,4,5]=>100010 [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>011011 [[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[1,6,5,2,7,3,4]=>011010 [[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,6,2,3,7,5,4]=>010011 [[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[1,6,2,3,7,4,5]=>010010 [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>101011 [[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,1,6,2,7,3,4]=>101010 [[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>001011 [[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[1,2,6,3,7,4,5]=>001010 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>110011 [[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,7,3,6]=>110010 [[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>100011 [[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,1,2,3,7,4,6]=>100010 [[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>010011 [[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[1,5,2,3,7,4,6]=>010010 [[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>100011 [[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[4,1,2,3,7,5,6]=>100010 [[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>000011 [[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[1,2,3,4,7,5,6]=>000010 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>111101 [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>111001 [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>110101 [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>111001 [[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>110001 [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>101101 [[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,5,2,3,7,4]=>101001 [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>110101 [[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>100101 [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>111001 [[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>110001 [[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>101001 [[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>110001 [[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>100001 [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>011101 [[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,6,5,2,3,7,4]=>011001 [[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,6,2,5,3,7,4]=>010101 [[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[1,6,4,2,3,7,5]=>011001 [[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,6,2,3,4,7,5]=>010001 [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>101101 [[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[5,1,6,2,3,7,4]=>101001 [[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>001101 [[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,2,6,3,4,7,5]=>001001 [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>110101 [[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>100101 [[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>010101 [[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>100101 [[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>000101 [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>111001 [[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>110001 [[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>101001 [[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>110001 [[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>100001 [[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>011001 [[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[1,5,2,3,4,7,6]=>010001 [[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>101001 [[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>001001 [[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>110001 [[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>100001 [[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>010001 [[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>100001 [[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>000001 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>111100 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>111010 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>111100 [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>111000 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>110110 [[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,5,1,4,2,3,7]=>110100 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>111010 [[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>110010 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>111100 [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>111000 [[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>110100 [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>111000 [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>110000 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>101110 [[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,1,5,4,2,3,7]=>101100 [[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,1,5,2,4,3,7]=>101010 [[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,1,5,3,2,4,7]=>101100 [[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,1,5,2,3,4,7]=>101000 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>110110 [[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,1,5,2,3,7]=>110100 [[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>100110 [[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,1,2,5,3,4,7]=>100100 [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>111010 [[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>110010 [[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>101010 [[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>110010 [[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>100010 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>111100 [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>111000 [[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>110100 [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>111000 [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>110000 [[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>101100 [[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,1,4,2,3,5,7]=>101000 [[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>110100 [[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>100100 [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>111000 [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>110000 [[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>101000 [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>110000 [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>100000 [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>011110 [[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[1,6,5,4,2,3,7]=>011100 [[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[1,6,5,2,4,3,7]=>011010 [[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[1,6,5,3,2,4,7]=>011100 [[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[1,6,5,2,3,4,7]=>011000 [[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[1,6,2,5,4,3,7]=>010110 [[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>010100 [[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[1,6,4,2,5,3,7]=>011010 [[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[1,6,2,3,5,4,7]=>010010 [[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[1,6,4,3,2,5,7]=>011100 [[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[1,6,4,2,3,5,7]=>011000 [[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[1,6,2,4,3,5,7]=>010100 [[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[1,6,3,2,4,5,7]=>011000 [[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[1,6,2,3,4,5,7]=>010000 [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>101110 [[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,1,6,4,2,3,7]=>101100 [[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[5,1,6,2,4,3,7]=>101010 [[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,1,6,3,2,4,7]=>101100 [[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[5,1,6,2,3,4,7]=>101000 [[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>001110 [[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[1,2,6,5,3,4,7]=>001100 [[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,2,6,3,5,4,7]=>001010 [[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[1,2,6,4,3,5,7]=>001100 [[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[1,2,6,3,4,5,7]=>001000 [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>110110 [[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,4,1,6,2,3,7]=>110100 [[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>100110 [[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,1,2,6,3,4,7]=>100100 [[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>010110 [[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[1,5,2,6,3,4,7]=>010100 [[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>100110 [[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[4,1,2,6,3,5,7]=>100100 [[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>000110 [[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[1,2,3,6,4,5,7]=>000100 [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>111010 [[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>110010 [[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>101010 [[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>110010 [[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>100010 [[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>011010 [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[1,5,2,3,6,4,7]=>010010 [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>101010 [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>001010 [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>110010 [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>100010 [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>010010 [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>100010 [[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>000010 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100 [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>111000 [[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>110100 [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>111000 [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>110000 [[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>101100 [[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,1,4,2,3,6,7]=>101000 [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>110100 [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>100100 [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>111000 [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>110000 [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>101000 [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>110000 [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>100000 [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>011100 [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[1,5,4,2,3,6,7]=>011000 [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[1,5,2,4,3,6,7]=>010100 [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[1,5,3,2,4,6,7]=>011000 [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[1,5,2,3,4,6,7]=>010000 [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>101100 [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,1,5,2,3,6,7]=>101000 [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>001100 [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[1,2,5,3,4,6,7]=>001000 [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>110100 [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>100100 [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>010100 [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>100100 [[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>000100 [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000 [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>110000 [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000 [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>110000 [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>100000 [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000 [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>010000 [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>101000 [[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000 [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000 [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000 [[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000 [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000 [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>1111110 [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>1111101 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>1111110 [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>1111100 [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>1111011 [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,1,4,2,3]=>1111010 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>1111101 [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>1111001 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>1111110 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>1111100 [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>1111010 [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>1111100 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>1111000 [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>1110111 [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[8,7,6,1,5,4,2,3]=>1110110 [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[8,7,6,1,5,2,4,3]=>1110101 [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[8,7,6,1,5,3,2,4]=>1110110 [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[8,7,6,1,5,2,3,4]=>1110100 [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>1111011 [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>1110011 [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>1111101 [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,1,2,5,3]=>1111001 [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[8,7,6,1,4,2,5,3]=>1110101 [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>1110001 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>1111110 [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>1111100 [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>1111010 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>1111100 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>1111000 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>1110110 [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[8,7,6,1,4,2,3,5]=>1110100 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,1,4,2,5]=>1111010 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>1110010 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>1111100 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>1111000 [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>1110100 [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>1111000 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>1110000 [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,7,1,6,5,4,3,2]=>1101111 [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[8,7,1,6,5,2,4,3]=>1101101 [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,7,1,6,5,3,2,4]=>1101110 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,7,1,6,2,5,4,3]=>1101011 [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,7,1,6,2,5,3,4]=>1101010 [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,7,1,6,2,3,5,4]=>1101001 [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,7,1,6,4,3,2,5]=>1101110 [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[8,7,1,6,4,2,3,5]=>1101100 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,7,1,6,2,3,4,5]=>1101000 [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>1110111 [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[8,7,5,1,6,4,2,3]=>1110110 [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[8,7,5,1,6,3,2,4]=>1110110 [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,7,5,1,6,2,3,4]=>1110100 [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[8,7,1,2,6,5,4,3]=>1100111 [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[8,7,1,2,6,5,3,4]=>1100110 [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[8,7,1,2,6,3,4,5]=>1100100 [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>1111011 [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[8,7,5,4,1,6,2,3]=>1111010 [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[8,7,5,1,2,6,4,3]=>1110011 [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[8,7,1,5,2,6,3,4]=>1101010 [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,7,4,1,2,6,5,3]=>1110011 [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[8,7,1,2,3,6,5,4]=>1100011 [.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[8,7,1,2,3,6,4,5]=>1100010 [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>1111101 [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>1111001 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[8,7,4,1,5,2,6,3]=>1110101 [.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[8,7,3,1,2,4,6,5]=>1110001 [.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[8,7,1,2,3,4,6,5]=>1100001 [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>1111110 [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>1111100 [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>1111010 [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>1111000 [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>1110110 [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[8,7,5,1,4,2,3,6]=>1110100 [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>1111010 [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[8,7,5,1,2,4,3,6]=>1110010 [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>1111100 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>1111000 [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>1110000 [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>1100110 [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,1,5,2,6]=>1111010 [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[8,7,1,4,2,5,3,6]=>1101010 [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>1111100 [.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>1110000 [.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[8,7,1,4,3,2,5,6]=>1101100 [.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[8,7,1,2,4,3,5,6]=>1100100 [.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>1111000 [.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[8,7,1,3,2,4,5,6]=>1101000 [.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>1110000 [.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>1100000 [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,1,7,6,5,4,3,2]=>1011111 [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[8,1,7,6,5,4,2,3]=>1011110 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[8,1,7,6,5,2,4,3]=>1011101 [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[8,1,7,6,5,3,2,4]=>1011110 [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[8,1,7,6,2,5,4,3]=>1011011 [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[8,1,7,6,4,2,5,3]=>1011101 [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[8,1,7,6,4,3,2,5]=>1011110 [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[8,1,7,6,4,2,3,5]=>1011100 [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[8,1,7,6,2,4,3,5]=>1011010 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,1,7,6,2,3,4,5]=>1011000 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,1,7,2,6,5,4,3]=>1010111 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,1,7,2,6,3,5,4]=>1010101 [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[8,1,7,2,6,4,3,5]=>1010110 [.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,1,7,2,6,3,4,5]=>1010100 [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[8,1,7,2,3,6,5,4]=>1010011 [.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[8,1,7,2,3,6,4,5]=>1010010 [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,1,7,5,4,2,6,3]=>1011101 [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[8,1,7,2,5,3,6,4]=>1010101 [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[8,1,7,5,4,3,2,6]=>1011110 [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[8,1,7,5,2,4,3,6]=>1011010 [.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,1,7,5,3,2,4,6]=>1011100 [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[8,1,7,2,5,4,3,6]=>1010110 [.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[8,1,7,2,5,3,4,6]=>1010100 [.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[8,1,7,2,3,4,5,6]=>1010000 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,6,1,7,5,4,3,2]=>1101111 [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[8,6,1,7,5,4,2,3]=>1101110 [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[8,6,1,7,5,2,4,3]=>1101101 [.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[8,6,1,7,5,2,3,4]=>1101100 [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[8,6,1,7,2,5,4,3]=>1101011 [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[8,6,1,7,4,2,5,3]=>1101101 [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[8,6,1,7,2,3,5,4]=>1101001 [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,6,1,7,4,3,2,5]=>1101110 [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[8,6,1,7,4,2,3,5]=>1101100 [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,6,1,7,2,3,4,5]=>1101000 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,1,2,7,6,5,4,3]=>1001111 [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[8,1,2,7,6,3,5,4]=>1001101 [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,1,2,7,6,3,4,5]=>1001100 [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[8,1,2,7,3,6,5,4]=>1001011 [.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[8,1,2,7,3,6,4,5]=>1001010 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[8,1,2,7,3,4,6,5]=>1001001 [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,1,2,7,5,4,3,6]=>1001110 [.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[8,1,2,7,5,3,4,6]=>1001100 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,1,2,7,3,4,5,6]=>1001000 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>1110111 [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[8,6,5,1,7,4,2,3]=>1110110 [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[8,6,5,1,7,2,4,3]=>1110101 [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[8,6,5,1,7,3,2,4]=>1110110 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,6,1,2,7,5,4,3]=>1100111 [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[8,6,1,2,7,5,3,4]=>1100110 [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,6,1,2,7,3,5,4]=>1100101 [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[8,6,1,2,7,4,3,5]=>1100110 [.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[8,6,1,2,7,3,4,5]=>1100100 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[8,1,6,2,7,3,5,4]=>1010101 [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[8,1,6,2,7,4,3,5]=>1010110 [.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,1,6,2,7,3,4,5]=>1010100 [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[8,5,1,2,7,6,4,3]=>1100111 [.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[8,5,1,2,7,6,3,4]=>1100110 [.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[8,5,1,2,7,3,4,6]=>1100100 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[8,1,2,3,7,6,5,4]=>1000111 [.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[8,1,2,3,7,5,4,6]=>1000110 [.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[8,1,2,3,7,4,5,6]=>1000100 [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,1,7,2,3]=>1111010 [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[8,6,1,5,2,7,4,3]=>1101011 [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[8,6,4,1,2,7,5,3]=>1110011 [.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[8,6,4,1,2,7,3,5]=>1110010 [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[8,1,6,5,2,7,4,3]=>1011011 [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[8,5,4,1,2,7,6,3]=>1110011 [.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[8,5,4,1,2,7,3,6]=>1110010 [.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,5,1,2,3,7,4,6]=>1100010 [.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[8,1,5,2,3,7,4,6]=>1010010 [.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,4,1,2,3,7,5,6]=>1100010 [.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[8,1,2,3,4,7,6,5]=>1000011 [.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[8,1,2,3,4,7,5,6]=>1000010 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>1111101 [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,1,2,7,3]=>1111001 [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>1111001 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,6,4,1,5,2,7,3]=>1110101 [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,6,1,2,5,3,7,4]=>1100101 [.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,6,4,1,2,3,7,5]=>1110001 [.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[8,6,3,1,2,4,7,5]=>1110001 [.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[8,6,1,2,3,4,7,5]=>1100001 [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,1,6,5,2,3,7,4]=>1011001 [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[8,1,6,2,5,3,7,4]=>1010101 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[8,5,1,6,4,2,7,3]=>1101101 [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[8,5,4,1,6,2,7,3]=>1110101 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[8,1,5,2,6,3,7,4]=>1010101 [.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[8,1,2,3,6,4,7,5]=>1000101 [.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[8,5,4,1,2,3,7,6]=>1110001 [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[8,5,1,4,2,3,7,6]=>1101001 [.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[8,1,2,5,3,4,7,6]=>1001001 [.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[8,4,3,1,2,5,7,6]=>1110001 [.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[8,1,4,2,3,5,7,6]=>1010001 [.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[8,3,1,2,4,5,7,6]=>1100001 [.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[8,1,2,3,4,5,7,6]=>1000001 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>1111110 [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>1111100 [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>1111010 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>1111100 [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>1111000 [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>1110110 [.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>1110010 [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>1111100 [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>1110100 [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>1110000 [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>1101110 [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,6,1,5,2,4,3,7]=>1101010 [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,6,1,5,3,2,4,7]=>1101100 [.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[8,6,1,5,2,3,4,7]=>1101000 [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>1110110 [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>[8,6,1,2,5,4,3,7]=>1100110 [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,4,1,2,5,3,7]=>1110010 [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[8,6,1,4,2,5,3,7]=>1101010 [.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[8,6,1,2,3,5,4,7]=>1100010 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>1111100 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>1110100 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>1111000 [.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>1110000 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>1101100 [.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,6,1,4,2,3,5,7]=>1101000 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,6,3,1,4,2,5,7]=>1110100 [.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[8,6,1,2,4,3,5,7]=>1100100 [.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>1100000 [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,1,6,5,4,3,2,7]=>1011110 [.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[8,1,6,5,2,3,4,7]=>1011000 [.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,1,6,2,5,3,4,7]=>1010100 [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[8,1,6,4,2,5,3,7]=>1011010 [.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,1,6,2,3,5,4,7]=>1010010 [.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[8,1,6,4,2,3,5,7]=>1011000 [.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,1,6,2,4,3,5,7]=>1010100 [.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[8,1,6,3,2,4,5,7]=>1011000 [.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,1,6,2,3,4,5,7]=>1010000 [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[8,5,1,6,4,3,2,7]=>1101110 [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[8,5,1,6,4,2,3,7]=>1101100 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,5,1,6,3,2,4,7]=>1101100 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,1,2,6,5,4,3,7]=>1001110 [.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[8,1,2,6,3,4,5,7]=>1001000 [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,5,4,1,6,2,3,7]=>1110100 [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,1,5,2,6,4,3,7]=>1010110 [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[8,4,1,2,6,5,3,7]=>1100110 [.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,4,1,2,6,3,5,7]=>1100100 [.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[8,1,2,3,6,5,4,7]=>1000110 [.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[8,1,2,3,6,4,5,7]=>1000100 [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[8,1,5,4,2,6,3,7]=>1011010 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,4,1,5,2,6,3,7]=>1101010 [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[8,4,3,1,2,6,5,7]=>1110010 [.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[8,1,4,2,3,6,5,7]=>1010010 [.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[8,3,1,2,4,6,5,7]=>1100010 [.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[8,1,2,3,4,6,5,7]=>1000010 [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>1111100 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>1111000 [.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>1110000 [.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>1100100 [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>1111000 [.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>1110000 [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>1100000 [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>1011100 [.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[8,1,5,4,2,3,6,7]=>1011000 [.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[8,1,5,3,2,4,6,7]=>1011000 [.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,1,5,2,3,4,6,7]=>1010000 [.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[8,4,1,5,3,2,6,7]=>1101100 [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>1001100 [.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[8,1,2,5,3,4,6,7]=>1001000 [.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[8,1,2,3,5,4,6,7]=>1000100 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>1111000 [.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[8,4,1,3,2,5,6,7]=>1101000 [.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>1110000 [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>1100000 [.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>1011000 [.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>1010000 [.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>1001000 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>1110000 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>1100000 [.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>1010000 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>1100000 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>1000000 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>0111111 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[1,8,7,6,5,4,2,3]=>0111110 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[1,8,7,6,5,2,4,3]=>0111101 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[1,8,7,6,5,3,2,4]=>0111110 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[1,8,7,6,5,2,3,4]=>0111100 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[1,8,7,6,2,5,4,3]=>0111011 [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[1,8,7,6,4,2,5,3]=>0111101 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[1,8,7,6,4,3,2,5]=>0111110 [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[1,8,7,6,4,2,3,5]=>0111100 [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[1,8,7,6,2,4,3,5]=>0111010 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[1,8,7,6,3,2,4,5]=>0111100 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[1,8,7,6,2,3,4,5]=>0111000 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[1,8,7,2,6,5,4,3]=>0110111 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[1,8,7,2,6,5,3,4]=>0110110 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[1,8,7,2,6,3,5,4]=>0110101 [[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[1,8,7,2,6,3,4,5]=>0110100 [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[1,8,7,2,3,6,4,5]=>0110010 [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[1,8,7,4,2,3,6,5]=>0111001 [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[1,8,7,5,4,3,2,6]=>0111110 [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[1,8,7,5,3,2,4,6]=>0111100 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[1,8,7,2,5,4,3,6]=>0110110 [[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[1,8,7,2,5,3,4,6]=>0110100 [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[1,8,7,4,3,2,5,6]=>0111100 [[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[1,8,7,4,2,3,5,6]=>0111000 [[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[1,8,7,3,2,4,5,6]=>0111000 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[1,8,7,2,3,4,5,6]=>0110000 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[1,8,2,7,6,5,4,3]=>0101111 [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[1,8,2,7,6,4,3,5]=>0101110 [[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[1,8,2,7,6,3,4,5]=>0101100 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[1,8,2,7,3,6,5,4]=>0101011 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[1,8,2,7,3,6,4,5]=>0101010 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[1,8,2,7,5,3,6,4]=>0101101 [[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[1,8,2,7,3,4,6,5]=>0101001 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[1,8,2,7,5,4,3,6]=>0101110 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[1,8,2,7,5,3,4,6]=>0101100 [[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[1,8,2,7,3,5,4,6]=>0101010 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[1,8,2,7,4,3,5,6]=>0101100 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[1,8,2,7,3,4,5,6]=>0101000 [[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[1,8,6,2,7,3,4,5]=>0110100 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[1,8,2,3,7,6,5,4]=>0100111 [[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[1,8,2,3,7,6,4,5]=>0100110 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[1,8,6,5,2,7,3,4]=>0111010 [[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[1,8,6,2,3,7,4,5]=>0110010 [[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[1,8,2,6,3,7,4,5]=>0101010 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[1,8,5,2,3,7,6,4]=>0110011 [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[1,8,5,2,3,7,4,6]=>0110010 [[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[1,8,2,3,4,7,6,5]=>0100011 [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[1,8,2,3,4,7,5,6]=>0100010 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[1,8,5,4,2,3,7,6]=>0111001 [[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[1,8,2,5,3,4,7,6]=>0101001 [[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[1,8,4,2,3,5,7,6]=>0110001 [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[1,8,2,3,4,5,7,6]=>0100001 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[1,8,6,5,4,3,2,7]=>0111110 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[1,8,6,5,3,2,4,7]=>0111100 [[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[1,8,6,2,5,3,4,7]=>0110100 [[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[1,8,6,4,2,3,5,7]=>0111000 [[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[1,8,6,2,4,3,5,7]=>0110100 [[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[1,8,6,3,2,4,5,7]=>0111000 [[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[1,8,6,2,3,4,5,7]=>0110000 [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[1,8,2,6,3,5,4,7]=>0101010 [[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[1,8,2,6,3,4,5,7]=>0101000 [[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[1,8,2,3,6,5,4,7]=>0100110 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[1,8,5,4,2,6,3,7]=>0111010 [[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[1,8,2,5,3,6,4,7]=>0101010 [[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[1,8,2,3,4,6,5,7]=>0100010 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[1,8,5,4,3,2,6,7]=>0111100 [[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[1,8,5,4,2,3,6,7]=>0111000 [[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[1,8,5,3,2,4,6,7]=>0111000 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[1,8,2,5,3,4,6,7]=>0101000 [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[1,8,4,2,5,3,6,7]=>0110100 [[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[1,8,2,3,5,4,6,7]=>0100100 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[1,8,4,3,2,5,6,7]=>0111000 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[1,8,4,2,3,5,6,7]=>0110000 [[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[1,8,2,4,3,5,6,7]=>0101000 [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[1,8,3,2,4,5,6,7]=>0110000 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[1,8,2,3,4,5,6,7]=>0100000 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,1,8,6,5,4,3,2]=>1011111 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[7,1,8,6,5,4,2,3]=>1011110 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[7,1,8,6,5,2,4,3]=>1011101 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,1,8,6,5,3,2,4]=>1011110 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[7,1,8,6,5,2,3,4]=>1011100 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[7,1,8,6,2,5,4,3]=>1011011 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[7,1,8,6,2,5,3,4]=>1011010 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[7,1,8,6,4,3,2,5]=>1011110 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[7,1,8,6,4,2,3,5]=>1011100 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[7,1,8,6,2,4,3,5]=>1011010 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[7,1,8,6,3,2,4,5]=>1011100 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[7,1,8,6,2,3,4,5]=>1011000 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[7,1,8,2,6,5,4,3]=>1010111 [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[7,1,8,2,6,3,5,4]=>1010101 [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[7,1,8,2,6,4,3,5]=>1010110 [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[7,1,8,2,3,6,5,4]=>1010011 [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[7,1,8,2,5,3,6,4]=>1010101 [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[7,1,8,5,4,3,2,6]=>1011110 [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[7,1,8,5,4,2,3,6]=>1011100 [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[7,1,8,5,3,2,4,6]=>1011100 [[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[7,1,8,5,2,3,4,6]=>1011000 [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[7,1,8,2,5,4,3,6]=>1010110 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[7,1,8,4,2,5,3,6]=>1011010 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[7,1,8,2,3,4,5,6]=>1010000 [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>0011111 [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[1,2,8,7,6,5,3,4]=>0011110 [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[1,2,8,7,6,4,3,5]=>0011110 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[1,2,8,7,6,3,4,5]=>0011100 [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[1,2,8,7,5,3,6,4]=>0011101 [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[1,2,8,7,3,4,6,5]=>0011001 [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[1,2,8,7,5,4,3,6]=>0011110 [[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[1,2,8,7,3,5,4,6]=>0011010 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[1,2,8,7,3,4,5,6]=>0011000 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[1,2,8,3,7,6,5,4]=>0010111 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[1,2,8,3,7,4,6,5]=>0010101 [[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[1,2,8,3,7,4,5,6]=>0010100 [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[1,2,8,6,3,7,5,4]=>0011011 [[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[1,2,8,6,3,7,4,5]=>0011010 [[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[1,2,8,3,4,7,6,5]=>0010011 [[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[1,2,8,6,3,4,7,5]=>0011001 [[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[1,2,8,3,6,4,7,5]=>0010101 [[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[1,2,8,3,4,5,7,6]=>0010001 [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[1,2,8,6,5,4,3,7]=>0011110 [[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[1,2,8,6,4,3,5,7]=>0011100 [[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[1,2,8,6,3,4,5,7]=>0011000 [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[1,2,8,3,6,5,4,7]=>0010110 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[1,2,8,3,6,4,5,7]=>0010100 [[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[1,2,8,5,3,6,4,7]=>0011010 [[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[1,2,8,3,4,6,5,7]=>0010010 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[1,2,8,5,4,3,6,7]=>0011100 [[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[1,2,8,5,3,4,6,7]=>0011000 [[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[1,2,8,3,5,4,6,7]=>0010100 [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[1,2,8,4,3,5,6,7]=>0011000 [[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[1,2,8,3,4,5,6,7]=>0010000 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,1,8,5,4,3,2]=>1101111 [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[7,6,1,8,5,4,2,3]=>1101110 [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[7,6,1,8,5,3,2,4]=>1101110 [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[7,6,1,8,5,2,3,4]=>1101100 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[7,6,1,8,2,5,4,3]=>1101011 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,6,1,8,2,5,3,4]=>1101010 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[7,6,1,8,4,2,5,3]=>1101101 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[7,6,1,8,2,3,5,4]=>1101001 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,1,8,4,3,2,5]=>1101110 [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[7,6,1,8,4,2,3,5]=>1101100 [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[7,6,1,8,3,2,4,5]=>1101100 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[7,6,1,8,2,3,4,5]=>1101000 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,1,2,8,6,5,4,3]=>1001111 [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[7,1,2,8,6,4,3,5]=>1001110 [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[7,1,2,8,3,6,5,4]=>1001011 [[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,1,2,8,3,6,4,5]=>1001010 [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[7,1,2,8,5,3,4,6]=>1001100 [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,1,2,8,3,5,4,6]=>1001010 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[7,1,2,8,3,4,5,6]=>1001000 [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[1,7,2,8,6,5,3,4]=>0101110 [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[1,7,2,8,6,3,5,4]=>0101101 [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[1,7,2,8,3,6,5,4]=>0101011 [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[1,7,2,8,3,6,4,5]=>0101010 [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[1,7,2,8,5,3,6,4]=>0101101 [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[1,7,2,8,5,4,3,6]=>0101110 [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[1,7,2,8,5,3,4,6]=>0101100 [[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[1,7,2,8,3,5,4,6]=>0101010 [[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[1,7,2,8,4,3,5,6]=>0101100 [[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[1,7,2,8,3,4,5,6]=>0101000 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[6,1,2,8,7,5,3,4]=>1001110 [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[6,1,2,8,7,4,3,5]=>1001110 [[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,1,2,8,7,3,4,5]=>1001100 [[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[6,1,2,8,3,7,4,5]=>1001010 [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[6,1,2,8,5,3,7,4]=>1001101 [[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[6,1,2,8,3,4,7,5]=>1001001 [[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[6,1,2,8,5,3,4,7]=>1001100 [[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[6,1,2,8,3,5,4,7]=>1001010 [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,1,2,8,4,3,5,7]=>1001100 [[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[6,1,2,8,3,4,5,7]=>1001000 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>0001111 [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[1,2,3,8,7,6,4,5]=>0001110 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[1,2,3,8,7,4,6,5]=>0001101 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[1,2,3,8,7,5,4,6]=>0001110 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[1,2,3,8,7,4,5,6]=>0001100 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,2,3,8,4,7,6,5]=>0001011 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[1,2,3,8,4,7,5,6]=>0001010 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[1,2,3,8,6,4,7,5]=>0001101 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[1,2,3,8,4,5,7,6]=>0001001 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[1,2,3,8,6,5,4,7]=>0001110 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[1,2,3,8,6,4,5,7]=>0001100 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[1,2,3,8,4,6,5,7]=>0001010 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[1,2,3,8,5,4,6,7]=>0001100 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[1,2,3,8,4,5,6,7]=>0001000 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,5,1,8,4,3,2]=>1110111 [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[7,6,5,1,8,4,2,3]=>1110110 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[7,6,5,1,8,2,4,3]=>1110101 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[7,6,5,1,8,3,2,4]=>1110110 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[7,6,5,1,8,2,3,4]=>1110100 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,1,2,8,5,4,3]=>1100111 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,1,6,2,8,5,4,3]=>1010111 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[7,1,6,2,8,3,5,4]=>1010101 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[7,1,6,2,8,4,3,5]=>1010110 [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[7,1,6,2,8,3,4,5]=>1010100 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,5,1,2,8,6,4,3]=>1100111 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[7,5,1,2,8,3,4,6]=>1100100 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,1,2,3,8,6,5,4]=>1000111 [[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[7,1,2,3,8,5,4,6]=>1000110 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[7,1,2,3,8,4,5,6]=>1000100 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[1,7,6,2,8,5,4,3]=>0110111 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[1,7,6,2,8,3,4,5]=>0110100 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[1,7,2,3,8,6,5,4]=>0100111 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[1,7,2,3,8,6,4,5]=>0100110 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[1,7,2,3,8,4,5,6]=>0100100 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[6,1,7,2,8,5,4,3]=>1010111 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[6,1,7,2,8,3,5,4]=>1010101 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,1,7,2,8,3,4,5]=>1010100 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[1,2,7,3,8,6,5,4]=>0010111 [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[1,2,7,3,8,6,4,5]=>0010110 [[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[1,2,7,3,8,5,4,6]=>0010110 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[1,2,7,3,8,4,5,6]=>0010100 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[6,5,1,2,8,7,4,3]=>1100111 [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[6,5,1,2,8,7,3,4]=>1100110 [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[6,5,1,2,8,3,7,4]=>1100101 [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[6,5,1,2,8,4,3,7]=>1100110 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,5,1,2,8,3,4,7]=>1100100 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[6,1,2,3,8,7,5,4]=>1000111 [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[6,1,2,3,8,7,4,5]=>1000110 [[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[6,1,2,3,8,4,7,5]=>1000101 [[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[6,1,2,3,8,5,4,7]=>1000110 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,1,2,3,8,4,5,7]=>1000100 [[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[1,6,2,3,8,7,4,5]=>0100110 [[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[1,6,2,3,8,5,4,7]=>0100110 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[1,6,2,3,8,4,5,7]=>0100100 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,1,2,3,8,7,6,4]=>1000111 [[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[5,1,2,3,8,7,4,6]=>1000110 [[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,1,2,3,8,4,7,6]=>1000101 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,1,2,3,8,4,6,7]=>1000100 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>0000111 [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[1,2,3,4,8,7,5,6]=>0000110 [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[1,2,3,4,8,5,7,6]=>0000101 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[1,2,3,4,8,6,5,7]=>0000110 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[1,2,3,4,8,5,6,7]=>0000100 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,1,8,3,2]=>1111011 [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,1,8,2,3]=>1111010 [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[7,6,5,1,2,8,4,3]=>1110011 [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6]=>[7,6,5,1,2,8,3,4]=>1110010 [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[7,6,1,2,3,8,5,4]=>1100011 [[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[7,6,1,2,3,8,4,5]=>1100010 [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[7,1,6,2,3,8,5,4]=>1010011 [[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,1,6,2,3,8,4,5]=>1010010 [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[7,5,1,6,2,8,4,3]=>1101011 [[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[7,1,2,6,3,8,4,5]=>1001010 [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[7,5,4,1,2,8,3,6]=>1110010 [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[7,5,1,2,3,8,6,4]=>1100011 [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[7,5,1,2,3,8,4,6]=>1100010 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[7,1,2,3,4,8,6,5]=>1000011 [[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[7,1,2,3,4,8,5,6]=>1000010 [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[1,7,6,5,2,8,4,3]=>0111011 [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[1,7,6,5,2,8,3,4]=>0111010 [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[1,7,2,6,3,8,5,4]=>0101011 [[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[1,7,2,6,3,8,4,5]=>0101010 [[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[1,7,2,3,4,8,6,5]=>0100011 [[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[1,7,2,3,4,8,5,6]=>0100010 [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,1,7,5,2,8,3,4]=>1011010 [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[1,2,7,6,3,8,5,4]=>0011011 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[1,2,7,6,3,8,4,5]=>0011010 [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[1,2,7,3,4,8,6,5]=>0010011 [[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[1,2,7,3,4,8,5,6]=>0010010 [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,5,1,7,2,8,4,3]=>1101011 [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[6,5,1,7,2,8,3,4]=>1101010 [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,1,2,7,3,8,5,4]=>1001011 [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[1,6,2,7,3,8,5,4]=>0101011 [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[1,6,2,7,3,8,4,5]=>0101010 [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[5,1,2,7,3,8,6,4]=>1001011 [[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[5,1,2,7,3,8,4,6]=>1001010 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[1,2,3,7,4,8,6,5]=>0001011 [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[1,2,3,7,4,8,5,6]=>0001010 [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,4,1,2,8,3,7]=>1110010 [[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>1100010 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[6,4,1,2,3,8,7,5]=>1100011 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,4,1,2,3,8,5,7]=>1100010 [[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[6,1,2,3,4,8,7,5]=>1000011 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,1,2,3,4,8,5,7]=>1000010 [[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[1,6,5,2,3,8,4,7]=>0110010 [[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[1,6,2,3,4,8,7,5]=>0100011 [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[1,6,2,3,4,8,5,7]=>0100010 [[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[5,1,6,2,3,8,4,7]=>1010010 [[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[1,2,6,3,4,8,7,5]=>0010011 [[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[1,2,6,3,4,8,5,7]=>0010010 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[5,4,1,2,3,8,7,6]=>1100011 [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[5,4,1,2,3,8,6,7]=>1100010 [[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[5,1,2,3,4,8,7,6]=>1000011 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[5,1,2,3,4,8,6,7]=>1000010 [[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[1,5,2,3,4,8,6,7]=>0100010 [[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[4,1,2,3,5,8,7,6]=>1000011 [[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[4,1,2,3,5,8,6,7]=>1000010 [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>0000011 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,8,6,7]=>0000010 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,1,8,2]=>1111101 [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,1,2,8,3]=>1111001 [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,6,5,1,4,2,8,3]=>1110101 [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,1,2,8,4]=>1111001 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,6,5,1,2,3,8,4]=>1110001 [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,6,1,5,4,2,8,3]=>1101101 [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[7,6,1,5,2,3,8,4]=>1101001 [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,6,4,1,5,2,8,3]=>1110101 [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,6,4,1,2,3,8,5]=>1110001 [[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,6,3,1,2,4,8,5]=>1110001 [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,6,1,2,3,4,8,5]=>1100001 [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[7,1,6,5,2,3,8,4]=>1011001 [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,6,2,5,3,8,4]=>1010101 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,2,6,5,3,8,4]=>1001101 [[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[7,1,2,6,3,4,8,5]=>1001001 [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[7,5,4,1,6,2,8,3]=>1110101 [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,2,6,3,8,4]=>1010101 [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,4,1,2,6,3,8,5]=>1100101 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,5,3,1,2,4,8,6]=>1110001 [[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,1,5,2,3,4,8,6]=>1010001 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,4,1,5,2,3,8,6]=>1101001 [[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[7,1,2,5,3,4,8,6]=>1001001 [[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,4,1,2,3,5,8,6]=>1100001 [[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,3,1,2,4,5,8,6]=>1100001 [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,1,2,3,4,5,8,6]=>1000001 [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[1,7,6,5,4,2,8,3]=>0111101 [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[1,7,6,2,5,3,8,4]=>0110101 [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[1,7,2,6,3,4,8,5]=>0101001 [[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[1,7,2,3,6,4,8,5]=>0100101 [[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[1,7,5,2,3,4,8,6]=>0110001 [[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[1,7,2,5,3,4,8,6]=>0101001 [[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[1,7,4,2,3,5,8,6]=>0110001 [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[1,7,2,3,4,5,8,6]=>0100001 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[6,1,7,5,4,2,8,3]=>1011101 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[6,1,7,2,5,3,8,4]=>1010101 [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>[6,1,7,2,3,4,8,5]=>1010001 [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[1,2,7,6,5,3,8,4]=>0011101 [[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[1,2,7,6,3,4,8,5]=>0011001 [[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[1,2,7,3,6,4,8,5]=>0010101 [[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[1,2,7,3,4,5,8,6]=>0010001 [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[6,5,1,7,4,2,8,3]=>1101101 [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[6,5,1,7,2,3,8,4]=>1101001 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,1,2,7,5,3,8,4]=>1001101 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[6,1,2,7,3,4,8,5]=>1001001 [[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[1,6,2,7,3,4,8,5]=>0101001 [[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,1,2,7,3,4,8,6]=>1001001 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[1,2,3,7,6,4,8,5]=>0001101 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[1,2,3,7,4,5,8,6]=>0001001 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,5,4,1,7,2,8,3]=>1110101 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,5,1,2,7,3,8,4]=>1100101 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[6,1,5,2,7,3,8,4]=>1010101 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[6,4,1,2,7,3,8,5]=>1100101 [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[6,1,2,3,7,4,8,5]=>1000101 [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[1,6,5,2,7,3,8,4]=>0110101 [[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[1,6,2,3,7,4,8,5]=>0100101 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>1010101 [[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[1,2,6,3,7,4,8,5]=>0010101 [[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[5,4,1,2,7,3,8,6]=>1100101 [[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,7,5,8,6]=>0000101 [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,1,2,8,7]=>1111001 [[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[6,5,1,2,3,4,8,7]=>1100001 [[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[6,1,5,2,3,4,8,7]=>1010001 [[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[6,1,4,2,3,5,8,7]=>1010001 [[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[6,1,2,3,4,5,8,7]=>1000001 [[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[1,6,2,5,3,4,8,7]=>0101001 [[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[1,6,2,3,4,5,8,7]=>0100001 [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[5,1,6,4,2,3,8,7]=>1011001 [[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[1,2,6,3,4,5,8,7]=>0010001 [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[5,4,1,6,2,3,8,7]=>1101001 [[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[1,5,2,6,3,4,8,7]=>0101001 [[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[4,1,2,6,3,5,8,7]=>1001001 [[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[1,2,3,6,4,5,8,7]=>0001001 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[5,1,2,3,4,6,8,7]=>1000001 [[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[1,5,2,3,4,6,8,7]=>0100001 [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[1,2,5,3,4,6,8,7]=>0010001 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,3,1,2,5,6,8,7]=>1100001 [[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[4,1,2,3,5,6,8,7]=>1000001 [[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[1,4,2,3,5,6,8,7]=>0100001 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[3,1,2,4,5,6,8,7]=>1000001 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>0000001 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>1111100 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,1,3,2,8]=>1111010 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>1111100 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>1111000 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>1110110 [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[7,6,5,1,4,2,3,8]=>1110100 [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,1,4,2,8]=>1111010 [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>1110010 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>1111100 [[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>1111000 [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>1110000 [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,6,1,5,2,4,3,8]=>1101010 [[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[7,6,4,1,5,2,3,8]=>1110100 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>1100110 [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,1,5,2,8]=>1111010 [[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,6,4,1,2,5,3,8]=>1110010 [[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[7,6,1,2,3,5,4,8]=>1100010 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>1111100 [[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>1111000 [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>1111000 [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>1111000 [[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>1100000 [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[7,1,6,5,4,3,2,8]=>1011110 [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[7,1,6,5,4,2,3,8]=>1011100 [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,1,6,5,2,4,3,8]=>1011010 [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,1,6,2,5,4,3,8]=>1010110 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,1,6,2,5,3,4,8]=>1010100 [[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,2,3,1,8]=>[7,1,6,4,2,5,3,8]=>1011010 [[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,1,6,4,2,3,5,8]=>1011000 [[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[7,1,6,2,3,4,5,8]=>1010000 [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[7,5,1,6,4,3,2,8]=>1101110 [[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[7,5,1,6,3,2,4,8]=>1101100 [[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,1,2,6,5,4,3,8]=>1001110 [[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[7,1,2,6,5,3,4,8]=>1001100 [[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,1,2,6,3,5,4,8]=>1001010 [[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[7,1,2,6,4,3,5,8]=>1001100 [[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,1,2,6,3,4,5,8]=>1001000 [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[7,5,4,1,6,3,2,8]=>1110110 [[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[7,5,4,1,6,2,3,8]=>1110100 [[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,1,5,2,6,4,3,8]=>1010110 [[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[7,1,5,2,6,3,4,8]=>1010100 [[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[7,4,1,2,6,5,3,8]=>1100110 [[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>1000110 [[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[7,1,2,3,6,4,5,8]=>1000100 [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[7,5,1,4,2,6,3,8]=>1101010 [[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[7,5,3,1,2,6,4,8]=>1110010 [[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[7,1,5,4,2,6,3,8]=>1011010 [[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,1,5,2,3,6,4,8]=>1010010 [[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[7,4,1,5,2,6,3,8]=>1101010 [[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[7,1,2,3,4,6,5,8]=>1000010 [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>1111100 [[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[7,5,4,3,1,2,6,8]=>1111000 [[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,5,1,4,2,3,6,8]=>1101000 [[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,1,2,4,3,6,8]=>1100100 [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>1111000 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>1110000 [[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[7,5,1,3,2,4,6,8]=>1101000 [[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>1100000 [[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>1011000 [[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,4,1,5,3,2,6,8]=>1101100 [[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,1,4,2,5,3,6,8]=>1010100 [[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>1100100 [[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>1000100 [[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>1111000 [[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>1100000 [[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>1011000 [[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[7,1,4,2,3,5,6,8]=>1010000 [[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>1001000 [[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>1110000 [[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>1100000 [[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>1010000 [[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>1100000 [[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>1000000 [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8]=>0111110 [[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[1,7,6,5,4,2,3,8]=>0111100 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[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>1010100 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[1,2,5,3,6,4,7,8]=>0010100 [[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[4,3,1,2,6,5,7,8]=>1100100 [[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[4,1,2,3,6,5,7,8]=>1000100 [[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[1,4,2,3,6,5,7,8]=>0100100 [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000 [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>1110000 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>1101000 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>1110000 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>1100000 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>1010000 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>1101000 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>1110000 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>1100000 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>1010000 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>1100000 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000 [[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000 [[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>0101000 [[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>0100000 [[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000 [[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>0010000 [[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>1001000 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[1,4,2,5,3,6,7,8]=>0101000 [[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000 [[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1100000 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1100000 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000 [[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0100000 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1010000 [[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000 [[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000 [[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000 [[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000 [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000 [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111 [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>11111110 [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>11111100 [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>11111000 [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>11110000 [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>11100000 [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>11000000 [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>10000000 [[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000 [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111 [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>111111110 [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>11111101 [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>111111100 [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>111111000 [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>111110000 [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>111100000 [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[9,8,1,7,2,3,4,5,6]=>11010000 [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>111000000 [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[9,1,8,2,3,4,5,6,7]=>10100000 [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>110000000 [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[1,9,2,3,4,5,6,7,8]=>01000000 [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>100000000 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000 [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>11111110 [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>11111110 [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>11111110 [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>11111110 [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>11111110 [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>11111110 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110 [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>111111110 [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>111111110 [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>111111110 [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>111111110 [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>111111110 [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>111111110 [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9]=>01111110 [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>111111110 [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110 [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>111100000 [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>101010101 [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>10101010101 [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>00000001 [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001 [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[3,1,2,4,5,6,7,9,8]=>10000001 [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>11000000 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001 [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>10100000 [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>11000000 [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>110000000 [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000 [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,7,8]=>00000010 [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,7,8]=>00000100 [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,9,5,6,7,8]=>00001000 [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[1,2,3,9,4,5,6,7,8]=>00010000 [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[1,2,9,3,4,5,6,7,8]=>00100000 [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>00000011 [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,8,9]=>000000010 [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,7,6,8]=>00000110 [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,7,8,9]=>000000100 [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[7,6,8,9,1,2,3,4,5]=>[1,2,3,4,9,6,5,7,8]=>00001100 [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,8,9]=>000001000 [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[6,5,7,8,9,1,2,3,4]=>[1,2,3,9,5,4,6,7,8]=>00011000 [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,8,9]=>000010000 [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[5,4,6,7,8,9,1,2,3]=>[1,2,9,4,3,5,6,7,8]=>00110000 [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[1,2,3,10,4,5,6,7,8,9]=>000100000 [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>[1,9,3,2,4,5,6,7,8]=>01100000 [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[1,2,10,3,4,5,6,7,8,9]=>001000000 [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[1,10,2,3,4,5,6,7,8,9]=>010000000 [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>01111111 [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>11111100 [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,2,3]=>01111110 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111 [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110 [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>111111100 [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>11111100 [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[1,9,8,7,6,5,3,2,4]=>01111110 [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[1,9,8,7,6,5,2,4,3]=>01111101 [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,2,3]=>011111110 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111 [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>111110000 [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>11111100000 [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[8,1,9,7,6,5,4,3,2]=>10111111 [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[8,7,1,9,6,5,4,3,2]=>11011111 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,1,9,5,4,3,2]=>11101111 [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,1,9,4,3,2]=>11110111 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,1,9,3,2]=>11111011 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,1,9,2]=>11111101 [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>00111111 [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1,10,8,7,6,5,4,3,2]=>101111111 [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[8,1,2,9,7,6,5,4,3]=>10011111 [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,1,10,7,6,5,4,3,2]=>110111111 [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,3,4,2,1,5]=>[8,7,1,2,9,6,5,4,3]=>11001111 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,1,10,3,2]=>111111011 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>111111101 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100 [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000 [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000 [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000 [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000 [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000 [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100 [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000 [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000 [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000 [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000 [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000 [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>01000000 [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000 [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>11110111 [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>11101111 [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,3,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>11011111 [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[9,1,8,7,6,5,4,3,2]=>10111111 [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,3,2]=>111111101 [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>111110111 [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>111101111 [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>101111111 [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[10,1,9,2,8,3,7,4,6,5]=>101010101 [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[9,1,2,3,4,5,6,8,7]=>10000001 [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000 [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,1,2,3,4,5,7,6,8]=>10000010 [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,6,7]=>10000010 [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001 [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>11000000 [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>10000000 [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000 [[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>10000000 [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000 [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000 [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010 [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000 [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>00100000 [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>00010000 [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>00001000 [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>00000100 [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>00000010 [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>010000000 [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>001000000 [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>000100000 [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>000010000 [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>000001000 [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>000000100 [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>000000010 [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[1,9,2,3,4,5,6,8,7]=>01000001 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,1,8,2]=>11111101 [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>11111000 [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000 [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>001111111 [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>011111110 [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[7,8,2,3,4,5,6,9,1]=>[9,1,2,3,4,7,5,6,8]=>10000100 [.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]=>[4,5,6,3,7,8,9,2,1]=>[9,8,4,1,2,3,5,6,7]=>11100000 [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[6,2,3,4,5,7,8,9,10,1]=>[10,1,2,3,5,4,6,7,8,9]=>100010000 [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[8,1,9,2,3,4,5,6,7]=>10100000 [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[1,8,2,3,4,5,6,7,9]=>01000000 [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>000000011 [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>11111000 [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>1111111110 [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>00000111 [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>00001111 [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>00011111 [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,8,6,9,7]=>00000101 [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>000000111 [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111 [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>000011111 [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>000111111 [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[9,8,10,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,3,2,4]=>011111110 [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110 [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>11111100 [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,1,2,9]=>111111100 [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000 [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>11111100 [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>11100000 [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>11000000 [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[1,9,7,6,5,4,3,2,8]=>01111110 [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[8,1,2,3,4,5,6,9,7]=>10000001 [[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>01000000 [[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[9,3,4,5,6,7,2,1,8]=>[8,7,1,2,3,4,5,9,6]=>11000001 [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,11,9,10]=>0000000010 [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,7,6]=>10000011 [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>[10,1,2,3,4,5,6,9,8,7]=>100000011 [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[9,2,3,4,5,6,1,7,8]=>[7,1,2,3,4,5,6,9,8]=>10000001 [[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[9,8,2,3,4,5,6,1,7]=>[8,1,2,3,4,5,9,7,6]=>10000011 [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[3,4,5,2,1,6,7,8,9]=>[5,4,1,2,3,6,7,8,9]=>11000000 [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[9,8,7,6,5,2,1,3,4]=>11111100
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.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.