Identifier
Mp00014: to 132-avoiding permutationPermutations
Mp00175: Permutations inverse Foata 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]=>[2,3,1]=>01 [[.,.],[.,.]]=>[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]=>[3,4,2,1]=>011 [.,[[.,.],[.,.]]]=>[4,2,3,1]=>[2,4,3,1]=>011 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>101 [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>001 [[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,4,3,2]=>011 [[.,.],[[.,.],.]]=>[3,4,1,2]=>[3,1,4,2]=>101 [[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,1,4,3]=>101 [[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,2,4,3]=>001 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>110 [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>010 [[[.,.],[.,.]],.]=>[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]=>[4,5,3,2,1]=>0111 [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[3,5,4,2,1]=>0111 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1]=>1011 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1]=>0011 [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[2,5,4,3,1]=>0111 [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[4,2,5,3,1]=>1011 [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[3,2,5,4,1]=>1011 [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[2,3,5,4,1]=>0011 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1]=>1101 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>0101 [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[2,4,3,5,1]=>0101 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1]=>1001 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1]=>0001 [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,5,4,3,2]=>0111 [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[4,1,5,3,2]=>1011 [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[3,1,5,4,2]=>1011 [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[4,3,1,5,2]=>1101 [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,4,1,5,2]=>0101 [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,1,5,4,3]=>1011 [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,2,1,5,3]=>1101 [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011 [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[1,4,2,5,3]=>0101 [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[3,2,1,5,4]=>1101 [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[2,3,1,5,4]=>0101 [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,3,2,5,4]=>0101 [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,1,3,5,4]=>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]=>[3,4,2,1,5]=>0110 [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[2,4,3,1,5]=>0110 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5]=>1010 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5]=>0010 [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[1,4,3,2,5]=>0110 [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,1,4,2,5]=>1010 [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,1,4,3,5]=>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]=>[2,3,1,4,5]=>0100 [[[[.,.],[.,.]],.],.]=>[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]=>[5,6,4,3,2,1]=>01111 [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[4,6,5,3,2,1]=>01111 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>10111 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>00111 [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>01111 [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[5,3,6,4,2,1]=>10111 [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[4,3,6,5,2,1]=>10111 [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[3,4,6,5,2,1]=>00111 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>11011 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>01011 [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[3,5,4,6,2,1]=>01011 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>10011 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>00011 [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[2,6,5,4,3,1]=>01111 [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[5,2,6,4,3,1]=>10111 [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[4,2,6,5,3,1]=>10111 [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[5,4,2,6,3,1]=>11011 [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[4,5,2,6,3,1]=>01011 [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[3,2,6,5,4,1]=>10111 [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[5,3,2,6,4,1]=>11011 [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[2,3,6,5,4,1]=>00111 [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[2,5,3,6,4,1]=>01011 [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>11011 [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[3,4,2,6,5,1]=>01011 [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[2,4,3,6,5,1]=>01011 [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>10011 [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[2,3,4,6,5,1]=>00011 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>11101 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>01101 [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[3,5,4,2,6,1]=>01101 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>10101 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>00101 [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[2,5,4,3,6,1]=>01101 [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[4,2,5,3,6,1]=>10101 [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[3,2,5,4,6,1]=>10101 [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[2,3,5,4,6,1]=>00101 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>11001 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>01001 [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[2,4,3,5,6,1]=>01001 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>10001 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>00001 [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>01111 [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[5,1,6,4,3,2]=>10111 [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[4,1,6,5,3,2]=>10111 [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[5,4,1,6,3,2]=>11011 [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[4,5,1,6,3,2]=>01011 [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[3,1,6,5,4,2]=>10111 [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[5,3,1,6,4,2]=>11011 [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[4,3,1,6,5,2]=>11011 [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[3,4,1,6,5,2]=>01011 [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[5,4,3,1,6,2]=>11101 [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[4,5,3,1,6,2]=>01101 [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[3,5,4,1,6,2]=>01101 [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[4,3,5,1,6,2]=>10101 [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[3,4,5,1,6,2]=>00101 [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,1,6,5,4,3]=>10111 [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,2,1,6,4,3]=>11011 [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[4,2,1,6,5,3]=>11011 [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,4,2,1,6,3]=>11101 [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[4,5,2,1,6,3]=>01101 [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>00111 [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[1,5,2,6,4,3]=>01011 [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,4,2,6,5,3]=>01011 [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[1,5,4,2,6,3]=>01101 [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>10101 [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[3,2,1,6,5,4]=>11011 [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,3,2,1,6,4]=>11101 [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[2,3,1,6,5,4]=>01011 [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[2,5,3,1,6,4]=>01101 [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,3,2,6,5,4]=>01011 [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[1,5,3,2,6,4]=>01101 [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,1,3,6,5,4]=>10011 [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,1,5,3,6,4]=>10101 [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>00011 [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[1,2,5,3,6,4]=>00101 [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[4,3,2,1,6,5]=>11101 [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[3,4,2,1,6,5]=>01101 [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[2,4,3,1,6,5]=>01101 [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[3,2,4,1,6,5]=>10101 [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[2,3,4,1,6,5]=>00101 [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,4,3,2,6,5]=>01101 [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[3,1,4,2,6,5]=>10101 [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,1,4,3,6,5]=>10101 [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,2,4,3,6,5]=>00101 [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[3,2,1,4,6,5]=>11001 [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[2,3,1,4,6,5]=>01001 [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[1,3,2,4,6,5]=>01001 [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,1,3,4,6,5]=>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]=>[4,5,3,2,1,6]=>01110 [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[3,5,4,2,1,6]=>01110 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>10110 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>00110 [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[2,5,4,3,1,6]=>01110 [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[4,2,5,3,1,6]=>10110 [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>10110 [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[2,3,5,4,1,6]=>00110 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>11010 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>01010 [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[2,4,3,5,1,6]=>01010 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>10010 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>00010 [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>01110 [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[4,1,5,3,2,6]=>10110 [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[3,1,5,4,2,6]=>10110 [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[4,3,1,5,2,6]=>11010 [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[3,4,1,5,2,6]=>01010 [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,1,5,4,3,6]=>10110 [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,2,1,5,3,6]=>11010 [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>00110 [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[1,4,2,5,3,6]=>01010 [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[3,2,1,5,4,6]=>11010 [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[2,3,1,5,4,6]=>01010 [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[1,3,2,5,4,6]=>01010 [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,1,3,5,4,6]=>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]=>[3,4,2,1,5,6]=>01100 [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[2,4,3,1,5,6]=>01100 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>10100 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>00100 [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>01100 [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>10100 [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[2,1,4,3,5,6]=>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]=>[2,3,1,4,5,6]=>01000 [[[[[.,.],[.,.]],.],.],.]=>[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]=>[6,7,5,4,3,2,1]=>011111 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[5,7,6,4,3,2,1]=>011111 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>101111 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>001111 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[4,7,6,5,3,2,1]=>011111 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[6,4,7,5,3,2,1]=>101111 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[5,4,7,6,3,2,1]=>101111 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[4,5,7,6,3,2,1]=>001111 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>110111 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>010111 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[4,6,5,7,3,2,1]=>010111 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>100111 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>000111 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[3,7,6,5,4,2,1]=>011111 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[6,3,7,5,4,2,1]=>101111 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[5,3,7,6,4,2,1]=>101111 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[6,5,3,7,4,2,1]=>110111 [.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[5,6,3,7,4,2,1]=>010111 [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>101111 [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[6,4,3,7,5,2,1]=>110111 [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>001111 [.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[3,6,4,7,5,2,1]=>010111 [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[5,4,3,7,6,2,1]=>110111 [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[4,5,3,7,6,2,1]=>010111 [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[3,5,4,7,6,2,1]=>010111 [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[4,3,5,7,6,2,1]=>100111 [.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[3,4,5,7,6,2,1]=>000111 [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>111011 [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>011011 [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[4,6,5,3,7,2,1]=>011011 [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>101011 [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>001011 [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[3,6,5,4,7,2,1]=>011011 [.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[5,3,6,4,7,2,1]=>101011 [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[4,3,6,5,7,2,1]=>101011 [.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[3,4,6,5,7,2,1]=>001011 [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>110011 [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>010011 [.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[3,5,4,6,7,2,1]=>010011 [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>100011 [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>000011 [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[2,7,6,5,4,3,1]=>011111 [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[6,2,7,5,4,3,1]=>101111 [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[5,2,7,6,4,3,1]=>101111 [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[6,5,2,7,4,3,1]=>110111 [.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[5,6,2,7,4,3,1]=>010111 [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[4,2,7,6,5,3,1]=>101111 [.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[6,4,2,7,5,3,1]=>110111 [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[5,4,2,7,6,3,1]=>110111 [.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[4,5,2,7,6,3,1]=>010111 [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[6,5,4,2,7,3,1]=>111011 [.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[5,6,4,2,7,3,1]=>011011 [.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[4,6,5,2,7,3,1]=>011011 [.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[5,4,6,2,7,3,1]=>101011 [.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,5,6,2,7,3,1]=>001011 [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[3,2,7,6,5,4,1]=>101111 [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[6,3,2,7,5,4,1]=>110111 [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[5,3,2,7,6,4,1]=>110111 [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[6,5,3,2,7,4,1]=>111011 [.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[5,6,3,2,7,4,1]=>011011 [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[2,3,7,6,5,4,1]=>001111 [.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,6,3,7,5,4,1]=>010111 [.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[2,5,3,7,6,4,1]=>010111 [.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[2,6,5,3,7,4,1]=>011011 [.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[5,2,6,3,7,4,1]=>101011 [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[4,3,2,7,6,5,1]=>110111 [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[6,4,3,2,7,5,1]=>111011 [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[3,4,2,7,6,5,1]=>010111 [.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[3,6,4,2,7,5,1]=>011011 [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[2,4,3,7,6,5,1]=>010111 [.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[2,6,4,3,7,5,1]=>011011 [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[3,2,4,7,6,5,1]=>100111 [.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[3,2,6,4,7,5,1]=>101011 [.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[2,3,4,7,6,5,1]=>000111 [.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[2,3,6,4,7,5,1]=>001011 [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>111011 [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[4,5,3,2,7,6,1]=>011011 [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>011011 [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[4,3,5,2,7,6,1]=>101011 [.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[3,4,5,2,7,6,1]=>001011 [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[2,5,4,3,7,6,1]=>011011 [.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[4,2,5,3,7,6,1]=>101011 [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[3,2,5,4,7,6,1]=>101011 [.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[2,3,5,4,7,6,1]=>001011 [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>110011 [.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[3,4,2,5,7,6,1]=>010011 [.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[2,4,3,5,7,6,1]=>010011 [.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>100011 [.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[2,3,4,5,7,6,1]=>000011 [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>111101 [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>011101 [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[4,6,5,3,2,7,1]=>011101 [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>101101 [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>001101 [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[3,6,5,4,2,7,1]=>011101 [.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[5,3,6,4,2,7,1]=>101101 [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[4,3,6,5,2,7,1]=>101101 [.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[3,4,6,5,2,7,1]=>001101 [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>110101 [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>010101 [.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[3,5,4,6,2,7,1]=>010101 [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>100101 [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>000101 [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[2,6,5,4,3,7,1]=>011101 [.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[5,2,6,4,3,7,1]=>101101 [.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[4,2,6,5,3,7,1]=>101101 [.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[5,4,2,6,3,7,1]=>110101 [.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[4,5,2,6,3,7,1]=>010101 [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[3,2,6,5,4,7,1]=>101101 [.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[5,3,2,6,4,7,1]=>110101 [.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,7,1]=>001101 [.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[2,5,3,6,4,7,1]=>010101 [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[4,3,2,6,5,7,1]=>110101 [.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[3,4,2,6,5,7,1]=>010101 [.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[2,4,3,6,5,7,1]=>010101 [.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[3,2,4,6,5,7,1]=>100101 [.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[2,3,4,6,5,7,1]=>000101 [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>111001 [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>011001 [.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[3,5,4,2,6,7,1]=>011001 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>101001 [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>001001 [.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[2,5,4,3,6,7,1]=>011001 [.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[4,2,5,3,6,7,1]=>101001 [.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[3,2,5,4,6,7,1]=>101001 [.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[2,3,5,4,6,7,1]=>001001 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>110001 [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>010001 [.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[2,4,3,5,6,7,1]=>010001 [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>100001 [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>000001 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>011111 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[6,1,7,5,4,3,2]=>101111 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[5,1,7,6,4,3,2]=>101111 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[6,5,1,7,4,3,2]=>110111 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[5,6,1,7,4,3,2]=>010111 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[4,1,7,6,5,3,2]=>101111 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[6,4,1,7,5,3,2]=>110111 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[5,4,1,7,6,3,2]=>110111 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[4,5,1,7,6,3,2]=>010111 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[6,5,4,1,7,3,2]=>111011 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[5,6,4,1,7,3,2]=>011011 [[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[4,6,5,1,7,3,2]=>011011 [[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[5,4,6,1,7,3,2]=>101011 [[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,5,6,1,7,3,2]=>001011 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[3,1,7,6,5,4,2]=>101111 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[6,3,1,7,5,4,2]=>110111 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[5,3,1,7,6,4,2]=>110111 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[6,5,3,1,7,4,2]=>111011 [[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[5,6,3,1,7,4,2]=>011011 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[4,3,1,7,6,5,2]=>110111 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[6,4,3,1,7,5,2]=>111011 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[3,4,1,7,6,5,2]=>010111 [[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[3,6,4,1,7,5,2]=>011011 [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[5,4,3,1,7,6,2]=>111011 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[4,5,3,1,7,6,2]=>011011 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[3,5,4,1,7,6,2]=>011011 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[4,3,5,1,7,6,2]=>101011 [[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[3,4,5,1,7,6,2]=>001011 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[6,5,4,3,1,7,2]=>111101 [[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[5,6,4,3,1,7,2]=>011101 [[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[4,6,5,3,1,7,2]=>011101 [[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[5,4,6,3,1,7,2]=>101101 [[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[4,5,6,3,1,7,2]=>001101 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[3,6,5,4,1,7,2]=>011101 [[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[5,3,6,4,1,7,2]=>101101 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[4,3,6,5,1,7,2]=>101101 [[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[3,4,6,5,1,7,2]=>001101 [[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[5,4,3,6,1,7,2]=>110101 [[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[4,5,3,6,1,7,2]=>010101 [[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[3,5,4,6,1,7,2]=>010101 [[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[4,3,5,6,1,7,2]=>100101 [[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[3,4,5,6,1,7,2]=>000101 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,1,7,6,5,4,3]=>101111 [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,2,1,7,5,4,3]=>110111 [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[5,2,1,7,6,4,3]=>110111 [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,5,2,1,7,4,3]=>111011 [[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[5,6,2,1,7,4,3]=>011011 [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[4,2,1,7,6,5,3]=>110111 [[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,4,2,1,7,5,3]=>111011 [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[5,4,2,1,7,6,3]=>111011 [[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[4,5,2,1,7,6,3]=>011011 [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,5,4,2,1,7,3]=>111101 [[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[5,6,4,2,1,7,3]=>011101 [[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[4,6,5,2,1,7,3]=>011101 [[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[5,4,6,2,1,7,3]=>101101 [[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,5,6,2,1,7,3]=>001101 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>001111 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[1,6,2,7,5,4,3]=>010111 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,5,2,7,6,4,3]=>010111 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[1,6,5,2,7,4,3]=>011011 [[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[5,1,6,2,7,4,3]=>101011 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,4,2,7,6,5,3]=>010111 [[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[1,6,4,2,7,5,3]=>011011 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,5,4,2,7,6,3]=>011011 [[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[4,1,5,2,7,6,3]=>101011 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[1,6,5,4,2,7,3]=>011101 [[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[5,1,6,4,2,7,3]=>101101 [[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[4,1,6,5,2,7,3]=>101101 [[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[5,4,1,6,2,7,3]=>110101 [[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,5,1,6,2,7,3]=>010101 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[3,2,1,7,6,5,4]=>110111 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,3,2,1,7,5,4]=>111011 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[5,3,2,1,7,6,4]=>111011 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,3,2,1,7,4]=>111101 [[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[5,6,3,2,1,7,4]=>011101 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[2,3,1,7,6,5,4]=>010111 [[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[2,6,3,1,7,5,4]=>011011 [[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[2,5,3,1,7,6,4]=>011011 [[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[2,6,5,3,1,7,4]=>011101 [[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[5,2,6,3,1,7,4]=>101101 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,3,2,7,6,5,4]=>010111 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[1,6,3,2,7,5,4]=>011011 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,5,3,2,7,6,4]=>011011 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[1,6,5,3,2,7,4]=>011101 [[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[5,1,6,3,2,7,4]=>101101 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,1,3,7,6,5,4]=>100111 [[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,1,6,3,7,5,4]=>101011 [[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,1,5,3,7,6,4]=>101011 [[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,1,6,5,3,7,4]=>101101 [[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,2,1,6,3,7,4]=>110101 [[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111 [[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[1,2,6,3,7,5,4]=>001011 [[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,2,5,3,7,6,4]=>001011 [[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[1,2,6,5,3,7,4]=>001101 [[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[1,5,2,6,3,7,4]=>010101 [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[4,3,2,1,7,6,5]=>111011 [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,4,3,2,1,7,5]=>111101 [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[3,4,2,1,7,6,5]=>011011 [[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[3,6,4,2,1,7,5]=>011101 [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[2,4,3,1,7,6,5]=>011011 [[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[2,6,4,3,1,7,5]=>011101 [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[3,2,4,1,7,6,5]=>101011 [[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[3,2,6,4,1,7,5]=>101101 [[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[2,3,4,1,7,6,5]=>001011 [[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[2,3,6,4,1,7,5]=>001101 [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,4,3,2,7,6,5]=>011011 [[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[1,6,4,3,2,7,5]=>011101 [[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[3,1,4,2,7,6,5]=>101011 [[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[3,1,6,4,2,7,5]=>101101 [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,1,4,3,7,6,5]=>101011 [[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,1,6,4,3,7,5]=>101101 [[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,2,4,3,7,6,5]=>001011 [[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[1,2,6,4,3,7,5]=>001101 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[3,2,1,4,7,6,5]=>110011 [[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[3,2,1,6,4,7,5]=>110101 [[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[2,3,1,4,7,6,5]=>010011 [[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[2,3,1,6,4,7,5]=>010101 [[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[1,3,2,4,7,6,5]=>010011 [[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[1,3,2,6,4,7,5]=>010101 [[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,1,3,4,7,6,5]=>100011 [[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,1,3,6,4,7,5]=>100101 [[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>000011 [[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[1,2,3,6,4,7,5]=>000101 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[5,4,3,2,1,7,6]=>111101 [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[4,5,3,2,1,7,6]=>011101 [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[3,5,4,2,1,7,6]=>011101 [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[4,3,5,2,1,7,6]=>101101 [[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[3,4,5,2,1,7,6]=>001101 [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[2,5,4,3,1,7,6]=>011101 [[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[4,2,5,3,1,7,6]=>101101 [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[3,2,5,4,1,7,6]=>101101 [[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[2,3,5,4,1,7,6]=>001101 [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[4,3,2,5,1,7,6]=>110101 [[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[3,4,2,5,1,7,6]=>010101 [[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[2,4,3,5,1,7,6]=>010101 [[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[3,2,4,5,1,7,6]=>100101 [[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[2,3,4,5,1,7,6]=>000101 [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,5,4,3,2,7,6]=>011101 [[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[4,1,5,3,2,7,6]=>101101 [[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[3,1,5,4,2,7,6]=>101101 [[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[4,3,1,5,2,7,6]=>110101 [[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[3,4,1,5,2,7,6]=>010101 [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,1,5,4,3,7,6]=>101101 [[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[4,2,1,5,3,7,6]=>110101 [[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,2,5,4,3,7,6]=>001101 [[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,4,2,5,3,7,6]=>010101 [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[3,2,1,5,4,7,6]=>110101 [[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[2,3,1,5,4,7,6]=>010101 [[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[1,3,2,5,4,7,6]=>010101 [[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,1,3,5,4,7,6]=>100101 [[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,2,3,5,4,7,6]=>000101 [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[4,3,2,1,5,7,6]=>111001 [[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[3,4,2,1,5,7,6]=>011001 [[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[2,4,3,1,5,7,6]=>011001 [[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[3,2,4,1,5,7,6]=>101001 [[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[2,3,4,1,5,7,6]=>001001 [[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[1,4,3,2,5,7,6]=>011001 [[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[3,1,4,2,5,7,6]=>101001 [[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[2,1,4,3,5,7,6]=>101001 [[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,2,4,3,5,7,6]=>001001 [[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[3,2,1,4,5,7,6]=>110001 [[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[2,3,1,4,5,7,6]=>010001 [[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[1,3,2,4,5,7,6]=>010001 [[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,1,3,4,5,7,6]=>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]=>[5,6,4,3,2,1,7]=>011110 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[4,6,5,3,2,1,7]=>011110 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>101110 [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>001110 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>011110 [[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[5,3,6,4,2,1,7]=>101110 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[4,3,6,5,2,1,7]=>101110 [[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[3,4,6,5,2,1,7]=>001110 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>110110 [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>010110 [[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[3,5,4,6,2,1,7]=>010110 [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>100110 [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>000110 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[2,6,5,4,3,1,7]=>011110 [[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[5,2,6,4,3,1,7]=>101110 [[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[4,2,6,5,3,1,7]=>101110 [[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[5,4,2,6,3,1,7]=>110110 [[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[4,5,2,6,3,1,7]=>010110 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[3,2,6,5,4,1,7]=>101110 [[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[5,3,2,6,4,1,7]=>110110 [[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,1,7]=>001110 [[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[2,5,3,6,4,1,7]=>010110 [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>110110 [[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[3,4,2,6,5,1,7]=>010110 [[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[2,4,3,6,5,1,7]=>010110 [[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>100110 [[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[2,3,4,6,5,1,7]=>000110 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>111010 [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>011010 [[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[3,5,4,2,6,1,7]=>011010 [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>101010 [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>001010 [[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[2,5,4,3,6,1,7]=>011010 [[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[4,2,5,3,6,1,7]=>101010 [[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[3,2,5,4,6,1,7]=>101010 [[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[2,3,5,4,6,1,7]=>001010 [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>110010 [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>010010 [[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[2,4,3,5,6,1,7]=>010010 [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>100010 [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>000010 [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>011110 [[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[5,1,6,4,3,2,7]=>101110 [[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[4,1,6,5,3,2,7]=>101110 [[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[5,4,1,6,3,2,7]=>110110 [[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[4,5,1,6,3,2,7]=>010110 [[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[3,1,6,5,4,2,7]=>101110 [[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[5,3,1,6,4,2,7]=>110110 [[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[4,3,1,6,5,2,7]=>110110 [[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[3,4,1,6,5,2,7]=>010110 [[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[5,4,3,1,6,2,7]=>111010 [[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[4,5,3,1,6,2,7]=>011010 [[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[3,5,4,1,6,2,7]=>011010 [[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[4,3,5,1,6,2,7]=>101010 [[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[3,4,5,1,6,2,7]=>001010 [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,1,6,5,4,3,7]=>101110 [[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,2,1,6,4,3,7]=>110110 [[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[4,2,1,6,5,3,7]=>110110 [[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,4,2,1,6,3,7]=>111010 [[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[4,5,2,1,6,3,7]=>011010 [[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>001110 [[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[1,5,2,6,4,3,7]=>010110 [[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[1,4,2,6,5,3,7]=>010110 [[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[1,5,4,2,6,3,7]=>011010 [[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,1,5,2,6,3,7]=>101010 [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[3,2,1,6,5,4,7]=>110110 [[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,3,2,1,6,4,7]=>111010 [[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[2,3,1,6,5,4,7]=>010110 [[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[2,5,3,1,6,4,7]=>011010 [[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[1,3,2,6,5,4,7]=>010110 [[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[1,5,3,2,6,4,7]=>011010 [[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,1,3,6,5,4,7]=>100110 [[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,1,5,3,6,4,7]=>101010 [[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>000110 [[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[1,2,5,3,6,4,7]=>001010 [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[4,3,2,1,6,5,7]=>111010 [[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[3,4,2,1,6,5,7]=>011010 [[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[2,4,3,1,6,5,7]=>011010 [[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[3,2,4,1,6,5,7]=>101010 [[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[2,3,4,1,6,5,7]=>001010 [[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[1,4,3,2,6,5,7]=>011010 [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[3,1,4,2,6,5,7]=>101010 [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,1,4,3,6,5,7]=>101010 [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[1,2,4,3,6,5,7]=>001010 [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[3,2,1,4,6,5,7]=>110010 [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[2,3,1,4,6,5,7]=>010010 [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[1,3,2,4,6,5,7]=>010010 [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,1,3,4,6,5,7]=>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]=>[4,5,3,2,1,6,7]=>011100 [[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[3,5,4,2,1,6,7]=>011100 [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>101100 [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>001100 [[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[2,5,4,3,1,6,7]=>011100 [[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[4,2,5,3,1,6,7]=>101100 [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>101100 [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[2,3,5,4,1,6,7]=>001100 [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>110100 [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>010100 [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[2,4,3,5,1,6,7]=>010100 [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>100100 [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>000100 [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>011100 [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,1,5,3,2,6,7]=>101100 [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[3,1,5,4,2,6,7]=>101100 [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,3,1,5,2,6,7]=>110100 [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[3,4,1,5,2,6,7]=>010100 [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[2,1,5,4,3,6,7]=>101100 [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,2,1,5,3,6,7]=>110100 [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>001100 [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[1,4,2,5,3,6,7]=>010100 [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[3,2,1,5,4,6,7]=>110100 [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[2,3,1,5,4,6,7]=>010100 [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[1,3,2,5,4,6,7]=>010100 [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[2,1,3,5,4,6,7]=>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]=>[3,4,2,1,5,6,7]=>011000 [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[2,4,3,1,5,6,7]=>011000 [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>101000 [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>001000 [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000 [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>101000 [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[2,1,4,3,5,6,7]=>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]=>[2,3,1,4,5,6,7]=>010000 [[[[[[.,.],[.,.]],.],.],.],.]=>[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]=>[7,8,6,5,4,3,2,1]=>0111111 [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[6,8,7,5,4,3,2,1]=>0111111 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[7,6,8,5,4,3,2,1]=>1011111 [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[6,7,8,5,4,3,2,1]=>0011111 [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[5,8,7,6,4,3,2,1]=>0111111 [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[7,5,8,6,4,3,2,1]=>1011111 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[6,5,8,7,4,3,2,1]=>1011111 [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[5,6,8,7,4,3,2,1]=>0011111 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[7,6,5,8,4,3,2,1]=>1101111 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[6,7,5,8,4,3,2,1]=>0101111 [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[5,7,6,8,4,3,2,1]=>0101111 [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[6,5,7,8,4,3,2,1]=>1001111 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>0001111 [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0111111 [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[7,4,8,6,5,3,2,1]=>1011111 [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[6,4,8,7,5,3,2,1]=>1011111 [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[7,6,4,8,5,3,2,1]=>1101111 [.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[6,7,4,8,5,3,2,1]=>0101111 [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[7,5,4,8,6,3,2,1]=>1101111 [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[4,5,8,7,6,3,2,1]=>0011111 [.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[4,7,5,8,6,3,2,1]=>0101111 [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[6,5,4,8,7,3,2,1]=>1101111 [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[5,6,4,8,7,3,2,1]=>0101111 [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[4,6,5,8,7,3,2,1]=>0101111 [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[4,5,6,8,7,3,2,1]=>0001111 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[7,6,5,4,8,3,2,1]=>1110111 [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[6,7,5,4,8,3,2,1]=>0110111 [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[5,7,6,4,8,3,2,1]=>0110111 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[6,5,7,4,8,3,2,1]=>1010111 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[5,6,7,4,8,3,2,1]=>0010111 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[4,7,6,5,8,3,2,1]=>0110111 [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[6,4,7,5,8,3,2,1]=>1010111 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[5,4,7,6,8,3,2,1]=>1010111 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[4,5,7,6,8,3,2,1]=>0010111 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[6,5,4,7,8,3,2,1]=>1100111 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[5,6,4,7,8,3,2,1]=>0100111 [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[4,6,5,7,8,3,2,1]=>0100111 [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[5,4,6,7,8,3,2,1]=>1000111 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[4,5,6,7,8,3,2,1]=>0000111 [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[3,8,7,6,5,4,2,1]=>0111111 [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[7,3,8,6,5,4,2,1]=>1011111 [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[6,3,8,7,5,4,2,1]=>1011111 [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[7,6,3,8,5,4,2,1]=>1101111 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[5,3,8,7,6,4,2,1]=>1011111 [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[7,5,3,8,6,4,2,1]=>1101111 [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[7,6,5,3,8,4,2,1]=>1110111 [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[6,7,5,3,8,4,2,1]=>0110111 [.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[6,5,7,3,8,4,2,1]=>1010111 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[5,6,7,3,8,4,2,1]=>0010111 [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[4,3,8,7,6,5,2,1]=>1011111 [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[7,6,4,3,8,5,2,1]=>1110111 [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[6,7,4,3,8,5,2,1]=>0110111 [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[3,4,8,7,6,5,2,1]=>0011111 [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[3,6,4,8,7,5,2,1]=>0101111 [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[3,7,6,4,8,5,2,1]=>0110111 [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[6,3,7,4,8,5,2,1]=>1010111 [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[5,4,3,8,7,6,2,1]=>1101111 [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[7,5,4,3,8,6,2,1]=>1110111 [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[3,7,5,4,8,6,2,1]=>0110111 [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[3,4,5,8,7,6,2,1]=>0001111 [.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[3,4,7,5,8,6,2,1]=>0010111 [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[6,5,4,3,8,7,2,1]=>1110111 [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[5,6,4,3,8,7,2,1]=>0110111 [.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[8,5,6,3,4,7,2,1]=>[5,3,6,4,8,7,2,1]=>1010111 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[4,3,6,5,8,7,2,1]=>1010111 [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[5,4,3,6,8,7,2,1]=>1100111 [.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[3,4,5,6,8,7,2,1]=>0000111 [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[7,6,5,4,3,8,2,1]=>1111011 [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[6,7,5,4,3,8,2,1]=>0111011 [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[5,7,6,4,3,8,2,1]=>0111011 [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[6,5,7,4,3,8,2,1]=>1011011 [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[5,6,7,4,3,8,2,1]=>0011011 [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[4,7,6,5,3,8,2,1]=>0111011 [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[5,4,7,6,3,8,2,1]=>1011011 [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[6,5,4,7,3,8,2,1]=>1101011 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[5,4,6,7,3,8,2,1]=>1001011 [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[4,5,6,7,3,8,2,1]=>0001011 [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[3,7,6,5,4,8,2,1]=>0111011 [.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[6,5,3,7,4,8,2,1]=>1101011 [.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[5,6,3,7,4,8,2,1]=>0101011 [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[4,3,7,6,5,8,2,1]=>1011011 [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[3,4,7,6,5,8,2,1]=>0011011 [.,[.,[[[.,[[.,.],.]],[.,.]],.]]]=>[7,4,5,3,6,8,2,1]=>[4,5,3,7,6,8,2,1]=>0101011 [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[3,5,4,7,6,8,2,1]=>0101011 [.,[.,[[[[.,[.,.]],.],[.,.]],.]]]=>[7,4,3,5,6,8,2,1]=>[4,3,5,7,6,8,2,1]=>1001011 [.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[3,4,5,7,6,8,2,1]=>0001011 [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[6,5,4,3,7,8,2,1]=>1110011 [.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[4,5,6,3,7,8,2,1]=>0010011 [.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[3,6,5,4,7,8,2,1]=>0110011 [.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[6,4,3,5,7,8,2,1]=>[4,3,6,5,7,8,2,1]=>1010011 [.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[3,4,6,5,7,8,2,1]=>0010011 [.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[5,4,3,6,7,8,2,1]=>1100011 [.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[3,5,4,6,7,8,2,1]=>0100011 [.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[4,3,5,6,7,8,2,1]=>1000011 [.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[3,4,5,6,7,8,2,1]=>0000011 [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[2,8,7,6,5,4,3,1]=>0111111 [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[7,2,8,6,5,4,3,1]=>1011111 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[6,2,8,7,5,4,3,1]=>1011111 [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[5,2,8,7,6,4,3,1]=>1011111 [.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[7,5,2,8,6,4,3,1]=>1101111 [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[6,5,2,8,7,4,3,1]=>1101111 [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[5,6,2,8,7,4,3,1]=>0101111 [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[7,6,5,2,8,4,3,1]=>1110111 [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[6,7,5,2,8,4,3,1]=>0110111 [.,[[.,.],[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,2,3,1]=>[6,5,7,2,8,4,3,1]=>1010111 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[5,6,7,2,8,4,3,1]=>0010111 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[4,2,8,7,6,5,3,1]=>1011111 [.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,2,3,1]=>[7,4,2,8,6,5,3,1]=>1101111 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[6,4,2,8,7,5,3,1]=>1101111 [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[7,6,4,2,8,5,3,1]=>1110111 [.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[6,7,4,2,8,5,3,1]=>0110111 [.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[4,7,5,2,8,6,3,1]=>0110111 [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[4,6,5,2,8,7,3,1]=>0110111 [.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[4,5,6,2,8,7,3,1]=>0010111 [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[7,6,5,4,2,8,3,1]=>1111011 [.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[6,5,7,4,2,8,3,1]=>1011011 [.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,2,3,1]=>[5,6,7,4,2,8,3,1]=>0011011 [.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[4,7,6,5,2,8,3,1]=>0111011 [.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[6,4,7,5,2,8,3,1]=>1011011 [.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,2,3,1]=>[5,6,4,7,2,8,3,1]=>0101011 [.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[5,4,6,7,2,8,3,1]=>1001011 [.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[4,5,6,7,2,8,3,1]=>0001011 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[3,2,8,7,6,5,4,1]=>1011111 [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[7,3,2,8,6,5,4,1]=>1101111 [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[6,3,2,8,7,5,4,1]=>1101111 [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[7,6,3,2,8,5,4,1]=>1110111 [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[5,3,2,8,7,6,4,1]=>1101111 [.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[7,5,3,2,8,6,4,1]=>1110111 [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[6,5,3,2,8,7,4,1]=>1110111 [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[7,6,5,3,2,8,4,1]=>1111011 [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[6,7,5,3,2,8,4,1]=>0111011 [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[5,6,7,3,2,8,4,1]=>0011011 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[2,3,8,7,6,5,4,1]=>0011111 [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[2,6,3,8,7,5,4,1]=>0101111 [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[2,7,6,3,8,5,4,1]=>0110111 [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[6,2,7,3,8,5,4,1]=>1010111 [.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[2,7,5,3,8,6,4,1]=>0110111 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[5,2,6,3,8,7,4,1]=>1010111 [.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[6,2,7,5,3,8,4,1]=>1011011 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[5,6,2,7,3,8,4,1]=>0101011 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[4,3,2,8,7,6,5,1]=>1101111 [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[6,4,3,2,8,7,5,1]=>1110111 [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[7,6,4,3,2,8,5,1]=>1111011 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[3,4,2,8,7,6,5,1]=>0101111 [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[3,7,4,2,8,6,5,1]=>0110111 [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[3,6,4,2,8,7,5,1]=>0110111 [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[3,7,6,4,2,8,5,1]=>0111011 [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[2,4,3,8,7,6,5,1]=>0101111 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[2,6,4,3,8,7,5,1]=>0110111 [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[2,7,6,4,3,8,5,1]=>0111011 [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[3,2,4,8,7,6,5,1]=>1001111 [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[3,2,6,4,8,7,5,1]=>1010111 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[2,3,4,8,7,6,5,1]=>0001111 [.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[2,6,3,7,4,8,5,1]=>0101011 [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[5,4,3,2,8,7,6,1]=>1110111 [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[7,5,4,3,2,8,6,1]=>1111011 [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[2,5,4,3,8,7,6,1]=>0110111 [.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,2,3,6,1]=>[2,7,5,4,3,8,6,1]=>0111011 [.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,2,3,6,1]=>[4,2,7,5,3,8,6,1]=>1011011 [.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[2,3,7,5,4,8,6,1]=>0011011 [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[4,3,2,5,8,7,6,1]=>1100111 [.,[[[.,[[.,.],.]],.],[.,[.,.]]]]=>[8,7,3,4,2,5,6,1]=>[3,4,2,5,8,7,6,1]=>0100111 [.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[3,4,2,7,5,8,6,1]=>0101011 [.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[3,2,4,7,5,8,6,1]=>1001011 [.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[2,3,4,5,8,7,6,1]=>0000111 [.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[2,3,4,7,5,8,6,1]=>0001011 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>1111011 [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>[4,6,5,3,2,8,7,1]=>0111011 [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[5,4,6,3,2,8,7,1]=>1011011 [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>[3,6,5,4,2,8,7,1]=>0111011 [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[5,3,6,4,2,8,7,1]=>1011011 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>1011011 [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[5,4,3,6,2,8,7,1]=>1101011 [.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[4,5,3,6,2,8,7,1]=>0101011 [.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[8,5,3,4,6,2,7,1]=>[3,5,4,6,2,8,7,1]=>0101011 [.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[3,4,5,6,2,8,7,1]=>0001011 [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[2,6,5,4,3,8,7,1]=>0111011 [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[4,2,6,5,3,8,7,1]=>1011011 [.,[[[.,.],[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,2,3,7,1]=>[5,4,2,6,3,8,7,1]=>1101011 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[3,2,6,5,4,8,7,1]=>1011011 [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[4,3,2,6,5,8,7,1]=>1101011 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[2,4,3,6,5,8,7,1]=>0101011 [.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[2,3,4,6,5,8,7,1]=>0001011 [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>1110011 [.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[4,5,3,2,6,8,7,1]=>0110011 [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[2,5,4,3,6,8,7,1]=>0110011 [.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>1100011 [.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[3,4,2,5,6,8,7,1]=>0100011 [.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[2,4,3,5,6,8,7,1]=>0100011 [.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[3,2,4,5,6,8,7,1]=>1000011 [.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[2,3,4,5,6,8,7,1]=>0000011 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,8,1]=>1111101 [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[6,7,5,4,3,2,8,1]=>0111101 [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[5,7,6,4,3,2,8,1]=>0111101 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[6,5,7,4,3,2,8,1]=>1011101 [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[5,6,7,4,3,2,8,1]=>0011101 [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[4,7,6,5,3,2,8,1]=>0111101 [.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[6,7,4,5,3,2,8,1]=>[6,4,7,5,3,2,8,1]=>1011101 [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[6,5,4,7,3,2,8,1]=>1101101 [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[4,6,5,7,3,2,8,1]=>0101101 [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[4,5,6,7,3,2,8,1]=>0001101 [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[4,3,7,6,5,2,8,1]=>1011101 [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>[3,4,7,6,5,2,8,1]=>0011101 [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[5,4,3,7,6,2,8,1]=>1101101 [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[4,5,3,7,6,2,8,1]=>0101101 [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[3,5,4,7,6,2,8,1]=>0101101 [.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[3,4,5,7,6,2,8,1]=>0001101 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[6,5,4,3,7,2,8,1]=>1110101 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[4,6,5,3,7,2,8,1]=>0110101 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1]=>1010101 [.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[4,5,6,3,7,2,8,1]=>0010101 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[3,6,5,4,7,2,8,1]=>0110101 [.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[5,3,6,4,7,2,8,1]=>1010101 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[4,3,6,5,7,2,8,1]=>1010101 [.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[3,4,6,5,7,2,8,1]=>0010101 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[5,4,3,6,7,2,8,1]=>1100101 [.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[4,5,3,6,7,2,8,1]=>0100101 [.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[3,5,4,6,7,2,8,1]=>0100101 [.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[4,3,5,6,7,2,8,1]=>1000101 [.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[3,4,5,6,7,2,8,1]=>0000101 [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[2,7,6,5,4,3,8,1]=>0111101 [.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[6,5,2,7,4,3,8,1]=>1101101 [.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[5,6,2,7,4,3,8,1]=>0101101 [.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[6,4,2,7,5,3,8,1]=>1101101 [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[5,4,2,7,6,3,8,1]=>1101101 [.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[4,5,2,7,6,3,8,1]=>0101101 [.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[5,6,4,2,7,3,8,1]=>0110101 [.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[4,6,5,2,7,3,8,1]=>0110101 [.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[5,4,6,2,7,3,8,1]=>1010101 [.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[4,5,6,2,7,3,8,1]=>0010101 [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[3,2,7,6,5,4,8,1]=>1011101 [.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[7,5,6,3,2,4,8,1]=>[5,3,2,7,6,4,8,1]=>1101101 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[6,5,3,2,7,4,8,1]=>1110101 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[2,3,7,6,5,4,8,1]=>0011101 [.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[2,5,3,7,6,4,8,1]=>0101101 [.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[5,2,6,3,7,4,8,1]=>1010101 [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[7,6,4,3,2,5,8,1]=>[4,3,2,7,6,5,8,1]=>1101101 [.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[7,6,3,4,2,5,8,1]=>[3,4,2,7,6,5,8,1]=>0101101 [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[2,4,3,7,6,5,8,1]=>0101101 [.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[2,6,4,3,7,5,8,1]=>0110101 [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[3,2,4,7,6,5,8,1]=>1001101 [.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[3,2,6,4,7,5,8,1]=>1010101 [.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[2,3,4,7,6,5,8,1]=>0001101 [.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[2,3,6,4,7,5,8,1]=>0010101 [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[5,4,3,2,7,6,8,1]=>1110101 [.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[7,5,3,4,2,6,8,1]=>[3,5,4,2,7,6,8,1]=>0110101 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[4,3,5,2,7,6,8,1]=>1010101 [.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[3,4,5,2,7,6,8,1]=>0010101 [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[2,5,4,3,7,6,8,1]=>0110101 [.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[4,2,5,3,7,6,8,1]=>1010101 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[3,2,5,4,7,6,8,1]=>1010101 [.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[2,3,5,4,7,6,8,1]=>0010101 [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[4,3,2,5,7,6,8,1]=>1100101 [.,[[[[.,[[.,.],.]],.],[.,.]],.]]=>[7,3,4,2,5,6,8,1]=>[3,4,2,5,7,6,8,1]=>0100101 [.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[2,4,3,5,7,6,8,1]=>0100101 [.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[3,2,4,5,7,6,8,1]=>1000101 [.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[2,3,4,5,7,6,8,1]=>0000101 [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1]=>1111001 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[5,4,6,3,2,7,8,1]=>1011001 [.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[4,5,6,3,2,7,8,1]=>0011001 [.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[3,6,5,4,2,7,8,1]=>0111001 [.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[3,4,6,5,2,7,8,1]=>0011001 [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[5,4,3,6,2,7,8,1]=>1101001 [.,[[[.,[[[.,.],[.,.]],.]],.],.]]=>[5,3,4,6,2,7,8,1]=>[3,5,4,6,2,7,8,1]=>0101001 [.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[4,3,5,6,2,7,8,1]=>1001001 [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[3,4,5,6,2,7,8,1]=>0001001 [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[2,6,5,4,3,7,8,1]=>0111001 [.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[5,4,2,6,3,7,8,1]=>1101001 [.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[4,5,2,6,3,7,8,1]=>0101001 [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[2,3,6,5,4,7,8,1]=>0011001 [.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[2,5,3,6,4,7,8,1]=>0101001 [.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[2,4,3,6,5,7,8,1]=>0101001 [.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[2,3,4,6,5,7,8,1]=>0001001 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1]=>1110001 [.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[4,5,3,2,6,7,8,1]=>0110001 [.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[3,5,4,2,6,7,8,1]=>0110001 [.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[4,3,5,2,6,7,8,1]=>1010001 [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[3,4,5,2,6,7,8,1]=>0010001 [.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[2,5,4,3,6,7,8,1]=>0110001 [.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[4,2,5,3,6,7,8,1]=>1010001 [.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[3,2,5,4,6,7,8,1]=>1010001 [.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[2,3,5,4,6,7,8,1]=>0010001 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[4,3,2,5,6,7,8,1]=>1100001 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[3,4,2,5,6,7,8,1]=>0100001 [.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[2,4,3,5,6,7,8,1]=>0100001 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,1]=>1000001 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1]=>0000001 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[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]=>[7,1,8,6,5,4,3,2]=>1011111 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[6,1,8,7,5,4,3,2]=>1011111 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[7,6,1,8,5,4,3,2]=>1101111 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[6,7,1,8,5,4,3,2]=>0101111 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[5,1,8,7,6,4,3,2]=>1011111 [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[7,5,1,8,6,4,3,2]=>1101111 [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[6,5,1,8,7,4,3,2]=>1101111 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[7,6,5,1,8,4,3,2]=>1110111 [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[6,7,5,1,8,4,3,2]=>0110111 [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[5,7,6,1,8,4,3,2]=>0110111 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[6,5,7,1,8,4,3,2]=>1010111 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[5,6,7,1,8,4,3,2]=>0010111 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[4,1,8,7,6,5,3,2]=>1011111 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[7,4,1,8,6,5,3,2]=>1101111 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[6,4,1,8,7,5,3,2]=>1101111 [[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[6,7,4,1,8,5,3,2]=>0110111 [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[5,4,1,8,7,6,3,2]=>1101111 [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[4,5,1,8,7,6,3,2]=>0101111 [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[4,7,5,1,8,6,3,2]=>0110111 [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[5,6,4,1,8,7,3,2]=>0110111 [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[7,6,5,4,1,8,3,2]=>1111011 [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[6,7,5,4,1,8,3,2]=>0111011 [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[5,7,6,4,1,8,3,2]=>0111011 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[4,7,6,5,1,8,3,2]=>0111011 [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[5,4,7,6,1,8,3,2]=>1011011 [[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[5,6,4,7,1,8,3,2]=>0101011 [[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[5,4,6,7,1,8,3,2]=>1001011 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[4,5,6,7,1,8,3,2]=>0001011 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[3,1,8,7,6,5,4,2]=>1011111 [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[7,3,1,8,6,5,4,2]=>1101111 [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,4,1,2]=>[6,3,1,8,7,5,4,2]=>1101111 [[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[6,7,3,1,8,5,4,2]=>0110111 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[5,3,1,8,7,6,4,2]=>1101111 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[7,5,3,1,8,6,4,2]=>1110111 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[6,5,3,1,8,7,4,2]=>1110111 [[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[5,6,3,1,8,7,4,2]=>0110111 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[7,6,5,3,1,8,4,2]=>1111011 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[6,7,5,3,1,8,4,2]=>0111011 [[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[5,7,6,3,1,8,4,2]=>0111011 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[6,5,7,3,1,8,4,2]=>1011011 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[5,6,7,3,1,8,4,2]=>0011011 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[4,3,1,8,7,6,5,2]=>1101111 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[7,4,3,1,8,6,5,2]=>1110111 [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2]=>[6,4,3,1,8,7,5,2]=>1110111 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[7,6,4,3,1,8,5,2]=>1111011 [[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[6,7,4,3,1,8,5,2]=>0111011 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[3,4,1,8,7,6,5,2]=>0101111 [[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[3,7,4,1,8,6,5,2]=>0110111 [[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[3,6,4,1,8,7,5,2]=>0110111 [[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[3,7,6,4,1,8,5,2]=>0111011 [[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[6,3,7,4,1,8,5,2]=>1011011 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[5,4,3,1,8,7,6,2]=>1110111 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[7,5,4,3,1,8,6,2]=>1111011 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[4,5,3,1,8,7,6,2]=>0110111 [[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[4,7,5,3,1,8,6,2]=>0111011 [[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[3,7,5,4,1,8,6,2]=>0111011 [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[4,3,7,5,1,8,6,2]=>1011011 [[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[3,4,5,1,8,7,6,2]=>0010111 [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[3,4,7,5,1,8,6,2]=>0011011 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[6,5,4,3,1,8,7,2]=>1111011 [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[5,4,6,3,1,8,7,2]=>1011011 [[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>[8,5,6,3,4,7,1,2]=>[5,3,6,4,1,8,7,2]=>1011011 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[4,3,6,5,1,8,7,2]=>1011011 [[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[8,6,3,4,5,7,1,2]=>[3,4,6,5,1,8,7,2]=>0011011 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[5,4,3,6,1,8,7,2]=>1101011 [[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[3,5,4,6,1,8,7,2]=>0101011 [[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[4,3,5,6,1,8,7,2]=>1001011 [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[3,4,5,6,1,8,7,2]=>0001011 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[7,6,5,4,3,1,8,2]=>1111101 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[6,7,5,4,3,1,8,2]=>0111101 [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,3,8,1,2]=>[5,7,6,4,3,1,8,2]=>0111101 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[6,5,7,4,3,1,8,2]=>1011101 [[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[5,6,7,4,3,1,8,2]=>0011101 [[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[4,5,7,6,3,1,8,2]=>0011101 [[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[5,4,6,7,3,1,8,2]=>1001101 [[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[4,5,6,7,3,1,8,2]=>0001101 [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[3,7,6,5,4,1,8,2]=>0111101 [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[5,3,7,6,4,1,8,2]=>1011101 [[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[5,6,3,7,4,1,8,2]=>0101101 [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[4,3,7,6,5,1,8,2]=>1011101 [[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[6,4,3,7,5,1,8,2]=>1101101 [[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[3,6,4,7,5,1,8,2]=>0101101 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[5,4,3,7,6,1,8,2]=>1101101 [[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[7,4,5,3,6,8,1,2]=>[4,5,3,7,6,1,8,2]=>0101101 [[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[3,5,4,7,6,1,8,2]=>0101101 [[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[3,4,5,7,6,1,8,2]=>0001101 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[6,5,4,3,7,1,8,2]=>1110101 [[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[5,6,4,3,7,1,8,2]=>0110101 [[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[4,6,5,3,7,1,8,2]=>0110101 [[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[5,4,6,3,7,1,8,2]=>1010101 [[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[4,5,6,3,7,1,8,2]=>0010101 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[5,3,6,4,7,1,8,2]=>1010101 [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[4,3,6,5,7,1,8,2]=>1010101 [[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[3,4,6,5,7,1,8,2]=>0010101 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[5,4,3,6,7,1,8,2]=>1100101 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[4,5,3,6,7,1,8,2]=>0100101 [[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[3,5,4,6,7,1,8,2]=>0100101 [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[4,3,5,6,7,1,8,2]=>1000101 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[3,4,5,6,7,1,8,2]=>0000101 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,1,8,7,6,5,4,3]=>1011111 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[7,2,1,8,6,5,4,3]=>1101111 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[6,2,1,8,7,5,4,3]=>1101111 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,6,2,1,8,5,4,3]=>1110111 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[6,7,2,1,8,5,4,3]=>0110111 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[5,2,1,8,7,6,4,3]=>1101111 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[7,5,2,1,8,6,4,3]=>1110111 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[6,5,2,1,8,7,4,3]=>1110111 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[7,6,5,2,1,8,4,3]=>1111011 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[6,7,5,2,1,8,4,3]=>0111011 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[6,5,7,2,1,8,4,3]=>1011011 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[5,6,7,2,1,8,4,3]=>0011011 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[4,2,1,8,7,6,5,3]=>1101111 [[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[7,4,2,1,8,6,5,3]=>1110111 [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[6,4,2,1,8,7,5,3]=>1110111 [[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,2,1,3]=>[6,7,4,2,1,8,5,3]=>0111011 [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[5,4,2,1,8,7,6,3]=>1110111 [[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[7,5,4,2,1,8,6,3]=>1111011 [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[4,5,2,1,8,7,6,3]=>0110111 [[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[4,7,5,2,1,8,6,3]=>0111011 [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[4,6,5,2,1,8,7,3]=>0111011 [[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[5,4,6,2,1,8,7,3]=>1011011 [[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[4,5,6,2,1,8,7,3]=>0011011 [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[7,6,5,4,2,1,8,3]=>1111101 [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[6,7,5,4,2,1,8,3]=>0111101 [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[4,7,6,5,2,1,8,3]=>0111101 [[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[6,4,7,5,2,1,8,3]=>1011101 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[5,4,7,6,2,1,8,3]=>1011101 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[4,5,6,7,2,1,8,3]=>0001101 [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>0011111 [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[1,7,6,2,8,5,4,3]=>0110111 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[6,1,7,2,8,5,4,3]=>1010111 [[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[1,7,5,2,8,6,4,3]=>0110111 [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[1,6,5,2,8,7,4,3]=>0110111 [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[5,1,6,2,8,7,4,3]=>1010111 [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[1,7,6,5,2,8,4,3]=>0111011 [[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[6,1,7,5,2,8,4,3]=>1011011 [[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[5,1,7,6,2,8,4,3]=>1011011 [[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[6,5,1,7,2,8,4,3]=>1101011 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[5,6,1,7,2,8,4,3]=>0101011 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[1,4,2,8,7,6,5,3]=>0101111 [[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[1,7,4,2,8,6,5,3]=>0110111 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[1,6,4,2,8,7,5,3]=>0110111 [[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[6,1,7,4,2,8,5,3]=>1011011 [[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[1,7,5,4,2,8,6,3]=>0111011 [[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[4,1,5,2,8,7,6,3]=>1010111 [[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[4,1,7,5,2,8,6,3]=>1011011 [[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[1,6,5,4,2,8,7,3]=>0111011 [[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[5,1,6,4,2,8,7,3]=>1011011 [[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[4,5,1,6,2,8,7,3]=>0101011 [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[1,7,6,5,4,2,8,3]=>0111101 [[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[6,1,7,5,4,2,8,3]=>1011101 [[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[5,1,7,6,4,2,8,3]=>1011101 [[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[6,5,1,7,4,2,8,3]=>1101101 [[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[5,6,1,7,4,2,8,3]=>0101101 [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[4,1,7,6,5,2,8,3]=>1011101 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[6,4,1,7,5,2,8,3]=>1101101 [[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[5,4,1,7,6,2,8,3]=>1101101 [[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[4,5,1,7,6,2,8,3]=>0101101 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[6,5,4,1,7,2,8,3]=>1110101 [[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[5,6,4,1,7,2,8,3]=>0110101 [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[5,4,6,1,7,2,8,3]=>1010101 [[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[4,5,6,1,7,2,8,3]=>0010101 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[3,2,1,8,7,6,5,4]=>1101111 [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[7,3,2,1,8,6,5,4]=>1110111 [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[6,3,2,1,8,7,5,4]=>1110111 [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[7,6,3,2,1,8,5,4]=>1111011 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[5,3,2,1,8,7,6,4]=>1110111 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,5,3,2,1,8,6,4]=>1111011 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[6,5,3,2,1,8,7,4]=>1111011 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[5,6,3,2,1,8,7,4]=>0111011 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,5,3,2,1,8,4]=>1111101 [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[5,7,6,3,2,1,8,4]=>0111101 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[5,6,7,3,2,1,8,4]=>0011101 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[2,3,1,8,7,6,5,4]=>0101111 [[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[6,2,7,3,1,8,5,4]=>1011011 [[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[2,7,5,3,1,8,6,4]=>0111011 [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[2,6,5,3,1,8,7,4]=>0111011 [[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[5,2,6,3,1,8,7,4]=>1011011 [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[2,7,6,5,3,1,8,4]=>0111101 [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[6,2,7,5,3,1,8,4]=>1011101 [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[5,2,7,6,3,1,8,4]=>1011101 [[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[6,5,2,7,3,1,8,4]=>1101101 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[5,6,2,7,3,1,8,4]=>0101101 [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[1,3,2,8,7,6,5,4]=>0101111 [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[1,7,3,2,8,6,5,4]=>0110111 [[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[6,1,7,3,2,8,5,4]=>1011011 [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[1,5,3,2,8,7,6,4]=>0110111 [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[1,7,5,3,2,8,6,4]=>0111011 [[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[1,6,5,3,2,8,7,4]=>0111011 [[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[5,1,6,3,2,8,7,4]=>1011011 [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[1,7,6,5,3,2,8,4]=>0111101 [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[6,1,7,5,3,2,8,4]=>1011101 [[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[5,6,1,7,3,2,8,4]=>0101101 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[2,1,3,8,7,6,5,4]=>1001111 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,1,7,3,8,6,5,4]=>1010111 [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[2,1,7,6,3,8,5,4]=>1011011 [[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[6,2,1,7,3,8,5,4]=>1101011 [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[2,1,5,3,8,7,6,4]=>1010111 [[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,1,7,5,3,8,6,4]=>1011011 [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[2,1,6,5,3,8,7,4]=>1011011 [[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[5,2,1,6,3,8,7,4]=>1101011 [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[2,1,7,6,5,3,8,4]=>1011101 [[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[6,2,1,7,5,3,8,4]=>1101101 [[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[5,2,1,7,6,3,8,4]=>1101101 [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,5,2,1,7,3,8,4]=>1110101 [[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[5,6,2,1,7,3,8,4]=>0110101 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[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]=>[1,2,7,3,8,6,5,4]=>0010111 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[1,2,6,3,8,7,5,4]=>0010111 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[1,2,7,6,3,8,5,4]=>0011011 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[1,6,2,7,3,8,5,4]=>0101011 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,2,5,3,8,7,6,4]=>0010111 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[1,2,7,5,3,8,6,4]=>0011011 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[1,2,6,5,3,8,7,4]=>0011011 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[1,5,2,6,3,8,7,4]=>0101011 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[1,2,7,6,5,3,8,4]=>0011101 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[1,6,2,7,5,3,8,4]=>0101101 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[1,5,2,7,6,3,8,4]=>0101101 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[1,6,5,2,7,3,8,4]=>0110101 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>1010101 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[4,3,2,1,8,7,6,5]=>1110111 [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[7,4,3,2,1,8,6,5]=>1111011 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[6,4,3,2,1,8,7,5]=>1111011 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[7,6,4,3,2,1,8,5]=>1111101 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[6,7,4,3,2,1,8,5]=>0111101 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[3,4,2,1,8,7,6,5]=>0110111 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[3,7,4,2,1,8,6,5]=>0111011 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[2,4,3,1,8,7,6,5]=>0110111 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[2,6,4,3,1,8,7,5]=>0111011 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[3,2,4,1,8,7,6,5]=>1010111 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[3,2,6,4,1,8,7,5]=>1011011 [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[3,2,7,6,4,1,8,5]=>1011101 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[6,3,2,7,4,1,8,5]=>1101101 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[2,3,4,1,8,7,6,5]=>0010111 [[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[2,3,7,4,1,8,6,5]=>0011011 [[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[8,6,7,2,3,4,1,5]=>[2,3,6,4,1,8,7,5]=>0011011 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[2,6,3,7,4,1,8,5]=>0101101 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[1,4,3,2,8,7,6,5]=>0110111 [[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[1,7,4,3,2,8,6,5]=>0111011 [[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,3,1,2,5]=>[1,6,4,3,2,8,7,5]=>0111011 [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,3,1,2,5]=>[1,7,6,4,3,2,8,5]=>0111101 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[6,1,7,4,3,2,8,5]=>1011101 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[3,1,4,2,8,7,6,5]=>1010111 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[3,1,7,4,2,8,6,5]=>1011011 [[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[3,1,7,6,4,2,8,5]=>1011101 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[6,3,1,7,4,2,8,5]=>1101101 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,1,4,3,8,7,6,5]=>1010111 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[2,1,6,4,3,8,7,5]=>1011011 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,2,1,7,4,3,8,5]=>1101101 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[1,2,4,3,8,7,6,5]=>0010111 [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[1,2,7,4,3,8,6,5]=>0011011 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[1,6,2,7,4,3,8,5]=>0101101 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[3,2,1,4,8,7,6,5]=>1100111 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,3,2,1,7,4,8,5]=>1110101 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[2,3,1,4,8,7,6,5]=>0100111 [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[2,3,1,7,4,8,6,5]=>0101011 [[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[2,3,1,7,6,4,8,5]=>0101101 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[2,6,3,1,7,4,8,5]=>0110101 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[1,3,2,4,8,7,6,5]=>0100111 [[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[1,3,2,7,4,8,6,5]=>0101011 [[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[1,3,2,6,4,8,7,5]=>0101011 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[1,6,3,2,7,4,8,5]=>0110101 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[2,1,3,4,8,7,6,5]=>1000111 [[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[2,1,3,7,4,8,6,5]=>1001011 [[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[2,1,3,6,4,8,7,5]=>1001011 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[2,1,6,3,7,4,8,5]=>1010101 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[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]=>[1,2,3,7,4,8,6,5]=>0001011 [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[1,2,3,6,4,8,7,5]=>0001011 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[1,2,3,7,6,4,8,5]=>0001101 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[1,2,6,3,7,4,8,5]=>0010101 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[5,4,3,2,1,8,7,6]=>1111011 [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,5,4,3,2,1,8,6]=>1111101 [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[4,5,3,2,1,8,7,6]=>0111011 [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[3,5,4,2,1,8,7,6]=>0111011 [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[4,3,5,2,1,8,7,6]=>1011011 [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[3,4,5,2,1,8,7,6]=>0011011 [[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[3,4,7,5,2,1,8,6]=>0011101 [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[2,5,4,3,1,8,7,6]=>0111011 [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[4,2,5,3,1,8,7,6]=>1011011 [[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[4,2,7,5,3,1,8,6]=>1011101 [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[3,2,5,4,1,8,7,6]=>1011011 [[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[3,2,7,5,4,1,8,6]=>1011101 [[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[2,3,7,5,4,1,8,6]=>0011101 [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[4,3,2,5,1,8,7,6]=>1101011 [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[4,3,2,7,5,1,8,6]=>1101101 [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[3,4,2,5,1,8,7,6]=>0101011 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[2,3,4,5,1,8,7,6]=>0001011 [[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[2,3,4,7,5,1,8,6]=>0001101 [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[1,5,4,3,2,8,7,6]=>0111011 [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[1,7,5,4,3,2,8,6]=>0111101 [[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[3,1,7,5,4,2,8,6]=>1011101 [[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[4,3,1,7,5,2,8,6]=>1101101 [[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[3,4,1,5,2,8,7,6]=>0101011 [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[2,1,5,4,3,8,7,6]=>1011011 [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,1,7,5,4,3,8,6]=>1011101 [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[1,2,5,4,3,8,7,6]=>0011011 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[1,2,7,5,4,3,8,6]=>0011101 [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[1,4,2,5,3,8,7,6]=>0101011 [[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[1,4,2,7,5,3,8,6]=>0101101 [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[3,2,1,7,5,4,8,6]=>1101101 [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[1,3,2,5,4,8,7,6]=>0101011 [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[1,3,2,7,5,4,8,6]=>0101101 [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[2,1,3,5,4,8,7,6]=>1001011 [[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,1,3,7,5,4,8,6]=>1001101 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[1,2,3,5,4,8,7,6]=>0001011 [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[1,2,3,7,5,4,8,6]=>0001101 [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[4,3,2,1,5,8,7,6]=>1110011 [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[4,3,2,1,7,5,8,6]=>1110101 [[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[3,4,2,1,7,5,8,6]=>0110101 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[3,2,4,1,5,8,7,6]=>1010011 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[3,2,4,1,7,5,8,6]=>1010101 [[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[2,3,4,1,5,8,7,6]=>0010011 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[2,3,4,1,7,5,8,6]=>0010101 [[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[1,4,3,2,5,8,7,6]=>0110011 [[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[1,4,3,2,7,5,8,6]=>0110101 [[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[3,1,4,2,5,8,7,6]=>1010011 [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[3,1,4,2,7,5,8,6]=>1010101 [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[2,1,4,3,5,8,7,6]=>1010011 [[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,1,4,3,7,5,8,6]=>1010101 [[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[1,2,4,3,5,8,7,6]=>0010011 [[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[1,2,4,3,7,5,8,6]=>0010101 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[3,2,1,4,5,8,7,6]=>1100011 [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[3,2,1,4,7,5,8,6]=>1100101 [[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[1,3,2,4,7,5,8,6]=>0100101 [[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[2,1,3,4,5,8,7,6]=>1000011 [[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,1,3,4,7,5,8,6]=>1000101 [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[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]=>[1,2,3,4,7,5,8,6]=>0000101 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[6,5,4,3,2,1,8,7]=>1111101 [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[5,6,4,3,2,1,8,7]=>0111101 [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[4,6,5,3,2,1,8,7]=>0111101 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[4,5,6,3,2,1,8,7]=>0011101 [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[3,6,5,4,2,1,8,7]=>0111101 [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[4,3,6,5,2,1,8,7]=>1011101 [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[3,4,5,6,2,1,8,7]=>0001101 [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[2,6,5,4,3,1,8,7]=>0111101 [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[4,2,6,5,3,1,8,7]=>1011101 [[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[4,5,2,6,3,1,8,7]=>0101101 [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[3,2,6,5,4,1,8,7]=>1011101 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[2,3,6,5,4,1,8,7]=>0011101 [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[4,3,2,6,5,1,8,7]=>1101101 [[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[8,6,3,4,2,5,1,7]=>[3,4,2,6,5,1,8,7]=>0101101 [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[2,4,3,6,5,1,8,7]=>0101101 [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[5,4,3,2,6,1,8,7]=>1110101 [[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[4,5,3,2,6,1,8,7]=>0110101 [[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[8,5,3,4,2,6,1,7]=>[3,5,4,2,6,1,8,7]=>0110101 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[4,3,5,2,6,1,8,7]=>1010101 [[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[3,4,5,2,6,1,8,7]=>0010101 [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[8,5,4,2,3,6,1,7]=>[2,5,4,3,6,1,8,7]=>0110101 [[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[4,2,5,3,6,1,8,7]=>1010101 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[3,2,5,4,6,1,8,7]=>1010101 [[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[8,4,3,2,5,6,1,7]=>[4,3,2,5,6,1,8,7]=>1100101 [[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[3,4,2,5,6,1,8,7]=>0100101 [[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[2,4,3,5,6,1,8,7]=>0100101 [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[2,3,4,5,6,1,8,7]=>0000101 [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[1,6,5,4,3,2,8,7]=>0111101 [[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[5,4,1,6,3,2,8,7]=>1101101 [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[3,1,6,5,4,2,8,7]=>1011101 [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[5,3,1,6,4,2,8,7]=>1101101 [[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[5,4,3,1,6,2,8,7]=>1110101 [[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[3,5,4,1,6,2,8,7]=>0110101 [[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[4,3,5,1,6,2,8,7]=>1010101 [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[3,4,5,1,6,2,8,7]=>0010101 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[2,1,6,5,4,3,8,7]=>1011101 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[4,2,1,6,5,3,8,7]=>1101101 [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>[4,5,2,1,6,3,8,7]=>0110101 [[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[1,4,2,6,5,3,8,7]=>0101101 [[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[1,5,4,2,6,3,8,7]=>0110101 [[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[4,1,5,2,6,3,8,7]=>1010101 [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[3,2,1,6,5,4,8,7]=>1101101 [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[5,3,2,1,6,4,8,7]=>1110101 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[2,3,1,6,5,4,8,7]=>0101101 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[2,5,3,1,6,4,8,7]=>0110101 [[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[8,6,5,3,1,2,4,7]=>[1,3,2,6,5,4,8,7]=>0101101 [[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[2,1,5,3,6,4,8,7]=>1010101 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[1,2,3,6,5,4,8,7]=>0001101 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[1,2,5,3,6,4,8,7]=>0010101 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[4,3,2,1,6,5,8,7]=>1110101 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[3,4,2,1,6,5,8,7]=>0110101 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[2,4,3,1,6,5,8,7]=>0110101 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[3,2,4,1,6,5,8,7]=>1010101 [[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[3,1,4,2,6,5,8,7]=>1010101 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[2,1,4,3,6,5,8,7]=>1010101 [[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[1,2,4,3,6,5,8,7]=>0010101 [[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[2,3,1,4,6,5,8,7]=>0100101 [[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,6,5,8,7]=>0000101 [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[5,4,3,2,1,6,8,7]=>1111001 [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[4,5,3,2,1,6,8,7]=>0111001 [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[4,3,5,2,1,6,8,7]=>1011001 [[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[3,4,5,2,1,6,8,7]=>0011001 [[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[8,5,4,2,3,1,6,7]=>[2,5,4,3,1,6,8,7]=>0111001 [[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[3,2,5,4,1,6,8,7]=>1011001 [[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[2,3,5,4,1,6,8,7]=>0011001 [[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[2,4,3,5,1,6,8,7]=>0101001 [[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[2,3,4,5,1,6,8,7]=>0001001 [[[[.,.],[[.,[.,.]],.]],.],[.,.]]=>[8,4,3,5,1,2,6,7]=>[4,3,1,5,2,6,8,7]=>1101001 [[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[1,2,5,4,3,6,8,7]=>0011001 [[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[1,4,2,5,3,6,8,7]=>0101001 [[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[2,1,3,5,4,6,8,7]=>1001001 [[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[1,2,3,5,4,6,8,7]=>0001001 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[4,3,2,1,5,6,8,7]=>1110001 [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[3,2,4,1,5,6,8,7]=>1010001 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[2,3,4,1,5,6,8,7]=>0010001 [[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[1,4,3,2,5,6,8,7]=>0110001 [[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[2,1,4,3,5,6,8,7]=>1010001 [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[1,2,4,3,5,6,8,7]=>0010001 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[3,2,1,4,5,6,8,7]=>1100001 [[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[2,3,1,4,5,6,8,7]=>0100001 [[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[1,3,2,4,5,6,8,7]=>0100001 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[2,1,3,4,5,6,8,7]=>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]=>[6,7,5,4,3,2,1,8]=>0111110 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[5,7,6,4,3,2,1,8]=>0111110 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[6,5,7,4,3,2,1,8]=>1011110 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>0011110 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[4,7,6,5,3,2,1,8]=>0111110 [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[6,4,7,5,3,2,1,8]=>1011110 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[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[5,4,3,1,6,2,7,8]=>1110100 [[[[.,.],[[[.,.],[.,.]],.]],.],.]=>[5,3,4,6,1,2,7,8]=>[3,5,4,1,6,2,7,8]=>0110100 [[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[4,3,5,6,1,2,7,8]=>[4,3,5,1,6,2,7,8]=>1010100 [[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[3,4,5,1,6,2,7,8]=>0010100 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,2,1,6,4,3,7,8]=>1101100 [[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[4,2,1,6,5,3,7,8]=>1101100 [[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,4,2,1,6,3,7,8]=>1110100 [[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100 [[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[1,5,2,6,4,3,7,8]=>0101100 [[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[1,5,4,2,6,3,7,8]=>0110100 [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[4,1,5,2,6,3,7,8]=>1010100 [[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[3,2,1,6,5,4,7,8]=>1101100 [[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,3,2,1,6,4,7,8]=>1110100 [[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[2,3,1,6,5,4,7,8]=>0101100 [[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[2,5,3,1,6,4,7,8]=>0110100 [[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[6,5,3,1,2,4,7,8]=>[1,3,2,6,5,4,7,8]=>0101100 [[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[1,5,3,2,6,4,7,8]=>0110100 [[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100 [[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[1,2,5,3,6,4,7,8]=>0010100 [[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[4,3,2,1,6,5,7,8]=>1110100 [[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[6,4,2,3,1,5,7,8]=>[2,4,3,1,6,5,7,8]=>0110100 [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[3,2,4,1,6,5,7,8]=>1010100 [[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[2,3,4,1,6,5,7,8]=>0010100 [[[[[.,.],[[.,.],.]],[.,.]],.],.]=>[6,3,4,1,2,5,7,8]=>[3,1,4,2,6,5,7,8]=>1010100 [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[2,1,4,3,6,5,7,8]=>1010100 [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[1,2,4,3,6,5,7,8]=>0010100 [[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[1,3,2,4,6,5,7,8]=>0100100 [[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[2,1,3,4,6,5,7,8]=>1000100 [[[[[[[.,.],.],.],.],[.,.]],.],.]=>[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]=>[4,5,3,2,1,6,7,8]=>0111000 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[3,5,4,2,1,6,7,8]=>0111000 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>1011000 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[3,4,5,2,1,6,7,8]=>0011000 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>0111000 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[4,2,5,3,1,6,7,8]=>1011000 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>1011000 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>0011000 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>1101000 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>0101000 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>0101000 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>1001000 [[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0001000 [[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000 [[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[3,4,1,5,2,6,7,8]=>0101000 [[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>1011000 [[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[4,5,2,1,3,6,7,8]=>[4,2,1,5,3,6,7,8]=>1101000 [[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[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]=>[1,4,2,5,3,6,7,8]=>0101000 [[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>1101000 [[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>0101000 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>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]=>[3,4,2,1,5,6,7,8]=>0110000 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>0110000 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>1010000 [[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0010000 [[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[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]=>[3,1,4,2,5,6,7,8]=>1010000 [[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>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]=>[2,3,1,4,5,6,7,8]=>0100000 [[[[[[[.,.],[.,.]],.],.],.],.],.]=>[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]=>[8,9,7,6,5,4,3,2,1]=>01111111 [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[7,8,9,6,5,4,3,2,1]=>00111111 [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[6,7,8,9,5,4,3,2,1]=>00011111 [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[5,6,7,8,9,4,3,2,1]=>00001111 [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[4,5,6,7,8,9,3,2,1]=>00000111 [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[3,4,5,6,7,8,9,2,1]=>00000011 [.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,1]=>00000001 [[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[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]=>[9,10,8,7,6,5,4,3,2,1]=>011111111 [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[7,9,8,6,5,4,3,2,1]=>01111111 [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[8,9,10,7,6,5,4,3,2,1]=>001111111 [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[8,6,9,7,5,4,3,2,1]=>10111111 [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[7,8,9,10,6,5,4,3,2,1]=>000111111 [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[7,8,9,5,6,4,3,2,1]=>[7,8,5,9,6,4,3,2,1]=>01011111 [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[6,7,8,9,10,5,4,3,2,1]=>000011111 [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[6,7,8,9,4,5,3,2,1]=>[6,7,8,4,9,5,3,2,1]=>00101111 [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[5,6,7,8,9,10,4,3,2,1]=>000001111 [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[5,6,7,8,3,9,4,2,1]=>00010111 [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[4,5,6,7,8,9,10,3,2,1]=>000000111 [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[4,5,6,7,8,2,9,3,1]=>00001011 [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[3,4,5,6,7,8,9,10,2,1]=>000000011 [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[3,4,5,6,7,8,1,9,2]=>00000101 [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,10,1]=>000000001 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[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]=>[8,7,9,6,5,4,3,2,1]=>10111111 [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[8,7,6,9,5,4,3,2,1]=>11011111 [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[8,7,6,5,9,4,3,2,1]=>11101111 [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[8,7,6,5,4,9,3,2,1]=>11110111 [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[8,7,6,5,4,3,9,2,1]=>11111011 [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,9,1]=>11111101 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[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]=>[9,8,10,7,6,5,4,3,2,1]=>101111111 [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[6,8,7,9,5,4,3,2,1]=>01011111 [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[9,8,7,10,6,5,4,3,2,1]=>110111111 [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[5,8,7,6,9,4,3,2,1]=>01101111 [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[9,8,7,6,10,5,4,3,2,1]=>111011111 [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>[4,8,7,6,5,9,3,2,1]=>01110111 [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[9,8,7,6,5,10,4,3,2,1]=>111101111 [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>[3,8,7,6,5,4,9,2,1]=>01111011 [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[9,8,7,6,5,4,10,3,2,1]=>111110111 [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[2,8,7,6,5,4,3,9,1]=>01111101 [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[9,8,7,6,5,4,3,10,2,1]=>111111011 [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[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]=>[9,8,7,6,5,4,3,2,10,1]=>111111101 [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110 [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[9,7,5,3,1,10,8,6,4,2]=>111101111 [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[5,6,4,7,3,8,2,9,1,10]=>010101010 [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>11111011111 [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[10,8,6,4,2,3,5,7,9,1]=>[2,4,3,6,5,8,7,10,9,1]=>010101011 [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[9,7,5,3,2,4,6,8,1,10]=>[3,2,5,4,7,6,9,8,1,10]=>101010110 [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[2,1,4,3,6,5,8,7,10,9]=>101010101 [.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[12,10,8,6,4,2,3,5,7,9,11,1]=>[2,4,3,6,5,8,7,10,9,12,11,1]=>01010101011 [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[11,9,7,5,3,2,4,6,8,10,1,12]=>[3,2,5,4,7,6,9,8,11,10,1,12]=>10101010110 [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>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]=>[2,1,3,4,5,6,7,9,8]=>10000001 [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,1]=>10000001 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001 [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,10,9]=>100000001 [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,9,8]=>01000001 [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,9,8]=>01000001 [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[2,4,3,5,6,7,8,9,1]=>01000001 [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[3,4,2,5,6,7,8,9,1]=>01000001 [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[3,2,4,5,6,7,8,9,10,1]=>100000001 [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001 [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,8,6,9,7]=>00000101 [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,7,4,8,5,9,6]=>00010101 [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[1,6,2,7,3,8,4,9,5]=>01010101 [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[5,6,1,7,2,8,3,9,4]=>01010101 [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[4,5,6,7,1,8,2,9,3]=>00010101 [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[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]=>[1,2,3,4,5,6,9,7,10,8]=>000000101 [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,8,5,9,6,10,7]=>000010101 [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,7,3,8,4,9,5,10,6]=>001010101 [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[6,1,7,2,8,3,9,4,10,5]=>101010101 [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[5,6,7,1,8,2,9,3,10,4]=>001010101 [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[4,5,6,7,8,1,9,2,10,3]=>000010101 [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[3,4,5,6,7,8,9,1,10,2]=>000000101 [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[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]=>[7,8,6,5,4,3,2,1,9]=>01111110 [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[8,1,9,7,6,5,4,3,2]=>10111111 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[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]=>[8,9,7,6,5,4,3,2,1,10]=>011111110 [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[7,6,8,5,4,3,2,1,9]=>10111110 [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[8,6,7,5,4,3,2,1,9]=>[6,8,7,5,4,3,2,1,9]=>01111110 [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[8,7,1,9,6,5,4,3,2]=>11011111 [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[7,1,9,8,6,5,4,3,2]=>10111111 [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[9,1,10,8,7,6,5,4,3,2]=>101111111 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[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]=>[6,5,7,4,8,3,9,2,10,1]=>101010101 [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[9,7,5,3,2,4,6,8,10,1]=>[3,2,5,4,7,6,9,8,10,1]=>101010101 [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,3,2,4,1,5,7,9]=>[3,2,4,1,6,5,8,7,10,9]=>101010101 [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[11,9,7,5,3,2,4,6,8,10,12,1]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>10101010101 [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[2,1,9,8,7,6,5,4,3]=>10111111 [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[3,2,1,9,8,7,6,5,4]=>11011111 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[4,3,2,1,9,8,7,6,5]=>11101111 [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[5,4,3,2,1,9,8,7,6]=>11110111 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[6,5,4,3,2,1,9,8,7]=>11111011 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,9,8]=>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]=>[2,1,10,9,8,7,6,5,4,3]=>101111111 [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[2,3,1,9,8,7,6,5,4]=>01011111 [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[3,2,1,10,9,8,7,6,5,4]=>110111111 [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,3,4,2,1,5]=>[3,4,2,1,9,8,7,6,5]=>01101111 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[4,3,2,1,10,9,8,7,6,5]=>111011111 [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[9,8,7,4,5,3,2,1,6]=>[4,5,3,2,1,9,8,7,6]=>01110111 [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[5,4,3,2,1,10,9,8,7,6]=>111101111 [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[9,8,5,6,4,3,2,1,7]=>[5,6,4,3,2,1,9,8,7]=>01111011 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[6,5,4,3,2,1,10,9,8,7]=>111110111 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[6,7,5,4,3,2,1,9,8]=>01111101 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,10,9,8]=>111111011 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,10,9]=>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 [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>01100000 [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[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]=>[5,9,8,7,6,4,3,2,1]=>01111111 [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[4,9,8,7,6,5,3,2,1]=>01111111 [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,3,4,2,1]=>[3,9,8,7,6,5,4,2,1]=>01111111 [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[2,9,8,7,6,5,4,3,1]=>01111111 [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[8,10,9,7,6,5,4,3,2,1]=>011111111 [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[6,10,9,8,7,5,4,3,2,1]=>011111111 [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[5,10,9,8,7,6,4,3,2,1]=>011111111 [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[2,10,9,8,7,6,5,4,3,1]=>011111111 [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[10,8,9,6,7,4,5,2,1,3]=>[8,6,4,2,1,10,9,7,5,3]=>111101111 [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,9,8,1]=>00000011 [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000 [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[2,1,3,4,5,6,8,7,9]=>10000010 [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[2,3,4,5,6,8,7,9,1]=>00000101 [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,10,9,1]=>000000011 [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[4,2,1,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>10100000 [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[5,3,2,1,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>11010000 [[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]=>[6,4,3,2,1,5,7,8,9]=>[4,3,2,1,6,5,7,8,9]=>11101000 [[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[5,4,3,2,1,7,6,8,9]=>11110100 [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[6,5,4,3,2,1,8,7,9]=>11111010 [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[3,4,5,6,7,8,2,9,1]=>00000101 [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[2,3,4,5,6,7,8,1,9]=>00000010 [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>01000000 [[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>00010000 [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>00000100 [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>01100000 [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[5,2,3,4,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>00110000 [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[6,2,3,4,5,1,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>00011000 [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[7,2,3,4,5,6,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>00001100 [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>[2,3,4,5,6,8,7,1,9]=>00000110 [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>000000010 [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[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]=>[3,4,5,6,7,1,9,8,2]=>00001011 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,9,8,1]=>11111011 [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[6,5,4,3,2,7,8,9,1]=>11110001 [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,9,8]=>01111101 [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[8,6,5,4,3,2,1,9,7]=>11111101 [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[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 [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,1,2,4]=>[1,3,2,9,8,7,6,5,4]=>01011111 [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>[2,1,8,7,6,5,4,3,9]=>10111110 [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>011111110 [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[9,2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,9,8]=>00010001 [.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]=>[4,5,6,3,7,8,9,2,1]=>[4,5,6,3,7,8,9,2,1]=>00100011 [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]=>[3,4,5,6,2,7,8,9,10,1]=>[3,4,5,6,2,7,8,9,10,1]=>000100001 [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[4,5,2,1,3,6,7,8,9]=>[4,2,1,5,3,6,7,8,9]=>11010000 [[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[5,3,1,2,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>01010000 [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[6,2,3,4,5,7,8,9,10,1]=>[2,3,4,6,5,7,8,9,10,1]=>000100001 [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,10,9,1]=>111111011 [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[3,4,5,6,7,1,8,2,9]=>00001010 [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[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]=>[6,7,8,5,4,3,2,1,9]=>00111110 [[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9]=>[6,5,4,3,2,7,8,1,9]=>11110010 [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[7,8,9,6,5,4,3,2,1,10]=>001111110 [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[10,9,8,7,6,5,4,3,2,11,1]=>1111111101 [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[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]=>[1,2,3,4,5,7,6,9,8]=>00000101 [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>000000111 [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[1,2,3,4,6,5,9,8,7]=>00001011 [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111 [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,4,9,8,7,6]=>00010111 [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>000011111 [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,1,2,3,5]=>[1,2,4,3,9,8,7,6,5]=>00101111 [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>000111111 [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>10100000 [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>[10,9,11,8,7,6,5,4,3,2,1]=>1011111111 [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[9,8,10,7,6,5,4,3,1,2]=>[9,8,1,10,7,6,5,4,3,2]=>110111111 [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>[8,2,9,7,6,5,4,3,1]=>10111111 [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[10,11,9,8,7,6,5,4,3,2,1]=>0111111111 [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[7,8,6,5,4,3,2,9,1]=>01111101 [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[8,9,7,6,5,4,3,2,10,1]=>011111101 [.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]=>[7,6,8,5,4,3,2,9,1]=>[7,6,8,5,4,3,2,9,1]=>10111101 [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>01100000 [.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[5,4,6,7,8,9,3,2,1]=>10000111 [.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[6,5,7,8,9,4,3,2,1]=>10001111 [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]=>[6,5,7,8,9,10,4,3,2,1]=>[6,5,7,8,9,10,4,3,2,1]=>100001111 [.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]=>[5,4,6,7,8,3,9,2,1]=>[5,4,6,7,8,3,9,2,1]=>10001011 [.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]=>[5,4,6,7,8,9,10,3,2,1]=>[5,4,6,7,8,9,10,3,2,1]=>100000111 [.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]=>[6,5,7,8,9,10,11,4,3,2,1]=>[6,5,7,8,9,10,11,4,3,2,1]=>1000001111 [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[7,6,5,4,3,2,8,1,9]=>11111010 [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[6,5,4,3,2,7,1,8,9]=>[6,5,4,3,2,7,1,8,9]=>11110100 [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]=>[5,4,3,2,6,1,7,8,9]=>[5,4,3,2,6,1,7,8,9]=>11101000 [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]=>[4,3,2,5,1,6,7,8,9]=>[4,3,2,5,1,6,7,8,9]=>11010000 [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>01110000 [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[3,2,4,5,6,7,8,1,9]=>10000010 [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>[5,4,3,2,1,8,7,6,9]=>11110110 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[9,7,6,5,4,3,2,1,8,10]=>[7,6,5,4,3,2,1,9,8,10]=>111111010 [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[9,6,7,8,5,4,3,2,1]=>[6,7,9,8,5,4,3,2,1]=>00111111 [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[8,7,6,5,4,3,1,9,2]=>11111101 [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>[2,8,7,6,5,4,3,1,9]=>01111110 [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,1,9,8]=>00000101 [[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>10100000 [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,9,2,10,1]=>[3,4,5,6,7,8,9,2,10,1]=>000000101 [[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[9,3,4,5,6,7,2,1,8]=>[3,4,5,6,7,2,1,9,8]=>00001101 [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[4,5,6,7,8,9,10,2,3,1]=>[4,5,6,7,8,9,2,10,3,1]=>000001011 [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]=>[3,4,5,6,2,1,7,8,9]=>[3,4,5,6,2,1,7,8,9]=>00011000 [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>[2,3,4,5,6,9,8,7,1]=>00000111 [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,10,9,8,1]=>000000111 [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[3,4,5,6,7,8,2,1,9]=>00000110 [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[3,4,5,6,7,2,1,8,9]=>[3,4,5,6,7,2,1,8,9]=>00001100 [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[6,7,5,4,3,2,1,8,9]=>01111100 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[9,10,7,6,5,4,3,2,1,8]=>[9,7,6,5,4,3,2,1,10,8]=>111111101 [[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[9,8,2,3,4,5,6,1,7]=>[2,3,4,5,6,1,9,8,7]=>00001011 [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[3,4,5,2,1,6,7,8,9]=>[3,4,5,2,1,6,7,8,9]=>00110000 [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[7,6,8,9,5,4,3,2,1]=>10011111 [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[11,9,10,8,7,6,5,4,3,2,1]=>[9,11,10,8,7,6,5,4,3,2,1]=>0111111111 [.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[7,6,8,5,9,4,3,2,1]=>[7,6,8,5,9,4,3,2,1]=>10101111 [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]=>[8,7,9,10,6,5,4,3,2,1]=>[8,7,9,10,6,5,4,3,2,1]=>100111111
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
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
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.