Identifier
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=> [.,[.,.]]=>[2,1]=>1 [[.,.],.]=>[1,2]=>0 [.,[.,[.,.]]]=>[3,2,1]=>11 [.,[[.,.],.]]=>[2,3,1]=>01 [[.,.],[.,.]]=>[3,1,2]=>10 [[.,[.,.]],.]=>[2,1,3]=>10 [[[.,.],.],.]=>[1,2,3]=>00 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>111 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>011 [.,[[.,.],[.,.]]]=>[4,2,3,1]=>101 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>101 [.,[[[.,.],.],.]]=>[2,3,4,1]=>001 [[.,.],[.,[.,.]]]=>[4,3,1,2]=>110 [[.,.],[[.,.],.]]=>[3,4,1,2]=>010 [[.,[.,.]],[.,.]]=>[4,2,1,3]=>110 [[[.,.],.],[.,.]]=>[4,1,2,3]=>100 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>110 [[.,[[.,.],.]],.]=>[2,3,1,4]=>010 [[[.,.],[.,.]],.]=>[3,1,2,4]=>100 [[[.,[.,.]],.],.]=>[2,1,3,4]=>100 [[[[.,.],.],.],.]=>[1,2,3,4]=>000 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>1111 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0111 [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>1011 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>1011 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0011 [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>1101 [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>0101 [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>1101 [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>1001 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>1101 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0101 [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>1001 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>1001 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0001 [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>1110 [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>0110 [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>1010 [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>1010 [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>0010 [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>1110 [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>0110 [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>1100 [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>0100 [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1110 [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>1010 [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1100 [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>1100 [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>1000 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1110 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0110 [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>1010 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1010 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0010 [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>1100 [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>0100 [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>1100 [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>1000 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>1100 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0100 [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>1000 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1000 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0000 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>11111 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>01111 [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>10111 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>10111 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>00111 [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>11011 [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>01011 [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>11011 [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>10011 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>11011 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>01011 [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>10011 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>10011 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>00011 [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>11101 [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>01101 [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>10101 [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>10101 [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>00101 [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>11101 [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>01101 [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>11001 [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>01001 [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>11101 [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>10101 [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>11001 [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>11001 [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>10001 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>11101 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>01101 [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>10101 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>10101 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>00101 [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>11001 [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>01001 [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>11001 [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>10001 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>11001 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>01001 [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>10001 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>10001 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>00001 [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>11110 [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>01110 [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>10110 [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>10110 [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>00110 [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>11010 [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>01010 [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>11010 [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>10010 [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>11010 [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>01010 [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>10010 [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>10010 [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>00010 [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>11110 [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>01110 [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>10110 [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>10110 [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>00110 [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>11100 [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>01100 [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>10100 [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>10100 [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>00100 [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>11110 [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>01110 [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>11010 [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>01010 [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>11100 [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>01100 [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>11100 [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>01100 [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>11000 [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>01000 [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>11110 [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>10110 [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>11010 [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>11010 [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>10010 [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>11100 [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>10100 [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>11100 [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>11000 [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>11100 [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>10100 [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>11000 [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>11000 [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>10000 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>11110 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>01110 [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>10110 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>10110 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>00110 [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>11010 [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>01010 [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>11010 [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>10010 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>11010 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>01010 [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>10010 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>10010 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>00010 [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>11100 [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>01100 [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>10100 [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>10100 [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>00100 [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>11100 [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>01100 [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>11000 [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>01000 [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>11100 [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>10100 [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>11000 [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>11000 [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>10000 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>11100 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>01100 [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>10100 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>10100 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>00100 [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>11000 [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>01000 [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>11000 [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>10000 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>11000 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>01000 [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>10000 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>10000 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>00000 [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>111111 [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>011111 [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>101111 [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>101111 [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>001111 [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>110111 [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>010111 [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>110111 [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>100111 [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>110111 [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>010111 [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>100111 [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>100111 [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>000111 [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>111011 [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>011011 [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>101011 [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>101011 [.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>001011 [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>111011 [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>011011 [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>110011 [.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>010011 [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>111011 [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>101011 [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>110011 [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>110011 [.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>100011 [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>111011 [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>011011 [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>101011 [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>101011 [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>001011 [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>110011 [.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>010011 [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>110011 [.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>100011 [.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>110011 [.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>010011 [.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>100011 [.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>100011 [.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>000011 [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>111101 [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>011101 [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>101101 [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>101101 [.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>001101 [.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>110101 [.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>010101 [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>110101 [.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>100101 [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>110101 [.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>010101 [.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>100101 [.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>100101 [.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>000101 [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>111101 [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>011101 [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>101101 [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>101101 [.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>001101 [.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>111001 [.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>011001 [.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>101001 [.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>101001 [.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>001001 [.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>111101 [.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>011101 [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>110101 [.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>010101 [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>111001 [.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>011001 [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>111001 [.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>011001 [.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>110001 [.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>010001 [.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>111101 [.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>101101 [.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>110101 [.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>110101 [.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>100101 [.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>111001 [.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>101001 [.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>111001 [.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>110001 [.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>111001 [.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>101001 [.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>110001 [.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>110001 [.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>100001 [.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>111101 [.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>011101 [.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>101101 [.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>101101 [.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>001101 [.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>110101 [.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>010101 [.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>110101 [.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>100101 [.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>110101 [.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>010101 [.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>100101 [.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>100101 [.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>000101 [.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>111001 [.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>011001 [.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>101001 [.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>101001 [.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>001001 [.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>111001 [.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>011001 [.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>110001 [.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>010001 [.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>111001 [.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>101001 [.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>110001 [.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>110001 [.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>100001 [.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>111001 [.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>011001 [.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>101001 [.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>101001 [.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>001001 [.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>110001 [.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>010001 [.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>110001 [.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>100001 [.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>110001 [.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>010001 [.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>100001 [.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>100001 [.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>000001 [[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>111110 [[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>011110 [[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>101110 [[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>101110 [[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>001110 [[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>110110 [[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>010110 [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>110110 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>100110 [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>110110 [[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>010110 [[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>100110 [[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>100110 [[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>000110 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>111010 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>011010 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>101010 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>101010 [[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>001010 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>111010 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>011010 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>110010 [[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>010010 [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>111010 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>101010 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>110010 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>110010 [[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>100010 [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>111010 [[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>011010 [[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>101010 [[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>101010 [[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>001010 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>110010 [[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>010010 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>110010 [[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>100010 [[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>110010 [[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>010010 [[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>100010 [[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>100010 [[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>000010 [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>111110 [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>011110 [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>101110 [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>101110 [[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>001110 [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>110110 [[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>010110 [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>110110 [[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>100110 [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>110110 [[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>010110 [[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>100110 [[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>100110 [[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>000110 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>111100 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>011100 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>101100 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>101100 [[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>001100 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>110100 [[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>010100 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>110100 [[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>100100 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>110100 [[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>010100 [[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>100100 [[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>100100 [[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>000100 [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>111110 [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>011110 [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>101110 [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>101110 [[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>001110 [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>111010 [[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>011010 [[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>101010 [[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>101010 [[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>001010 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>111100 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>011100 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>101100 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>101100 [[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>001100 [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>111100 [[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>011100 [[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>101100 [[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>101100 [[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>001100 [[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>111000 [[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>011000 [[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>101000 [[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>101000 [[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>001000 [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>111110 [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>011110 [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>110110 [[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>010110 [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>111010 [[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>011010 [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>111010 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[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>111000 [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>101000 [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>111000 [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>110000 [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>111000 [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>101000 [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>110000 [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>110000 [[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>100000 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>111100 [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>011100 [[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>101100 [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>101100 [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>001100 [[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>110100 [[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>010100 [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>110100 [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>100100 [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>110100 [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>010100 [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>100100 [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>100100 [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>000100 [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>111000 [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>011000 [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>101000 [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>101000 [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>001000 [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>111000 [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>011000 [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>110000 [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>010000 [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>111000 [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>101000 [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>110000 [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>110000 [[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>100000 [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>111000 [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>011000 [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>101000 [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>101000 [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>001000 [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>110000 [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>010000 [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>110000 [[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>100000 [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>110000 [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>010000 [[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>100000 [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>100000 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>000000 [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>1111111 [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>0111111 [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>1011111 [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>1011111 [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>0011111 [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>1101111 [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>0101111 [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>1101111 [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>1001111 [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>1101111 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>0101111 [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>1001111 [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>1001111 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>0001111 [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>1110111 [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>0110111 [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>1010111 [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>1010111 [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>1110111 [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>1100111 [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>1110111 [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>1010111 [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>1100111 [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>1100111 [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>1000111 [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>1110111 [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>0110111 [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>1010111 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>1010111 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>0010111 [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>1100111 [.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>0100111 [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>1100111 [.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>1000111 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>1100111 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>0100111 [.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>1000111 [.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>1000111 [.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>0000111 [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>1111011 [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>0111011 [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>1011011 [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>1011011 [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>1101011 [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>0101011 [.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>1001011 [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>1101011 [.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>0101011 [.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>1001011 [.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>0001011 [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>1111011 [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>0111011 [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>1011011 [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>1011011 [.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>0011011 [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>1110011 [.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>0110011 [.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>1010011 [.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>1010011 [.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>0010011 [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>1111011 [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>0111011 [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>1101011 [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>1110011 [.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>0110011 [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>1110011 [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>1100011 [.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>0100011 [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>1111011 [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>1101011 [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>1110011 [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>1110011 [.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>1100011 [.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>1100011 [.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>1000011 [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>1111011 [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>0111011 [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>1011011 [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>1011011 [.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>0011011 [.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>0101011 [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>1101011 [.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>1001011 [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>1101011 [.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>1001011 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>1001011 [.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>0001011 [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>1110011 [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>1110011 [.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>1100011 [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>1110011 [.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>1100011 [.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>1000011 [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>1110011 [.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>0010011 [.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>1100011 [.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>1000011 [.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>1100011 [.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>1000011 [.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>1000011 [.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>0000011 [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>1111101 [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>0111101 [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>1011101 [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>1011101 [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>1101101 [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>1101101 [.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>1001101 [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>1101101 [.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>0101101 [.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>1001101 [.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>0001101 [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>1110101 [.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>1010101 [.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>1010101 [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>1110101 [.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>1100101 [.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>0100101 [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>1110101 [.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>1010101 [.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>1100101 [.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>1000101 [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>1110101 [.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>1010101 [.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>1010101 [.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>0100101 [.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>0000101 [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>1111101 [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>0111101 [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>1011101 [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>1011101 [.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>0011101 [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>1101101 [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>1101101 [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>1001101 [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>1101101 [.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>0101101 [.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>0001101 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>1111001 [.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>1011001 [.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>1011001 [.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>0011001 [.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>1101001 [.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>0101001 [.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>1101001 [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>1001001 [.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>1101001 [.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>0101001 [.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>1001001 [.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>0001001 [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>1111101 [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>0111101 [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>1011101 [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>1011101 [.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>0011101 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>1110101 [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>0110101 [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>1010101 [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>1010101 [.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>0010101 [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>1111001 [.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>1011001 [.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>1011001 [.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>0011001 [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>1111001 [.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>0111001 [.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>1011001 [.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>0011001 [.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>1110001 [.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>0110001 [.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>1010001 [.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>1010001 [.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>0010001 [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>1111101 [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>0111101 [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>1110101 [.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>0110101 [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>1110101 [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>1111001 [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>1111001 [.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>0111001 [.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>0101001 [.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>0110001 [.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>0110001 [.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>1100001 [.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>0100001 [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>1111101 [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[8,5,6,4,3,2,7,1]=>1011101 [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>1101101 [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>1101101 [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>1110101 [.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>1010101 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>1110101 [.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>1100101 [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>1110101 [.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>1010101 [.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>1100101 [.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>1000101 [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>1111001 [.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>1011001 [.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>1101001 [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>1111001 [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>1111001 [.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>1110001 [.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>1100001 [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>1111001 [.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>1011001 [.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>1101001 [.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>1001001 [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>1110001 [.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>1010001 [.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>1100001 [.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>1110001 [.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>1010001 [.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>1100001 [.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>1100001 [.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>1000001 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>1111101 [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>0111101 [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>1011101 [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>1011101 [.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>0011101 [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>1101101 [.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[6,7,4,5,3,2,8,1]=>0101101 [.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>1001101 [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>1101101 [.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>1001101 [.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>0001101 [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>1110101 [.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>1010101 [.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>1010101 [.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>0010101 [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>1110101 [.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>1100101 [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>1110101 [.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>1010101 [.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>1100101 [.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>1000101 [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>1110101 [.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>1010101 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>1010101 [.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>0010101 [.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>1100101 [.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>0100101 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>1100101 [.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>1000101 [.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>1100101 [.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>0100101 [.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>1000101 [.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>0000101 [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>1111001 [.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>0111001 [.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>1011001 [.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>1011001 [.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>0011001 [.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>1101001 [.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>0101001 [.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>1101001 [.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>1001001 [.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>1101001 [.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>0101001 [.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>1001001 [.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>1001001 [.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>0001001 [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>1111001 [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>0111001 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>1011001 [.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>1110001 [.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>1010001 [.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>0010001 [.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>0111001 [.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>1110001 [.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>1110001 [.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>0110001 [.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>1100001 [.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>0100001 [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>1111001 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>1101001 [.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>1110001 [.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>1010001 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>1110001 [.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>1100001 [.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>1110001 [.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>1100001 [.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>1100001 [.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>1000001 [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>1111001 [.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>1011001 [.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>0011001 [.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>1101001 [.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>1001001 [.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>1101001 [.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>1001001 [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>0001001 [.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>1110001 [.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>0110001 [.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>1010001 [.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>1010001 [.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>0010001 [.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>1110001 [.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>1100001 [.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>1000001 [.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>1110001 [.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>0110001 [.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>1010001 [.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>1010001 [.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>0010001 [.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>1100001 [.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>0100001 [.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>1100001 [.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>1000001 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>1100001 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>0100001 [.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>1000001 [.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>1000001 [.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>0000001 [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>1111110 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>0111110 [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>1011110 [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>1011110 [[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>0011110 [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>1101110 [[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>0101110 [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>1101110 [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>1101110 [[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>0101110 [[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>1001110 [[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>1001110 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>0001110 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>1110110 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>0110110 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>1010110 [[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>0010110 [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>1110110 [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>1010110 [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>1100110 [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>1100110 [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>1110110 [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>1010110 [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>1010110 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>1100110 [[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>0100110 [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>1100110 [[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>0100110 [[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>1000110 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>0000110 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>1111010 [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>0111010 [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>1011010 [[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>0011010 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>1101010 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>0101010 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>1101010 [[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>1001010 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>1101010 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>0101010 [[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>1001010 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>1001010 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>0001010 [[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>0011010 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>1110010 [[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>1010010 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>0111010 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>1101010 [[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>0101010 [[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>0110010 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>1110010 [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>0110010 [[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>1100010 [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>0100010 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>1111010 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>1110010 [[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>1100010 [[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>1100010 [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>1000010 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>1111010 [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,3,8,1,2]=>1011010 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>1011010 [[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>0011010 [[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>0101010 [[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>0101010 [[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>1001010 [[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>0001010 [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>1110010 [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>1010010 [[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>0010010 [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>1110010 [[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>1100010 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>1110010 [[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>1100010 [[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>1000010 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>1110010 [[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>0110010 [[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>1010010 [[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>0010010 [[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>1100010 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>0100010 [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>1100010 [[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>1000010 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>1100010 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>0100010 [[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>1000010 [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>1000010 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>0000010 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>1111110 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>0111110 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>1011110 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>1011110 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>0011110 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>1101110 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>0101110 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>1101110 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>1101110 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>0101110 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>1001110 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>1001110 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>0001110 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>1110110 [[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>1010110 [[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>1010110 [[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>1100110 [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>1110110 [[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>1100110 [[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>1000110 [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>1110110 [[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>0110110 [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>1010110 [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>1010110 [[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>0010110 [[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>1100110 [[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>1000110 [[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>1000110 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>0000110 [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>1111100 [[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>0111100 [[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>1011100 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>0011100 [[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>0101100 [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>1101100 [[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>1001100 [[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>1101100 [[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>0101100 [[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>1001100 [[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>1001100 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>0001100 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>1110100 [[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>1010100 [[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>0010100 [[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>1110100 [[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>0110100 [[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>1100100 [[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>0100100 [[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>1010100 [[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>1100100 [[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>1100100 [[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>1000100 [[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>1110100 [[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>0110100 [[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>1010100 [[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>1010100 [[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>0010100 [[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>1100100 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>0100100 [[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>1100100 [[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>1000100 [[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>1100100 [[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>0100100 [[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>1000100 [[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>1000100 [[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>0000100 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>1111110 [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>0111110 [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>1011110 [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>1011110 [[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>0011110 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>1101110 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>0101110 [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>1101110 [[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>1001110 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1101110 [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>0101110 [[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>1001110 [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>1001110 [[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>0001110 [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>1111010 [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>0111010 [[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>1011010 [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>1011010 [[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>0011010 [[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>1101010 [[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>0101010 [[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>1101010 [[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>1001010 [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>1101010 [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>0101010 [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1001010 [[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>1001010 [[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>0001010 [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>1111100 [[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>0111100 [[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>1011100 [[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>1011100 [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>1101100 [[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>0101100 [[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>1101100 [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>0101100 [[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>1001100 [[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>1001100 [[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>0001100 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>1111100 [[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>0111100 [[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>1011100 [[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>0011100 [[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>1101100 [[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>0101100 [[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>1101100 [[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>1001100 [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>1101100 [[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>0101100 [[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>1001100 [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1001100 [[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>0001100 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>1111000 [[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>0111000 [[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>1011000 [[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>1011000 [[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>0011000 [[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>1101000 [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>0101000 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>1101000 [[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>1001000 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>1101000 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>0101000 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>1001000 [[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>1001000 [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>0001000 [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>1111110 [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>0111110 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>1011110 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>1011110 [[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>0011110 [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>1110110 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>0110110 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>0010110 [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>1111010 [[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>1011010 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>1011010 [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>0011010 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>1111010 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>1011010 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>0011010 [[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>1110010 [[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[8,6,7,2,3,4,1,5]=>1010010 [[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>1010010 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>0010010 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>1111100 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>0011100 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>1110100 [[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>0110100 [[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>1010100 [[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>0010100 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>1111100 [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>0111100 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>1011100 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>0011100 [[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>1111000 [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>0111000 [[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>1011000 [[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>0011000 [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>1111100 [[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>0111100 [[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>1011100 [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>1011100 [[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>0011100 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>1110100 [[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>0110100 [[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>1010100 [[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>1010100 [[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>0010100 [[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>1111000 [[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>0111000 [[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>1011000 [[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>1011000 [[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>0011000 [[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>1111000 [[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>0111000 [[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>1011000 [[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>0011000 [[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>1110000 [[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>0110000 [[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>1010000 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>1010000 [[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>0010000 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>1111110 [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>0111110 [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>1101110 [[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6]=>0101110 [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>1110110 [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>1110110 [[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>1100110 [[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>0100110 [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>1101010 [[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>0101010 [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>1111010 [[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>0110010 [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>1111010 [[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>0111010 [[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>1101010 [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>0101010 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>1100010 [[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>0100010 [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>1111100 [[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>0111100 [[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>1110100 [[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>0110100 [[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>1100100 [[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>0100100 [[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>0111100 [[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>1111000 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>0111000 [[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>1101000 [[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>0101000 [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>1111100 [[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>0111100 [[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>1110100 [[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>1111000 [[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>0111000 [[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>1111000 [[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>0111000 [[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>1110000 [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>0110000 [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>1111100 [[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>0111100 [[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>1101100 [[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>0101100 [[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>0110100 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>1110100 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>0110100 [[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>1100100 [[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>0100100 [[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>0111000 [[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>1101000 [[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>0101000 [[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>1111000 [[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>0111000 [[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>1110000 [[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>0110000 [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>1111000 [[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>0111000 [[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>1101000 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>0101000 [[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>0110000 [[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>1110000 [[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>0110000 [[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>1100000 [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>0100000 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1111110 [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>1011110 [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>1101110 [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>1101110 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>1001110 [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>1110110 [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>1010110 [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>1110110 [[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>1010110 [[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>1100110 [[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>1000110 [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>1111010 [[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>1011010 [[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>1101010 [[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>1001010 [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>1111010 [[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>1110010 [[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>1010010 [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>1111010 [[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>1110010 [[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>1110010 [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>1111010 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>1101010 [[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[8,5,4,2,3,6,1,7]=>1110010 [[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>1010010 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>1110010 [[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>1100010 [[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>1010010 [[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>1100010 [[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>1000010 [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1111100 [[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>1101100 [[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>1110100 [[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1010100 [[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>1100100 [[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>1110100 [[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>1010100 [[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>1100100 [[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>1100100 [[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>1000100 [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1111100 [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>1011100 [[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>1101100 [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>1001100 [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>1111000 [[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>1011000 [[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>1101000 [[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>1001000 [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>1111100 [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>1011100 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>1110100 [[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>1010100 [[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>1011000 [[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>1111000 [[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>1011000 [[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>1110000 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>1010000 [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1111100 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>1101100 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>1110100 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>1110100 [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>1100100 [[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>1111000 [[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>1101000 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1111000 [[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>1110000 [[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>1100000 [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>1111100 [[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>1011100 [[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>1101100 [[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>1001100 [[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>1010100 [[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>1100100 [[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>1100100 [[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>1000100 [[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>1101000 [[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>1001000 [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>1111000 [[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>1110000 [[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>1010000 [[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>1111000 [[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>1110000 [[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>1110000 [[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>1100000 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>1111000 [[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>1011000 [[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>1101000 [[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1001000 [[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>1010000 [[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>1110000 [[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1100000 [[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1110000 [[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>1010000 [[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1100000 [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1100000 [[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1000000 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>1111110 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0111110 [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>1011110 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>1011110 [[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0011110 [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>1101110 [[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>0101110 [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>1101110 [[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>1001110 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>1101110 [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>0101110 [[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>1001110 [[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>0001110 [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>1110110 [[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>0110110 [[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>1010110 [[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>1010110 [[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>0010110 [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>1110110 [[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>0110110 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>1100110 [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>1110110 [[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>1010110 [[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>1000110 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>1110110 [[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>0110110 [[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>1010110 [[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>1100110 [[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>0000110 [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>1111010 [[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>0111010 [[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>1011010 [[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>0011010 [[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>1101010 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[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>001111111 [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>01011111 [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>000111111 [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>000011111 [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>000001111 [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>000000111 [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>00000101 [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>000000011 [[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>00000010 [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>000000001 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>000000000 [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>10111111 [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>11011111 [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>11101111 [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>11110111 [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>11111011 [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>11111101 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>11111110 [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>101111111 [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>10011111 [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>110111111 [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>11001111 [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>111011111 [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>11100111 [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>111101111 [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>11110011 [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>111110111 [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>11111001 [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>111111011 [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>11111100 [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>111111101 [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>111111110 [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>010101010 [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[9,10,6,7,4,5,2,3,1,8]=>010101010 [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>010101010 [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010 [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>111110000 [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>11111100000 [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>10000000 [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>100000000 [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>11000000 [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>10000001 [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000 [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>110000000 [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>11000000 [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>10100000 [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>10000001 [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>01000001 [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>100000001 [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001 [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>01000000 [[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>00100000 [[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>00010000 [[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>00001000 [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>00000100 [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>11000000 [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>010000000 [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>10100000 [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>001000000 [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[7,6,8,9,1,2,3,4,5]=>10010000 [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>000100000 [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[6,5,7,8,9,1,2,3,4]=>10001000 [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>000010000 [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[5,4,6,7,8,9,1,2,3]=>10000100 [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>000001000 [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>10000010 [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>000000100 [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>000000010 [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>11111110 [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>01111110 [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>01111110 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>111111110 [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110 [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>011111110 [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>10111110 [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[8,6,7,5,4,3,2,1,9]=>10111110 [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>10111110 [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>10111110 [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>011111110 [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110 [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>101010101 [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[9,8,10,6,7,4,5,2,3,1]=>101010101 [[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[6,4,5,7,3,8,2,9,1,10]=>100101010 [.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[8,9,6,7,4,5,2,3,10,1]=>010101001 [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>11111110 [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>11111110 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>11111110 [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>11111110 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>11111110 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>11111110 [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>11111100 [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>111111110 [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>11111010 [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>111111110 [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,3,4,2,1,5]=>11110110 [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>111111110 [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[9,8,7,4,5,3,2,1,6]=>11101110 [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>111111110 [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[9,8,5,6,4,3,2,1,7]=>11011110 [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>111111110 [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>10111110 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>111111110 [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>111111110 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>11111100 [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>11111000 [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>11110000 [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>11100000 [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>11000000 [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>10000000 [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>111111100 [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>111111000 [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>111110000 [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[6,5,4,3,1,2,7,8,9]=>11110000 [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>111100000 [[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[5,4,3,1,2,6,7,8,9]=>11100000 [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>111000000 [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>11000000 [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>110000000 [[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>10000000 [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>100000000 [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>11101111 [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>11110111 [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,3,4,2,1]=>11111011 [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>11111101 [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>101111111 [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>111011111 [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>111101111 [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>111111101 [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>101010101 [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[10,8,9,6,7,4,5,2,1,3]=>101010110 [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>10000001 [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000 [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>11000000 [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[8,9,2,1,3,4,5,6,7]=>01100000 [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>10000001 [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>01000001 [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>100000001 [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>11111100 [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>00000101 [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>00000010 [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>01000000 [[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>00010000 [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>00000100 [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>10100000 [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[5,2,3,4,1,6,7,8,9]=>10010000 [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[6,2,3,4,5,1,7,8,9]=>10001000 [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[7,2,3,4,5,6,1,8,9]=>10000100 [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>10000010 [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>000000010 [[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>10000000 [[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>10000000 [[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>10000000 [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>10000000 [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>10000000 [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>100000000 [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>100000000 [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>100000000 [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>100000000 [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>100000000 [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>100000000 [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>100000000 [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>10000010 [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>11111101 [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>11110001 [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>11111100 [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>01111110 [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000 [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>111111100 [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,1,2,4]=>11111100 [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>11111100 [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>111111100 [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,2,3,1]=>10111101 [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[7,8,2,3,4,5,6,9,1]=>01000001 [[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[3,4,5,1,2,6,7,8,9]=>00100000 [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[9,2,3,4,5,1,6,7,8]=>10001000 [.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]=>[4,5,6,3,7,8,9,2,1]=>00100011 [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]=>[3,4,5,6,2,7,8,9,10,1]=>000100001 [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[4,5,2,1,3,6,7,8,9]=>01100000 [[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[5,3,1,2,4,6,7,8,9]=>11000000 [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[6,2,3,4,5,7,8,9,10,1]=>100000001 [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>111111101 [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,3,1,2]=>00000110 [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>00000110 [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>00000100 [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>01111110 [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>110000000 [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>00111110 [[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9]=>11110010 [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>001111110 [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>1111111101 [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>11100000 [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>11110000 [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>11111000 [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>11000000 [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>111000000 [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>11100000 [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>111100000 [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[9,8,7,5,1,2,3,4,6]=>11110000 [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>111110000 [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,1,2,3,5]=>11111000 [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>111111000 [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>10100000 [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>1011111111 [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[9,8,10,7,6,5,4,3,1,2]=>101111110 [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>01111101 [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>0111111111 [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>01111101 [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>011111101 [.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]=>[7,6,8,5,4,3,2,9,1]=>10111101 [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>01100000 [.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>10000111 [.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>10001111 [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]=>[6,5,7,8,9,10,4,3,2,1]=>100001111 [.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]=>[5,4,6,7,8,3,9,2,1]=>10001011 [.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]=>[5,4,6,7,8,9,10,3,2,1]=>100000111 [.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]]=>[6,5,7,8,9,10,11,4,3,2,1]=>1000001111 [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>11111010 [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[6,5,4,3,2,7,1,8,9]=>11110100 [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]=>[5,4,3,2,6,1,7,8,9]=>11101000 [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]=>[4,3,2,5,1,6,7,8,9]=>11010000 [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]=>[8,9,7,6,4,3,2,1,5]=>01111110 [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>01110000 [[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,4,3,2,1,5]=>000011110 [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>10000010 [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>11111100 [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[9,7,6,5,4,3,2,1,8,10]=>111111100 [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[9,6,7,8,5,4,3,2,1]=>10011111 [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>11111010 [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>11111010 [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>10000010 [[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>01000000 [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,9,2,10,1]=>000000101 [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[4,5,6,7,8,3,9,1,2]=>00001010 [[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[9,3,4,5,6,7,2,1,8]=>10000110 [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[4,5,6,7,8,9,10,2,3,1]=>000000101 [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]=>[3,4,5,6,2,1,7,8,9]=>00011000 [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>0100000000 [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,1,2,3,9]=>11111000 [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>11000001 [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>110000001 [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>00000110 [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>110000000 [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[9,2,3,4,5,6,1,7,8]=>10000100 [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>111111100 [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[3,4,5,6,7,2,1,8,9]=>00001100 [[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]=>[5,6,7,4,8,9,1,2,3]=>00100100 [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>01111100 [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[9,10,7,6,5,4,3,2,1,8]=>011111110 [[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[9,8,2,3,4,5,6,1,7]=>11000010 [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[3,4,5,2,1,6,7,8,9]=>00110000 [.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[9,3,4,5,6,7,8,2,1]=>10000011 [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>10011111 [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[11,9,10,8,7,6,5,4,3,2,1]=>1011111111 [.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[7,6,8,5,9,4,3,2,1]=>10101111 [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]=>[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
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.