Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00069: Permutations —complement⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[1,2]=>0
[[.,.],.]=>[1,2]=>[2,1]=>1
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>00
[.,[[.,.],.]]=>[2,3,1]=>[2,1,3]=>10
[[.,.],[.,.]]=>[3,1,2]=>[1,3,2]=>01
[[.,[.,.]],.]=>[2,1,3]=>[2,3,1]=>01
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>11
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>000
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,3,4]=>100
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>010
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[2,3,1,4]=>010
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,2,1,4]=>110
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,2,4,3]=>001
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>101
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[1,3,4,2]=>001
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,4,3,2]=>011
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,4,1]=>001
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,4,1]=>011
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,4,3,1]=>011
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[3,4,2,1]=>101
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>111
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>0000
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,3,4,5]=>1000
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,3,2,4,5]=>0100
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,3,1,4,5]=>0100
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,2,1,4,5]=>1100
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,2,4,3,5]=>0010
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,1,4,3,5]=>1010
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,3,4,2,5]=>0010
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>0110
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[2,3,4,1,5]=>0010
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,2,4,1,5]=>0110
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[2,4,3,1,5]=>0110
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,4,2,1,5]=>1010
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,3,2,1,5]=>1110
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,2,3,5,4]=>0001
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,3,2,5,4]=>0101
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,3,1,5,4]=>0101
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2,1,5,4]=>1101
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[1,2,4,5,3]=>0001
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,1,4,5,3]=>1001
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,1,5,4,3]=>1011
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[1,3,4,5,2]=>0001
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[1,4,3,5,2]=>0011
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,3,5,4,2]=>0011
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[1,4,5,3,2]=>0101
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,5,4,3,2]=>0111
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,5,1]=>0001
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,2,4,5,1]=>0101
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[2,4,3,5,1]=>0011
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,4,2,5,1]=>0011
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,3,2,5,1]=>0111
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[2,3,5,4,1]=>0011
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,2,5,4,1]=>0111
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,5,3,1]=>0101
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,5,4,3,1]=>0111
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,4,5,2,1]=>1001
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[4,3,5,2,1]=>1011
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,5,4,2,1]=>1011
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[4,5,3,2,1]=>1101
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>1111
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>10000
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>01000
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>01000
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>11000
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>10100
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>00100
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>01100
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>00100
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>01100
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>01100
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>10100
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>11100
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>00010
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>10010
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>01010
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>11010
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>00010
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>10010
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>00110
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>10110
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>00010
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>00110
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>00110
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>01010
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>00010
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>01010
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>00110
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>00110
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>01110
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>00110
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>01110
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>01010
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>01110
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>10010
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>10110
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>10110
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>11010
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>11110
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>00001
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>01001
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>01001
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>11001
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>00101
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>00101
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>01101
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>00101
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>01101
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>01101
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>10101
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>11101
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>00001
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>10001
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>01001
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>01001
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>11001
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>00011
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>10011
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>01011
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>01011
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>00001
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>10001
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>00011
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>10011
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>00011
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>10011
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>00101
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>10101
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>00111
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>10111
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>00001
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>00101
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>00011
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>00011
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>00111
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>00011
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>00111
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>00101
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>00111
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>01001
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>01011
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>01011
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>01101
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>01111
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>00001
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>01001
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>00101
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>00101
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>01101
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>00011
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>01011
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>00011
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>00111
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>00011
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>00111
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>00111
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>01011
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>01111
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>00011
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>01011
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>00111
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>00111
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>01111
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>00101
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>01101
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>00111
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>01111
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>01001
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>01011
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>01011
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>01101
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>01111
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>10001
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>10101
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>10011
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>10011
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>10111
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>10011
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>10111
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>10101
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>10111
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>11001
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>11011
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>11011
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>11101
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>100000
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>010000
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>010000
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>110000
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>001000
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>101000
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>001000
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>011000
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>001000
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>011000
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>011000
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>101000
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>111000
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>000100
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>100100
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>010100
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>010100
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>110100
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>000100
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>100100
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>101100
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>000100
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>001100
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>001100
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>010100
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>011100
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>000100
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>010100
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>001100
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>001100
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>011100
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>001100
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>011100
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>010100
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>011100
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>100100
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>101100
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>101100
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>110100
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>111100
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>000010
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>100010
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>010010
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>110010
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>001010
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>101010
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>001010
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>011010
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>001010
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>011010
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>011010
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>101010
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>111010
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>000010
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>100010
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>010010
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>010010
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>110010
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>000110
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>100110
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>010110
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>010110
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>110110
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>000010
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>100010
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>000110
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>100110
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>000110
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>100110
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>001010
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>101010
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>001110
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>101110
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>000010
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>001010
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>000110
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>000110
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>001110
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>000110
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>001110
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>001010
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>001110
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>010010
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>010110
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>010110
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>011010
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>000010
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>010010
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>001010
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>001010
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>011010
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>000110
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>010110
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>000110
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>001110
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>000110
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>001110
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>001110
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>010110
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>011110
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>000110
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>010110
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>001110
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>001110
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>011110
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>001010
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>011010
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>001110
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>011110
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>010010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>010110
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>010110
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>011010
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>011110
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>100010
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>101010
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>100110
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>100110
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>101110
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>100110
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>101110
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>101010
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>101110
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>110010
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>110110
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>110110
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>111010
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>111110
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>000001
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>010001
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>010001
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>110001
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>001001
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>101001
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>001001
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>011001
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>001001
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>011001
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>011001
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>101001
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>111001
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>000101
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>100101
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>010101
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>010101
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>110101
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>000101
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>100101
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>001101
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>000101
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>001101
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>001101
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>010101
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>011101
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>000101
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>010101
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>001101
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>001101
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>011101
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>001101
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>011101
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>010101
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>011101
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>100101
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>101101
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>101101
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>110101
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>111101
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>000001
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>100001
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>010001
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>010001
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>110001
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>001001
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>101001
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>001001
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>011001
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>001001
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>011001
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>011001
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>101001
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>111001
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>000011
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>100011
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>010011
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>010011
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>001011
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>101011
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>001011
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>011011
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>001011
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>011011
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>011011
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>101011
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>111011
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>000001
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>100001
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>010001
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>010001
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>110001
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>000011
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>100011
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>010011
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>010011
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>110011
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>000011
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>100011
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>010011
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>010011
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>110011
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>000101
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>100101
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>010101
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>010101
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>110101
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>100111
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>010111
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>010111
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>110111
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>000001
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>100001
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>000101
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>100101
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>000011
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>100011
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>000011
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>100011
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>000111
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>100111
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>000011
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>100011
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>000111
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>100111
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>000101
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>100101
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>000111
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>100111
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>001001
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>101001
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>001011
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>101011
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>001011
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>101011
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>001101
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>101101
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>001111
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>101111
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>000001
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>001001
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>000101
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>000101
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>001101
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>000011
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>001011
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>000011
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>000111
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>000011
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>000111
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>000111
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>001011
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>001111
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>000011
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>001011
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>000111
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>000111
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>001111
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>000101
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>001101
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>000111
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>001111
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>001001
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>001011
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>001011
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>001101
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>001111
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>010001
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>010101
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>010011
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>010011
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>010111
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>010011
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>010111
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>010101
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>010111
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>011001
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>011011
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>011011
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>011101
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>011111
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>000001
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>010001
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>001001
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>001001
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>011001
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>000101
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>010101
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>000101
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>001101
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>000101
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>001101
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>001101
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>010101
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>011101
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>000011
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>010011
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>001011
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>001011
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>011011
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>000011
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>010011
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>000111
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>010111
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>000011
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>000111
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>000111
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>001011
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>001111
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>000011
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>001011
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>000111
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>000111
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>001111
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>000111
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>001111
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>001011
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>001111
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>010011
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>010111
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>010111
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>011011
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>011111
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>000011
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>010011
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>001011
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>001011
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>011011
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>000111
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>010111
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>000111
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>001111
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>000111
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>001111
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>001111
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>010111
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>011111
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>000101
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>010101
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>001101
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>001101
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>011101
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>000111
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>010111
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>001111
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>001111
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>011111
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>001001
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>011001
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>001011
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>011011
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>001011
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>011011
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>001101
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>011101
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>001111
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>011111
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>010001
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>010101
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>010011
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>010011
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>010111
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>010011
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>010111
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>010101
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>010111
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>011001
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>011011
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>011011
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>011101
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>011111
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>100001
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>101001
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>100101
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>100101
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>101101
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>100011
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>101011
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>100011
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>100111
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>100011
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>100111
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>100111
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>101011
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>101111
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>100011
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>101011
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>100111
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>100111
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>101111
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>100101
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>101101
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>100111
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>101111
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>101001
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>101011
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>101011
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>101101
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>101111
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>110001
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>110101
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>110011
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>110011
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>110111
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>110011
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>110111
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>110101
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>110111
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>111001
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>111011
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>111011
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>111101
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8]=>1000000
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,3,2,4,5,6,7,8]=>0100000
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,3,1,4,5,6,7,8]=>0100000
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[3,2,1,4,5,6,7,8]=>1100000
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,4,3,5,6,7,8]=>0010000
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,1,4,3,5,6,7,8]=>1010000
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,3,4,2,5,6,7,8]=>0010000
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,4,3,2,5,6,7,8]=>0110000
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,3,4,1,5,6,7,8]=>0010000
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[3,2,4,1,5,6,7,8]=>0110000
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[2,4,3,1,5,6,7,8]=>0110000
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[3,4,2,1,5,6,7,8]=>1010000
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[4,3,2,1,5,6,7,8]=>1110000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[2,1,3,5,4,6,7,8]=>1001000
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,3,2,5,4,6,7,8]=>0101000
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[2,3,1,5,4,6,7,8]=>0101000
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[3,2,1,5,4,6,7,8]=>1101000
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[2,1,4,5,3,6,7,8]=>1001000
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[1,2,5,4,3,6,7,8]=>0011000
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,1,5,4,3,6,7,8]=>1011000
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,3,4,5,2,6,7,8]=>0001000
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,3,5,4,2,6,7,8]=>0011000
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,4,5,3,2,6,7,8]=>0101000
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,5,4,3,2,6,7,8]=>0111000
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[2,3,4,5,1,6,7,8]=>0001000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[3,2,4,5,1,6,7,8]=>0101000
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[2,4,3,5,1,6,7,8]=>0011000
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[3,4,2,5,1,6,7,8]=>0011000
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[4,3,2,5,1,6,7,8]=>0111000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[2,3,5,4,1,6,7,8]=>0011000
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[3,2,5,4,1,6,7,8]=>0111000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[2,4,5,3,1,6,7,8]=>0101000
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[2,5,4,3,1,6,7,8]=>0111000
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[3,4,5,2,1,6,7,8]=>1001000
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[4,3,5,2,1,6,7,8]=>1011000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[3,5,4,2,1,6,7,8]=>1011000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[4,5,3,2,1,6,7,8]=>1101000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[5,4,3,2,1,6,7,8]=>1111000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,3,4,6,5,7,8]=>0000100
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[2,1,3,4,6,5,7,8]=>1000100
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,3,2,4,6,5,7,8]=>0100100
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,1,4,3,6,5,7,8]=>1010100
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[2,3,4,1,6,5,7,8]=>0010100
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[3,2,4,1,6,5,7,8]=>0110100
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[2,4,3,1,6,5,7,8]=>0110100
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[4,3,2,1,6,5,7,8]=>1110100
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,3,5,6,4,7,8]=>0000100
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,3,2,5,6,4,7,8]=>0100100
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[2,3,1,5,6,4,7,8]=>0100100
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[3,2,1,5,6,4,7,8]=>1100100
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,2,3,6,5,4,7,8]=>0001100
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[1,3,2,6,5,4,7,8]=>0101100
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[2,3,1,6,5,4,7,8]=>0101100
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[3,2,1,6,5,4,7,8]=>1101100
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,4,5,6,3,7,8]=>0000100
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[1,2,4,6,5,3,7,8]=>0001100
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[2,1,4,6,5,3,7,8]=>1001100
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,2,5,6,4,3,7,8]=>0010100
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[2,1,5,6,4,3,7,8]=>1010100
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>0011100
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,3,4,5,6,2,7,8]=>0000100
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[1,4,3,5,6,2,7,8]=>0010100
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[1,3,5,4,6,2,7,8]=>0001100
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,4,5,3,6,2,7,8]=>0001100
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[8,4,5,6,3,7,2,1]=>[1,5,4,3,6,2,7,8]=>0011100
[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]=>[8,5,6,3,4,7,2,1]=>[1,4,3,6,5,2,7,8]=>0011100
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[1,3,5,6,4,2,7,8]=>0010100
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,4,5,6,3,2,7,8]=>0100100
[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]=>[8,4,5,3,6,7,2,1]=>[1,5,4,6,3,2,7,8]=>0101100
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[1,4,6,5,3,2,7,8]=>0101100
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[1,5,6,4,3,2,7,8]=>0110100
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[1,6,5,4,3,2,7,8]=>0111100
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[2,3,4,5,6,1,7,8]=>0000100
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[3,2,4,5,6,1,7,8]=>0100100
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[3,4,2,5,6,1,7,8]=>0010100
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[4,3,2,5,6,1,7,8]=>0110100
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[2,3,5,4,6,1,7,8]=>0001100
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[3,4,5,2,6,1,7,8]=>0001100
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[4,3,5,2,6,1,7,8]=>0011100
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[3,5,4,2,6,1,7,8]=>0011100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[4,5,3,2,6,1,7,8]=>0101100
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[5,4,3,2,6,1,7,8]=>0111100
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[2,3,4,6,5,1,7,8]=>0001100
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[7,5,6,3,4,8,2,1]=>[2,4,3,6,5,1,7,8]=>0011100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[4,3,2,6,5,1,7,8]=>0111100
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[2,3,5,6,4,1,7,8]=>0010100
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[2,3,6,5,4,1,7,8]=>0011100
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[2,4,5,6,3,1,7,8]=>0100100
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[2,4,6,5,3,1,7,8]=>0101100
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[3,4,5,6,2,1,7,8]=>1000100
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[5,4,3,6,2,1,7,8]=>1011100
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[4,3,6,5,2,1,7,8]=>1011100
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[3,6,5,4,2,1,7,8]=>1011100
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[4,5,6,3,2,1,7,8]=>1100100
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[5,4,6,3,2,1,7,8]=>1101100
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[5,6,4,3,2,1,7,8]=>1110100
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[6,5,4,3,2,1,7,8]=>1111100
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>0000010
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[2,1,3,4,5,7,6,8]=>1000010
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[2,3,1,4,5,7,6,8]=>0100010
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,2,3,1]=>[3,2,1,4,5,7,6,8]=>1100010
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,2,4,3,5,7,6,8]=>0010010
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[1,3,4,2,5,7,6,8]=>0010010
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,4,3,2,5,7,6,8]=>0110010
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[2,3,4,1,5,7,6,8]=>0010010
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[3,2,4,1,5,7,6,8]=>0110010
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[4,3,2,1,5,7,6,8]=>1110010
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,2,3,5,4,7,6,8]=>0001010
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[2,3,1,5,4,7,6,8]=>0101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[3,2,1,5,4,7,6,8]=>1101010
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,2,4,5,3,7,6,8]=>0001010
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[2,1,5,4,3,7,6,8]=>1011010
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,4,5,2,7,6,8]=>0001010
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,4,3,5,2,7,6,8]=>0011010
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,5,4,2,7,6,8]=>0011010
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,2,3,1]=>[1,4,5,3,2,7,6,8]=>0101010
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[1,5,4,3,2,7,6,8]=>0111010
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[2,3,4,5,1,7,6,8]=>0001010
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[2,4,3,5,1,7,6,8]=>0011010
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,4,2,5,1,7,6,8]=>0011010
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[2,3,5,4,1,7,6,8]=>0011010
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[3,2,5,4,1,7,6,8]=>0111010
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[2,4,5,3,1,7,6,8]=>0101010
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[2,5,4,3,1,7,6,8]=>0111010
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[3,4,5,2,1,7,6,8]=>1001010
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[3,5,4,2,1,7,6,8]=>1011010
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[4,5,3,2,1,7,6,8]=>1101010
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[5,4,3,2,1,7,6,8]=>1111010
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,2,3,4,6,7,5,8]=>0000010
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[2,1,3,4,6,7,5,8]=>1000010
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[2,3,1,4,6,7,5,8]=>0100010
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,2,4,3,6,7,5,8]=>0010010
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[2,1,4,3,6,7,5,8]=>1010010
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>0010010
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[1,4,3,2,6,7,5,8]=>0110010
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[2,3,4,1,6,7,5,8]=>0010010
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[3,2,4,1,6,7,5,8]=>0110010
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,2,1,6,7,5,8]=>1110010
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,2,3,4,7,6,5,8]=>0000110
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,3,2,4,7,6,5,8]=>0100110
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[3,2,1,4,7,6,5,8]=>1100110
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[2,3,4,1,7,6,5,8]=>0010110
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[3,2,4,1,7,6,5,8]=>0110110
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,3,2,1,7,6,5,8]=>1110110
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,2,3,5,6,7,4,8]=>0000010
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,3,2,5,6,7,4,8]=>0100010
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[2,3,1,5,6,7,4,8]=>0100010
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[3,2,1,5,6,7,4,8]=>1100010
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,2,3,6,5,7,4,8]=>0000110
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,3,2,6,5,7,4,8]=>0100110
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[2,3,1,6,5,7,4,8]=>0100110
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[3,2,1,6,5,7,4,8]=>1100110
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,2,3,5,7,6,4,8]=>0000110
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,3,2,5,7,6,4,8]=>0100110
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[3,2,1,5,7,6,4,8]=>1100110
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,2,3,6,7,5,4,8]=>0001010
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[2,1,3,6,7,5,4,8]=>1001010
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,3,2,6,7,5,4,8]=>0101010
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[7,6,8,3,2,4,5,1]=>[2,3,1,6,7,5,4,8]=>0101010
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[3,2,1,6,7,5,4,8]=>1101010
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,2,3,7,6,5,4,8]=>0001110
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,3,2,7,6,5,4,8]=>0101110
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[3,2,1,7,6,5,4,8]=>1101110
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,2,4,5,6,7,3,8]=>0000010
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[2,1,4,5,6,7,3,8]=>1000010
[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]=>[8,7,4,5,3,2,6,1]=>[1,2,5,4,6,7,3,8]=>0001010
[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[7,8,4,5,3,2,6,1]=>[2,1,5,4,6,7,3,8]=>1001010
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[1,2,5,6,4,7,3,8]=>0000110
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,2,4,6,7,5,3,8]=>0001010
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[2,1,4,6,7,5,3,8]=>1001010
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[1,2,5,6,7,4,3,8]=>0010010
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[2,1,5,6,7,4,3,8]=>1010010
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,2,5,7,6,4,3,8]=>0010110
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[8,7,3,2,4,5,6,1]=>[1,2,6,7,5,4,3,8]=>0011010
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[2,1,6,7,5,4,3,8]=>1011010
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[1,2,7,6,5,4,3,8]=>0011110
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[2,1,7,6,5,4,3,8]=>1011110
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,3,4,5,6,7,2,8]=>0000010
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>[1,3,5,4,6,7,2,8]=>0001010
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[1,4,5,3,6,7,2,8]=>0001010
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[8,4,5,6,3,2,7,1]=>[1,5,4,3,6,7,2,8]=>0011010
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>[1,3,4,6,5,7,2,8]=>0000110
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,4,3,6,5,7,2,8]=>0010110
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,3,5,6,4,7,2,8]=>0000110
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,3,6,5,4,7,2,8]=>0001110
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,4,5,6,3,7,2,8]=>0000110
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,5,4,6,3,7,2,8]=>0001110
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,3,4,5,7,6,2,8]=>0000110
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,4,3,5,7,6,2,8]=>0010110
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,3,5,4,7,6,2,8]=>0001110
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[1,3,4,6,7,5,2,8]=>0001010
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[1,3,5,6,7,4,2,8]=>0010010
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[8,6,3,4,2,5,7,1]=>[1,3,6,5,7,4,2,8]=>0010110
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,3,5,7,6,4,2,8]=>0010110
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[1,3,7,6,5,4,2,8]=>0011110
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,4,5,6,7,3,2,8]=>0100010
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[1,5,4,6,7,3,2,8]=>0101010
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,4,6,5,7,3,2,8]=>0100110
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[8,4,3,5,2,6,7,1]=>[1,5,6,4,7,3,2,8]=>0100110
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[1,5,4,7,6,3,2,8]=>0101110
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[8,5,3,2,4,6,7,1]=>[1,4,6,7,5,3,2,8]=>0101010
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[1,4,7,6,5,3,2,8]=>0101110
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[1,5,6,7,4,3,2,8]=>0110010
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[1,6,5,7,4,3,2,8]=>0110110
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[1,6,7,5,4,3,2,8]=>0111010
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>0111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[2,3,4,5,6,7,1,8]=>0000010
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[3,2,4,5,6,7,1,8]=>0100010
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[3,4,2,5,6,7,1,8]=>0010010
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[4,3,2,5,6,7,1,8]=>0110010
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[2,3,5,4,6,7,1,8]=>0001010
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[2,4,5,3,6,7,1,8]=>0001010
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[2,5,4,3,6,7,1,8]=>0011010
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[3,4,5,2,6,7,1,8]=>0001010
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[3,5,4,2,6,7,1,8]=>0011010
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[5,4,3,2,6,7,1,8]=>0111010
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[2,3,4,6,5,7,1,8]=>0000110
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[2,4,3,6,5,7,1,8]=>0010110
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[3,4,2,6,5,7,1,8]=>0010110
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[4,3,2,6,5,7,1,8]=>0110110
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[2,3,5,6,4,7,1,8]=>0000110
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[6,7,3,4,5,2,8,1]=>[3,2,6,5,4,7,1,8]=>0101110
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[2,5,4,6,3,7,1,8]=>0001110
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[3,4,5,6,2,7,1,8]=>0000110
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[4,3,5,6,2,7,1,8]=>0010110
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[3,5,4,6,2,7,1,8]=>0001110
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[4,5,3,6,2,7,1,8]=>0001110
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[5,4,3,6,2,7,1,8]=>0011110
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[3,4,6,5,2,7,1,8]=>0001110
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[3,5,6,4,2,7,1,8]=>0010110
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[3,6,5,4,2,7,1,8]=>0011110
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[5,4,6,3,2,7,1,8]=>0101110
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[5,6,4,3,2,7,1,8]=>0110110
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[6,5,4,3,2,7,1,8]=>0111110
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[2,3,4,5,7,6,1,8]=>0000110
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[3,4,2,5,7,6,1,8]=>0010110
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[4,3,2,5,7,6,1,8]=>0110110
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[3,2,5,4,7,6,1,8]=>0101110
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[3,4,5,2,7,6,1,8]=>0001110
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[4,3,5,2,7,6,1,8]=>0011110
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[3,5,4,2,7,6,1,8]=>0011110
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[4,5,3,2,7,6,1,8]=>0101110
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[5,4,3,2,7,6,1,8]=>0111110
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[2,3,4,6,7,5,1,8]=>0001010
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[3,2,4,6,7,5,1,8]=>0101010
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[3,4,2,6,7,5,1,8]=>0011010
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[4,3,2,6,7,5,1,8]=>0111010
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[2,3,4,7,6,5,1,8]=>0001110
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[6,5,7,2,3,4,8,1]=>[3,4,2,7,6,5,1,8]=>0011110
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[7,6,4,3,2,5,8,1]=>[2,3,5,6,7,4,1,8]=>0010010
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[3,2,5,6,7,4,1,8]=>0110010
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[7,6,3,4,2,5,8,1]=>[2,3,6,5,7,4,1,8]=>0010110
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[6,7,3,4,2,5,8,1]=>[3,2,6,5,7,4,1,8]=>0110110
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[2,3,5,7,6,4,1,8]=>0010110
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[3,2,5,7,6,4,1,8]=>0110110
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[2,3,6,7,5,4,1,8]=>0011010
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[3,2,6,7,5,4,1,8]=>0111010
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[2,3,7,6,5,4,1,8]=>0011110
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[3,2,7,6,5,4,1,8]=>0111110
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[2,4,5,6,7,3,1,8]=>0100010
[.,[[[.,[.,[[.,.],.]]],[.,.]],.]]=>[7,4,5,3,2,6,8,1]=>[2,5,4,6,7,3,1,8]=>0101010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[2,5,6,4,7,3,1,8]=>0100110
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[2,5,4,7,6,3,1,8]=>0101110
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[2,4,6,7,5,3,1,8]=>0101010
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[2,5,6,7,4,3,1,8]=>0110010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[2,5,7,6,4,3,1,8]=>0110110
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[2,6,7,5,4,3,1,8]=>0111010
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[2,7,6,5,4,3,1,8]=>0111110
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[3,4,5,6,7,2,1,8]=>1000010
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[5,4,3,6,7,2,1,8]=>1011010
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[4,3,6,5,7,2,1,8]=>1010110
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[3,5,6,4,7,2,1,8]=>1000110
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[3,6,5,4,7,2,1,8]=>1001110
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[5,4,6,3,7,2,1,8]=>1001110
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[5,6,4,3,7,2,1,8]=>1010110
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[6,5,4,3,7,2,1,8]=>1011110
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[4,3,5,7,6,2,1,8]=>1010110
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[3,5,4,7,6,2,1,8]=>1001110
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[4,5,3,7,6,2,1,8]=>1001110
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[5,4,3,7,6,2,1,8]=>1011110
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[3,4,7,6,5,2,1,8]=>1001110
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[4,3,7,6,5,2,1,8]=>1011110
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[6,4,3,2,5,7,8,1]=>[3,5,6,7,4,2,1,8]=>1010010
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[3,5,7,6,4,2,1,8]=>1010110
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[4,5,6,7,3,2,1,8]=>1100010
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[5,4,6,7,3,2,1,8]=>1101010
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[4,6,5,7,3,2,1,8]=>1100110
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[5,6,4,7,3,2,1,8]=>1100110
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[6,5,4,7,3,2,1,8]=>1101110
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[4,5,7,6,3,2,1,8]=>1100110
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[5,4,7,6,3,2,1,8]=>1101110
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[4,6,7,5,3,2,1,8]=>1101010
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[4,7,6,5,3,2,1,8]=>1101110
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[5,6,7,4,3,2,1,8]=>1110010
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[6,5,7,4,3,2,1,8]=>1110110
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[5,7,6,4,3,2,1,8]=>1110110
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[6,7,5,4,3,2,1,8]=>1111010
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>0000001
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[1,3,2,4,5,6,8,7]=>0100001
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[2,3,1,4,5,6,8,7]=>0100001
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[3,2,1,4,5,6,8,7]=>1100001
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[1,2,4,3,5,6,8,7]=>0010001
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[1,3,4,2,5,6,8,7]=>0010001
[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,3,1,2]=>[1,4,3,2,5,6,8,7]=>0110001
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,3,4,1,5,6,8,7]=>0010001
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[3,2,4,1,5,6,8,7]=>0110001
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[3,4,2,1,5,6,8,7]=>1010001
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[4,3,2,1,5,6,8,7]=>1110001
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[1,2,3,5,4,6,8,7]=>0001001
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,4,5,3,6,8,7]=>1001001
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[1,2,5,4,3,6,8,7]=>0011001
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,3,1,2]=>[1,3,4,5,2,6,8,7]=>0001001
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[1,3,5,4,2,6,8,7]=>0011001
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[1,4,5,3,2,6,8,7]=>0101001
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,3,4,5,1,6,8,7]=>0001001
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[2,4,3,5,1,6,8,7]=>0011001
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[2,3,5,4,1,6,8,7]=>0011001
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[3,2,5,4,1,6,8,7]=>0111001
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,4,5,3,1,6,8,7]=>0101001
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[2,5,4,3,1,6,8,7]=>0111001
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[3,4,5,2,1,6,8,7]=>1001001
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[4,3,5,2,1,6,8,7]=>1011001
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[4,5,3,2,1,6,8,7]=>1101001
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[5,4,3,2,1,6,8,7]=>1111001
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[1,2,3,4,6,5,8,7]=>0000101
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,4,1,2]=>[1,3,2,4,6,5,8,7]=>0100101
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,3,1,4,6,5,8,7]=>0100101
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7]=>0010101
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[1,3,4,2,6,5,8,7]=>0010101
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,3,4,1,6,5,8,7]=>0010101
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[3,2,4,1,6,5,8,7]=>0110101
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,4,3,1,6,5,8,7]=>0110101
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[3,4,2,1,6,5,8,7]=>1010101
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,3,2,1,6,5,8,7]=>1110101
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[1,2,3,5,6,4,8,7]=>0000101
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,3,5,6,4,8,7]=>1000101
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2]=>[1,3,2,5,6,4,8,7]=>0100101
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[1,2,3,6,5,4,8,7]=>0001101
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,3,6,5,4,8,7]=>1001101
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[1,3,2,6,5,4,8,7]=>0101101
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[2,3,1,6,5,4,8,7]=>0101101
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[3,2,1,6,5,4,8,7]=>1101101
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[1,2,4,5,6,3,8,7]=>0000101
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,4,5,6,3,8,7]=>1000101
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,5,4,6,3,8,7]=>1001101
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,4,6,5,3,8,7]=>1001101
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,5,6,4,3,8,7]=>1010101
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[1,3,4,5,6,2,8,7]=>0000101
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[8,6,3,4,5,7,1,2]=>[1,3,6,5,4,2,8,7]=>0011101
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[8,4,5,3,6,7,1,2]=>[1,5,4,6,3,2,8,7]=>0101101
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[1,5,6,4,3,2,8,7]=>0110101
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[1,6,5,4,3,2,8,7]=>0111101
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,3,4,5,6,1,8,7]=>0000101
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,3,8,1,2]=>[2,4,3,5,6,1,8,7]=>0010101
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[3,4,2,5,6,1,8,7]=>0010101
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[4,3,2,5,6,1,8,7]=>0110101
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[3,2,5,4,6,1,8,7]=>0101101
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,4,5,3,6,1,8,7]=>0001101
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[2,5,4,3,6,1,8,7]=>0011101
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[3,4,5,2,6,1,8,7]=>0001101
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[4,3,5,2,6,1,8,7]=>0011101
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[3,5,4,2,6,1,8,7]=>0011101
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[4,5,3,2,6,1,8,7]=>0101101
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[5,4,3,2,6,1,8,7]=>0111101
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,4,3,6,5,1,8,7]=>0011101
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[3,4,2,6,5,1,8,7]=>0011101
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[4,3,2,6,5,1,8,7]=>0111101
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[2,3,5,6,4,1,8,7]=>0010101
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[3,2,5,6,4,1,8,7]=>0110101
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,3,6,5,4,1,8,7]=>0011101
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[3,2,6,5,4,1,8,7]=>0111101
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,4,6,5,3,1,8,7]=>0101101
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,6,5,4,3,1,8,7]=>0111101
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[3,4,5,6,2,1,8,7]=>1000101
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[4,3,5,6,2,1,8,7]=>1010101
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[4,5,3,6,2,1,8,7]=>1001101
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[5,4,3,6,2,1,8,7]=>1011101
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[3,4,6,5,2,1,8,7]=>1001101
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[4,3,6,5,2,1,8,7]=>1011101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[3,5,6,4,2,1,8,7]=>1010101
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[3,6,5,4,2,1,8,7]=>1011101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[4,5,6,3,2,1,8,7]=>1100101
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[5,4,6,3,2,1,8,7]=>1101101
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[4,6,5,3,2,1,8,7]=>1101101
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[5,6,4,3,2,1,8,7]=>1110101
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[6,5,4,3,2,1,8,7]=>1111101
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>0000001
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[2,1,3,4,5,7,8,6]=>1000001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[1,3,2,4,5,7,8,6]=>0100001
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>0100001
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[3,2,1,4,5,7,8,6]=>1100001
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[1,2,4,3,5,7,8,6]=>0010001
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,1,4,3,5,7,8,6]=>1010001
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[1,3,4,2,5,7,8,6]=>0010001
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[1,4,3,2,5,7,8,6]=>0110001
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[2,3,4,1,5,7,8,6]=>0010001
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,2,4,1,5,7,8,6]=>0110001
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[4,3,2,1,5,7,8,6]=>1110001
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[1,2,3,5,4,7,8,6]=>0001001
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[2,1,3,5,4,7,8,6]=>1001001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,8,6]=>0101001
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[1,2,4,5,3,7,8,6]=>0001001
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[1,2,5,4,3,7,8,6]=>0011001
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[1,3,4,5,2,7,8,6]=>0001001
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,2,1,3]=>[1,4,3,5,2,7,8,6]=>0011001
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[1,3,5,4,2,7,8,6]=>0011001
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[1,4,5,3,2,7,8,6]=>0101001
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[1,5,4,3,2,7,8,6]=>0111001
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[2,3,4,5,1,7,8,6]=>0001001
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[2,4,3,5,1,7,8,6]=>0011001
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,4,2,5,1,7,8,6]=>0011001
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[4,3,2,5,1,7,8,6]=>0111001
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,2,5,4,1,7,8,6]=>0111001
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[2,4,5,3,1,7,8,6]=>0101001
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[2,5,4,3,1,7,8,6]=>0111001
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,4,5,2,1,7,8,6]=>1001001
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,5,4,2,1,7,8,6]=>1011001
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[5,4,3,2,1,7,8,6]=>1111001
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>0000011
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[2,1,3,4,5,8,7,6]=>1000011
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[1,3,2,4,5,8,7,6]=>0100011
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,1,2,3]=>[1,2,4,3,5,8,7,6]=>0010011
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[2,1,4,3,5,8,7,6]=>1010011
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[1,3,4,2,5,8,7,6]=>0010011
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[1,4,3,2,5,8,7,6]=>0110011
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[2,3,4,1,5,8,7,6]=>0010011
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,4,1,5,8,7,6]=>0110011
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[2,4,3,1,5,8,7,6]=>0110011
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,4,2,1,5,8,7,6]=>1010011
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,3,2,1,5,8,7,6]=>1110011
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[1,2,3,5,4,8,7,6]=>0001011
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[2,1,3,5,4,8,7,6]=>1001011
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[1,3,2,5,4,8,7,6]=>0101011
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[1,2,4,5,3,8,7,6]=>0001011
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[2,1,4,5,3,8,7,6]=>1001011
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]=>0011011
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[2,1,5,4,3,8,7,6]=>1011011
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[1,3,4,5,2,8,7,6]=>0001011
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[1,4,3,5,2,8,7,6]=>0011011
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[1,4,5,3,2,8,7,6]=>0101011
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[1,5,4,3,2,8,7,6]=>0111011
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[2,3,4,5,1,8,7,6]=>0001011
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,4,5,1,8,7,6]=>0101011
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[2,4,3,5,1,8,7,6]=>0011011
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,4,2,5,1,8,7,6]=>0011011
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[4,3,2,5,1,8,7,6]=>0111011
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[2,3,5,4,1,8,7,6]=>0011011
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,5,4,1,8,7,6]=>0111011
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[2,4,5,3,1,8,7,6]=>0101011
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[2,5,4,3,1,8,7,6]=>0111011
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,4,5,2,1,8,7,6]=>1001011
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[4,3,5,2,1,8,7,6]=>1011011
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[3,5,4,2,1,8,7,6]=>1011011
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[4,5,3,2,1,8,7,6]=>1101011
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[5,4,3,2,1,8,7,6]=>1111011
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>0000001
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[2,1,3,4,6,7,8,5]=>1000001
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[1,3,2,4,6,7,8,5]=>0100001
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[2,3,1,4,6,7,8,5]=>0100001
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[3,2,1,4,6,7,8,5]=>1100001
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[1,2,4,3,6,7,8,5]=>0010001
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,1,4,3,6,7,8,5]=>1010001
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[1,3,4,2,6,7,8,5]=>0010001
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[1,4,3,2,6,7,8,5]=>0110001
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>0010001
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[3,2,4,1,6,7,8,5]=>0110001
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[2,4,3,1,6,7,8,5]=>0110001
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[3,4,2,1,6,7,8,5]=>1010001
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,3,2,1,6,7,8,5]=>1110001
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[1,2,3,4,7,6,8,5]=>0000011
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[2,1,3,4,7,6,8,5]=>1000011
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[1,3,2,4,7,6,8,5]=>0100011
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[2,3,1,4,7,6,8,5]=>0100011
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[1,2,4,3,7,6,8,5]=>0010011
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[2,1,4,3,7,6,8,5]=>1010011
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[1,3,4,2,7,6,8,5]=>0010011
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[1,4,3,2,7,6,8,5]=>0110011
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[2,3,4,1,7,6,8,5]=>0010011
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[3,2,4,1,7,6,8,5]=>0110011
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>0110011
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[3,4,2,1,7,6,8,5]=>1010011
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,3,2,1,7,6,8,5]=>1110011
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>0000011
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[1,3,2,4,6,8,7,5]=>0100011
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[3,2,1,4,6,8,7,5]=>1100011
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[1,2,4,3,6,8,7,5]=>0010011
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[2,1,4,3,6,8,7,5]=>1010011
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[1,3,4,2,6,8,7,5]=>0010011
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[1,4,3,2,6,8,7,5]=>0110011
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[2,3,4,1,6,8,7,5]=>0010011
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>0110011
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[2,4,3,1,6,8,7,5]=>0110011
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,4,2,1,6,8,7,5]=>1010011
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,3,2,1,6,8,7,5]=>1110011
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>0000101
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,1,3,4,7,8,6,5]=>1000101
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[2,3,1,4,7,8,6,5]=>0100101
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,2,1,4,7,8,6,5]=>1100101
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[1,2,4,3,7,8,6,5]=>0010101
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,1,4,3,7,8,6,5]=>1010101
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[1,3,4,2,7,8,6,5]=>0010101
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[2,3,4,1,7,8,6,5]=>0010101
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[3,2,4,1,7,8,6,5]=>0110101
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[2,4,3,1,7,8,6,5]=>0110101
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[3,4,2,1,7,8,6,5]=>1010101
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,2,1,7,8,6,5]=>1110101
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>0000111
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]=>1000111
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[1,3,2,4,8,7,6,5]=>0100111
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[2,3,1,4,8,7,6,5]=>0100111
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[3,2,1,4,8,7,6,5]=>1100111
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,2,4,3,8,7,6,5]=>0010111
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,1,4,3,8,7,6,5]=>1010111
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[1,3,4,2,8,7,6,5]=>0010111
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[1,4,3,2,8,7,6,5]=>0110111
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[2,3,4,1,8,7,6,5]=>0010111
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[3,2,4,1,8,7,6,5]=>0110111
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[2,4,3,1,8,7,6,5]=>0110111
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[3,4,2,1,8,7,6,5]=>1010111
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>0000001
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,1,3,5,6,7,8,4]=>1000001
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[1,3,2,5,6,7,8,4]=>0100001
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,1,5,6,7,8,4]=>0100001
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[3,2,1,5,6,7,8,4]=>1100001
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[1,2,3,6,5,7,8,4]=>0000101
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[1,3,2,6,5,7,8,4]=>0100101
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[3,2,1,6,5,7,8,4]=>1100101
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[1,2,3,5,7,6,8,4]=>0000011
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[2,1,3,5,7,6,8,4]=>1000011
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[1,3,2,5,7,6,8,4]=>0100011
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[2,3,1,5,7,6,8,4]=>0100011
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,2,1,5,7,6,8,4]=>1100011
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[1,2,3,6,7,5,8,4]=>0000011
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[1,3,2,6,7,5,8,4]=>0100011
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[2,3,1,6,7,5,8,4]=>0100011
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[3,2,1,6,7,5,8,4]=>1100011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[1,2,3,7,6,5,8,4]=>0000111
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[8,6,7,2,3,4,1,5]=>[1,3,2,7,6,5,8,4]=>0100111
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[2,3,1,7,6,5,8,4]=>0100111
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[3,2,1,7,6,5,8,4]=>1100111
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>0000011
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,3,1,2,5]=>[1,3,2,5,6,8,7,4]=>0100011
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,2,1,5,6,8,7,4]=>1100011
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[1,2,3,6,5,8,7,4]=>0000111
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[2,1,3,6,5,8,7,4]=>1000111
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[1,3,2,6,5,8,7,4]=>0100111
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[2,3,1,6,5,8,7,4]=>0100111
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[3,2,1,6,5,8,7,4]=>1100111
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>0000101
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[1,3,2,5,7,8,6,4]=>0100101
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[2,3,1,5,7,8,6,4]=>0100101
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[3,2,1,5,7,8,6,4]=>1100101
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>0000111
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[1,3,2,5,8,7,6,4]=>0100111
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[3,2,1,5,8,7,6,4]=>1100111
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>0001001
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,1,3,6,7,8,5,4]=>1001001
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[1,3,2,6,7,8,5,4]=>0101001
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[2,3,1,6,7,8,5,4]=>0101001
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[3,2,1,6,7,8,5,4]=>1101001
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[1,2,3,7,6,8,5,4]=>0001011
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[1,3,2,7,6,8,5,4]=>0101011
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[2,3,1,7,6,8,5,4]=>0101011
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[3,2,1,7,6,8,5,4]=>1101011
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>0001011
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[2,1,3,6,8,7,5,4]=>1001011
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[1,3,2,6,8,7,5,4]=>0101011
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[2,3,1,6,8,7,5,4]=>0101011
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[3,2,1,6,8,7,5,4]=>1101011
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>0001101
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[2,1,3,7,8,6,5,4]=>1001101
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[2,3,1,7,8,6,5,4]=>0101101
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[3,2,1,7,8,6,5,4]=>1101101
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>0001111
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[2,1,3,8,7,6,5,4]=>1001111
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[1,3,2,8,7,6,5,4]=>0101111
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[2,3,1,8,7,6,5,4]=>0101111
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]=>1101111
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>0000001
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,1,4,5,6,7,8,3]=>1000001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[1,2,5,4,6,7,8,3]=>0001001
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6]=>[2,1,5,4,6,7,8,3]=>1001001
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[1,2,4,6,5,7,8,3]=>0000101
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[1,2,5,6,4,7,8,3]=>0000101
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,1,5,6,4,7,8,3]=>1000101
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[1,2,6,5,4,7,8,3]=>0001101
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[1,2,5,4,7,6,8,3]=>0001011
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[2,1,5,4,7,6,8,3]=>1001011
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[2,1,4,6,7,5,8,3]=>1000011
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[1,2,4,7,6,5,8,3]=>0000111
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[2,1,4,7,6,5,8,3]=>1000111
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[1,2,5,6,7,4,8,3]=>0000011
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[2,1,5,6,7,4,8,3]=>1000011
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[2,1,6,5,7,4,8,3]=>1000111
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[1,2,5,7,6,4,8,3]=>0000111
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[2,1,5,7,6,4,8,3]=>1000111
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[2,1,6,7,5,4,8,3]=>1001011
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[1,2,7,6,5,4,8,3]=>0001111
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[2,1,7,6,5,4,8,3]=>1001111
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>0000011
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[2,1,4,5,6,8,7,3]=>1000011
[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,3,1,2,6]=>[1,2,5,4,6,8,7,3]=>0001011
[[[.,.],[.,[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,3,1,2,6]=>[2,1,5,4,6,8,7,3]=>1001011
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[1,2,4,6,5,8,7,3]=>0000111
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[2,1,4,6,5,8,7,3]=>1000111
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[2,1,5,6,4,8,7,3]=>1000111
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[1,2,6,5,4,8,7,3]=>0001111
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[2,1,6,5,4,8,7,3]=>1001111
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[1,2,4,5,7,8,6,3]=>0000101
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[2,1,4,5,7,8,6,3]=>1000101
[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,2,1,3,6]=>[1,2,5,4,7,8,6,3]=>0001101
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,1,5,4,7,8,6,3]=>1001101
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[1,2,4,5,8,7,6,3]=>0000111
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[2,1,4,5,8,7,6,3]=>1000111
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[1,2,5,4,8,7,6,3]=>0001111
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,1,5,4,8,7,6,3]=>1001111
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[1,2,4,6,7,8,5,3]=>0001001
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,1,4,6,7,8,5,3]=>1001001
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[1,2,4,7,6,8,5,3]=>0001011
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[2,1,4,7,6,8,5,3]=>1001011
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>0001011
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[2,1,4,6,8,7,5,3]=>1001011
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[1,2,4,7,8,6,5,3]=>0001101
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,1,4,7,8,6,5,3]=>1001101
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>0001111
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[2,1,4,8,7,6,5,3]=>1001111
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[1,2,5,6,7,8,4,3]=>0010001
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,1,5,6,7,8,4,3]=>1010001
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[1,2,6,5,7,8,4,3]=>0010101
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[2,1,6,5,7,8,4,3]=>1010101
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[2,1,5,7,6,8,4,3]=>1010011
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[2,1,6,7,5,8,4,3]=>1010011
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[1,2,7,6,5,8,4,3]=>0010111
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[2,1,7,6,5,8,4,3]=>1010111
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[1,2,5,6,8,7,4,3]=>0010011
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[2,1,5,6,8,7,4,3]=>1010011
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[1,2,6,5,8,7,4,3]=>0010111
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[2,1,6,5,8,7,4,3]=>1010111
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[2,1,5,7,8,6,4,3]=>1010101
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]=>0010111
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[2,1,5,8,7,6,4,3]=>1010111
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[1,2,6,7,8,5,4,3]=>0011001
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,1,6,7,8,5,4,3]=>1011001
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[1,2,7,6,8,5,4,3]=>0011011
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[2,1,7,6,8,5,4,3]=>1011011
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[2,1,6,8,7,5,4,3]=>1011011
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[1,2,7,8,6,5,4,3]=>0011101
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[2,1,7,8,6,5,4,3]=>1011101
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>0011111
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,1,8,7,6,5,4,3]=>1011111
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>0000001
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[1,4,3,5,6,7,8,2]=>0010001
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[1,3,5,4,6,7,8,2]=>0001001
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[1,4,5,3,6,7,8,2]=>0001001
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[1,5,4,3,6,7,8,2]=>0011001
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[1,3,4,6,5,7,8,2]=>0000101
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[1,4,3,6,5,7,8,2]=>0010101
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[1,3,5,6,4,7,8,2]=>0000101
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[1,5,4,6,3,7,8,2]=>0001101
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[1,6,5,4,3,7,8,2]=>0011101
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[1,3,4,5,7,6,8,2]=>0000011
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[1,3,5,4,7,6,8,2]=>0001011
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[1,3,4,6,7,5,8,2]=>0000011
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[8,5,6,3,2,4,1,7]=>[1,4,3,6,7,5,8,2]=>0010011
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[1,3,4,7,6,5,8,2]=>0000111
[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[1,3,5,6,7,4,8,2]=>0000011
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[8,6,3,4,2,5,1,7]=>[1,3,6,5,7,4,8,2]=>0000111
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[1,3,5,7,6,4,8,2]=>0000111
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[1,4,5,6,7,3,8,2]=>0000011
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[1,5,4,6,7,3,8,2]=>0001011
[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]=>[8,5,3,4,2,6,1,7]=>[1,4,6,5,7,3,8,2]=>0000111
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[1,5,6,4,7,3,8,2]=>0000111
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[1,4,6,7,5,3,8,2]=>0001011
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[8,4,3,2,5,6,1,7]=>[1,5,6,7,4,3,8,2]=>0010011
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[1,6,5,7,4,3,8,2]=>0010111
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[1,6,7,5,4,3,8,2]=>0011011
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[1,7,6,5,4,3,8,2]=>0011111
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>0000011
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[1,4,5,3,6,8,7,2]=>0001011
[[[.,.],[.,[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,3,1,2,7]=>[1,5,4,3,6,8,7,2]=>0011011
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[1,4,3,6,5,8,7,2]=>0010111
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[1,3,6,5,4,8,7,2]=>0001111
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[1,4,5,6,3,8,7,2]=>0000111
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[1,4,6,5,3,8,7,2]=>0001111
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[1,5,6,4,3,8,7,2]=>0010111
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[1,6,5,4,3,8,7,2]=>0011111
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[1,3,4,5,7,8,6,2]=>0000101
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[1,4,3,5,7,8,6,2]=>0010101
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[1,3,5,4,7,8,6,2]=>0001101
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[1,4,5,3,7,8,6,2]=>0001101
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[1,3,4,5,8,7,6,2]=>0000111
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[1,4,3,5,8,7,6,2]=>0010111
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[1,3,5,4,8,7,6,2]=>0001111
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[1,4,5,3,8,7,6,2]=>0001111
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[1,5,4,3,8,7,6,2]=>0011111
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[1,3,4,6,7,8,5,2]=>0001001
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[1,4,3,6,7,8,5,2]=>0011001
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[1,3,4,7,6,8,5,2]=>0001011
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[1,4,3,7,6,8,5,2]=>0011011
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[1,4,3,6,8,7,5,2]=>0011011
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[1,4,3,7,8,6,5,2]=>0011101
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>0001111
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[1,4,3,8,7,6,5,2]=>0011111
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>0010001
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[1,3,6,5,7,8,4,2]=>0010101
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[1,3,5,7,6,8,4,2]=>0010011
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[1,3,6,7,5,8,4,2]=>0010011
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[1,3,5,6,8,7,4,2]=>0010011
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>0010101
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>0010111
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>0011001
[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[8,6,3,1,2,4,5,7]=>[1,3,6,8,7,5,4,2]=>0011011
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[1,3,7,8,6,5,4,2]=>0011101
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]=>0011111
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>0100001
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[1,5,4,6,7,8,3,2]=>0101001
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[1,5,6,4,7,8,3,2]=>0100101
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[1,6,5,4,7,8,3,2]=>0101101
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[1,4,6,7,5,8,3,2]=>0100011
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[1,4,7,6,5,8,3,2]=>0100111
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[1,7,6,5,4,8,3,2]=>0101111
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[8,4,5,3,1,2,6,7]=>[1,5,4,6,8,7,3,2]=>0101011
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[1,4,6,5,8,7,3,2]=>0100111
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[1,6,5,4,8,7,3,2]=>0101111
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[1,4,5,7,8,6,3,2]=>0100101
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[1,5,4,7,8,6,3,2]=>0101101
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[1,4,5,8,7,6,3,2]=>0100111
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[1,4,6,7,8,5,3,2]=>0101001
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[1,4,6,8,7,5,3,2]=>0101011
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[1,4,7,8,6,5,3,2]=>0101101
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[1,4,8,7,6,5,3,2]=>0101111
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>0110001
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[1,6,5,7,8,4,3,2]=>0110101
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[1,5,7,6,8,4,3,2]=>0110011
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[1,6,7,5,8,4,3,2]=>0110011
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[1,7,6,5,8,4,3,2]=>0110111
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[1,6,5,8,7,4,3,2]=>0110111
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>0110111
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>0111001
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[1,7,6,8,5,4,3,2]=>0111011
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>0111011
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>0111101
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>0111111
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>0000001
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[3,2,4,5,6,7,8,1]=>0100001
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[2,4,3,5,6,7,8,1]=>0010001
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[3,4,2,5,6,7,8,1]=>0010001
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[4,3,2,5,6,7,8,1]=>0110001
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[2,3,5,4,6,7,8,1]=>0001001
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[3,2,5,4,6,7,8,1]=>0101001
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[2,4,5,3,6,7,8,1]=>0001001
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[2,5,4,3,6,7,8,1]=>0011001
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[3,4,5,2,6,7,8,1]=>0001001
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[4,3,5,2,6,7,8,1]=>0011001
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[3,5,4,2,6,7,8,1]=>0011001
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[4,5,3,2,6,7,8,1]=>0101001
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[5,4,3,2,6,7,8,1]=>0111001
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[2,3,4,6,5,7,8,1]=>0000101
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[2,4,3,6,5,7,8,1]=>0010101
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[3,4,2,6,5,7,8,1]=>0010101
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[4,3,2,6,5,7,8,1]=>0110101
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[2,3,5,6,4,7,8,1]=>0000101
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[3,2,5,6,4,7,8,1]=>0100101
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[2,3,6,5,4,7,8,1]=>0001101
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[2,4,5,6,3,7,8,1]=>0000101
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[2,5,4,6,3,7,8,1]=>0001101
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[7,5,3,4,6,2,1,8]=>[2,4,6,5,3,7,8,1]=>0001101
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[2,5,6,4,3,7,8,1]=>0010101
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[2,6,5,4,3,7,8,1]=>0011101
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[3,4,5,6,2,7,8,1]=>0000101
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[4,3,5,6,2,7,8,1]=>0010101
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[3,5,4,6,2,7,8,1]=>0001101
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[5,4,3,6,2,7,8,1]=>0011101
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[6,5,3,4,7,2,1,8]=>[3,4,6,5,2,7,8,1]=>0001101
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[3,5,6,4,2,7,8,1]=>0010101
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[3,6,5,4,2,7,8,1]=>0011101
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[4,5,6,3,2,7,8,1]=>0100101
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[4,5,3,6,7,2,1,8]=>[5,4,6,3,2,7,8,1]=>0101101
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[6,5,4,3,2,7,8,1]=>0111101
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[2,3,4,5,7,6,8,1]=>0000011
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[3,2,4,5,7,6,8,1]=>0100011
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[2,4,3,5,7,6,8,1]=>0010011
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,2,3,1,8]=>[3,4,2,5,7,6,8,1]=>0010011
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[4,3,2,5,7,6,8,1]=>0110011
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[2,3,5,4,7,6,8,1]=>0001011
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,2,5,4,7,6,8,1]=>0101011
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[2,5,4,3,7,6,8,1]=>0011011
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[3,4,5,2,7,6,8,1]=>0001011
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[4,3,5,2,7,6,8,1]=>0011011
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[3,5,4,2,7,6,8,1]=>0011011
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[5,4,3,2,7,6,8,1]=>0111011
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[2,3,4,6,7,5,8,1]=>0000011
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[2,4,3,6,7,5,8,1]=>0010011
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[3,4,2,6,7,5,8,1]=>0010011
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,3,2,6,7,5,8,1]=>0110011
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[2,3,4,7,6,5,8,1]=>0000111
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[3,2,4,7,6,5,8,1]=>0100111
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[2,4,3,7,6,5,8,1]=>0010111
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[3,4,2,7,6,5,8,1]=>0010111
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[4,3,2,7,6,5,8,1]=>0110111
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[2,3,5,6,7,4,8,1]=>0000011
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[3,2,5,6,7,4,8,1]=>0100011
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[3,2,6,5,7,4,8,1]=>0100111
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[2,3,5,7,6,4,8,1]=>0000111
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[3,2,5,7,6,4,8,1]=>0100111
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[3,2,6,7,5,4,8,1]=>0101011
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[2,3,7,6,5,4,8,1]=>0001111
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[3,2,7,6,5,4,8,1]=>0101111
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[2,4,5,6,7,3,8,1]=>0000011
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[2,5,4,6,7,3,8,1]=>0001011
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[2,4,6,5,7,3,8,1]=>0000111
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[2,5,4,7,6,3,8,1]=>0001111
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[2,4,6,7,5,3,8,1]=>0001011
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[2,5,6,7,4,3,8,1]=>0010011
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[7,3,4,2,5,6,1,8]=>[2,6,5,7,4,3,8,1]=>0010111
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[2,7,6,5,4,3,8,1]=>0011111
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[3,4,5,6,7,2,8,1]=>0000011
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[6,4,5,3,2,7,1,8]=>[3,5,4,6,7,2,8,1]=>0001011
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[4,5,3,6,7,2,8,1]=>0001011
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[4,5,6,3,2,7,1,8]=>[5,4,3,6,7,2,8,1]=>0011011
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[6,5,3,4,2,7,1,8]=>[3,4,6,5,7,2,8,1]=>0000111
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[4,3,6,5,7,2,8,1]=>0010111
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[3,5,6,4,7,2,8,1]=>0000111
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[3,6,5,4,7,2,8,1]=>0001111
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[4,5,6,3,7,2,8,1]=>0000111
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[5,4,6,3,7,2,8,1]=>0001111
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[4,6,5,3,7,2,8,1]=>0001111
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[6,5,4,3,7,2,8,1]=>0011111
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[3,4,5,7,6,2,8,1]=>0000111
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[6,4,5,2,3,7,1,8]=>[3,5,4,7,6,2,8,1]=>0001111
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[4,5,3,7,6,2,8,1]=>0001111
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[5,4,3,7,6,2,8,1]=>0011111
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[3,4,6,7,5,2,8,1]=>0001011
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[4,3,6,7,5,2,8,1]=>0011011
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[6,5,2,3,4,7,1,8]=>[3,4,7,6,5,2,8,1]=>0001111
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[4,3,7,6,5,2,8,1]=>0011111
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[6,4,3,2,5,7,1,8]=>[3,5,6,7,4,2,8,1]=>0010011
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[3,5,7,6,4,2,8,1]=>0010111
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[4,5,6,7,3,2,8,1]=>0100011
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[4,6,5,7,3,2,8,1]=>0100111
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[6,5,4,7,3,2,8,1]=>0101111
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[4,6,7,5,3,2,8,1]=>0101011
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[4,7,6,5,3,2,8,1]=>0101111
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[5,6,7,4,3,2,8,1]=>0110011
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[6,5,7,4,3,2,8,1]=>0110111
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[5,7,6,4,3,2,8,1]=>0110111
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[6,7,5,4,3,2,8,1]=>0111011
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,8,1]=>0111111
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>0000011
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[3,2,4,5,6,8,7,1]=>0100011
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[2,4,3,5,6,8,7,1]=>0010011
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[3,4,2,5,6,8,7,1]=>0010011
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[4,3,2,5,6,8,7,1]=>0110011
[[[.,.],[.,[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,3,1,2,8]=>[3,2,5,4,6,8,7,1]=>0101011
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,3,1,2,8]=>[2,4,5,3,6,8,7,1]=>0001011
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[2,5,4,3,6,8,7,1]=>0011011
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[4,5,3,2,6,8,7,1]=>0101011
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[5,4,3,2,6,8,7,1]=>0111011
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[2,3,4,6,5,8,7,1]=>0000111
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[6,7,5,3,4,1,2,8]=>[3,2,4,6,5,8,7,1]=>0100111
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[2,4,3,6,5,8,7,1]=>0010111
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[3,4,2,6,5,8,7,1]=>0010111
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[5,6,7,3,4,1,2,8]=>[4,3,2,6,5,8,7,1]=>0110111
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[7,6,4,3,5,1,2,8]=>[2,3,5,6,4,8,7,1]=>0000111
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[3,2,6,5,4,8,7,1]=>0101111
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[2,4,5,6,3,8,7,1]=>0000111
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[2,4,6,5,3,8,7,1]=>0001111
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[7,3,4,5,6,1,2,8]=>[2,6,5,4,3,8,7,1]=>0011111
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[3,4,5,6,2,8,7,1]=>0000111
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[3,5,4,6,2,8,7,1]=>0001111
[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[5,4,6,3,7,1,2,8]=>[4,5,3,6,2,8,7,1]=>0001111
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[4,5,6,3,7,1,2,8]=>[5,4,3,6,2,8,7,1]=>0011111
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[4,3,6,5,2,8,7,1]=>0011111
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[3,5,6,4,2,8,7,1]=>0010111
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[3,6,5,4,2,8,7,1]=>0011111
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[5,4,3,6,7,1,2,8]=>[4,5,6,3,2,8,7,1]=>0100111
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[5,4,6,3,2,8,7,1]=>0101111
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[5,3,4,6,7,1,2,8]=>[4,6,5,3,2,8,7,1]=>0101111
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[6,5,4,3,2,8,7,1]=>0111111
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[2,3,4,5,7,8,6,1]=>0000101
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[3,2,4,5,7,8,6,1]=>0100101
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[3,4,2,5,7,8,6,1]=>0010101
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[4,3,2,5,7,8,6,1]=>0110101
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[2,3,5,4,7,8,6,1]=>0001101
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[3,2,5,4,7,8,6,1]=>0101101
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[2,4,5,3,7,8,6,1]=>0001101
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[2,5,4,3,7,8,6,1]=>0011101
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[3,4,5,2,7,8,6,1]=>0001101
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[5,4,3,2,7,8,6,1]=>0111101
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>0000111
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[2,4,3,5,8,7,6,1]=>0010111
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[3,4,2,5,8,7,6,1]=>0010111
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[4,3,2,5,8,7,6,1]=>0110111
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[2,3,5,4,8,7,6,1]=>0001111
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[2,4,5,3,8,7,6,1]=>0001111
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[2,5,4,3,8,7,6,1]=>0011111
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[4,3,5,2,8,7,6,1]=>0011111
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[4,5,3,2,8,7,6,1]=>0101111
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[5,4,3,2,8,7,6,1]=>0111111
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>0001001
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[7,5,6,3,2,1,4,8]=>[2,4,3,6,7,8,5,1]=>0011001
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[2,3,4,7,6,8,5,1]=>0001011
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[2,3,4,6,8,7,5,1]=>0001011
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[2,4,3,6,8,7,5,1]=>0011011
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[4,3,2,6,8,7,5,1]=>0111011
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[2,3,4,7,8,6,5,1]=>0001101
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[3,2,4,7,8,6,5,1]=>0101101
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[6,5,7,2,1,3,4,8]=>[3,4,2,7,8,6,5,1]=>0011101
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[4,3,2,7,8,6,5,1]=>0111101
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>0001111
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[3,2,4,8,7,6,5,1]=>0101111
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[2,4,3,8,7,6,5,1]=>0011111
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[3,4,2,8,7,6,5,1]=>0011111
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[4,3,2,8,7,6,5,1]=>0111111
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>0010001
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[3,2,5,6,7,8,4,1]=>0110001
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[2,3,5,7,6,8,4,1]=>0010011
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[3,2,5,7,6,8,4,1]=>0110011
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[2,3,7,6,5,8,4,1]=>0010111
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[2,3,5,6,8,7,4,1]=>0010011
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[2,3,6,5,8,7,4,1]=>0010111
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[3,2,6,5,8,7,4,1]=>0110111
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>0010101
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[6,7,4,2,1,3,5,8]=>[3,2,5,7,8,6,4,1]=>0110101
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[2,3,5,8,7,6,4,1]=>0010111
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[2,3,6,7,8,5,4,1]=>0011001
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[3,2,6,8,7,5,4,1]=>0111011
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[6,7,2,1,3,4,5,8]=>[3,2,7,8,6,5,4,1]=>0111101
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>0011111
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[3,2,8,7,6,5,4,1]=>0111111
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[2,4,5,6,7,8,3,1]=>0100001
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[2,5,4,6,7,8,3,1]=>0101001
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[2,4,6,5,7,8,3,1]=>0100101
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[2,5,6,4,7,8,3,1]=>0100101
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[2,6,5,4,7,8,3,1]=>0101101
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[7,4,5,2,3,1,6,8]=>[2,5,4,7,6,8,3,1]=>0101011
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[2,4,6,7,5,8,3,1]=>0100011
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[2,4,7,6,5,8,3,1]=>0100111
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[2,5,6,7,4,8,3,1]=>0100011
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[7,3,2,4,5,1,6,8]=>[2,6,7,5,4,8,3,1]=>0101011
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[2,7,6,5,4,8,3,1]=>0101111
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[2,4,6,5,8,7,3,1]=>0100111
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[7,4,3,5,1,2,6,8]=>[2,5,6,4,8,7,3,1]=>0100111
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[2,6,5,4,8,7,3,1]=>0101111
[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[7,5,4,2,1,3,6,8]=>[2,4,5,7,8,6,3,1]=>0100101
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[2,5,4,7,8,6,3,1]=>0101101
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[2,5,4,8,7,6,3,1]=>0101111
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>0101001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>0101011
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[2,4,7,8,6,5,3,1]=>0101101
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>0101111
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>0110001
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[2,6,5,7,8,4,3,1]=>0110101
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[2,6,7,5,8,4,3,1]=>0110011
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[2,5,8,7,6,4,3,1]=>0110111
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>0111001
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[2,7,6,8,5,4,3,1]=>0111011
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[2,6,8,7,5,4,3,1]=>0111011
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[2,7,8,6,5,4,3,1]=>0111101
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>0111111
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>1000001
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[4,3,5,6,7,8,2,1]=>1010001
[[[.,[.,[.,[[.,.],[.,.]]]]],.],.]=>[6,4,5,3,2,1,7,8]=>[3,5,4,6,7,8,2,1]=>1001001
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[5,4,3,6,7,8,2,1]=>1011001
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[3,4,6,5,7,8,2,1]=>1000101
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[4,3,6,5,7,8,2,1]=>1010101
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[6,4,3,5,2,1,7,8]=>[3,5,6,4,7,8,2,1]=>1000101
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[3,6,5,4,7,8,2,1]=>1001101
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[4,5,6,3,7,8,2,1]=>1000101
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[6,5,4,3,7,8,2,1]=>1011101
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[6,5,4,2,3,1,7,8]=>[3,4,5,7,6,8,2,1]=>1000011
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[4,3,5,7,6,8,2,1]=>1010011
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[3,5,4,7,6,8,2,1]=>1001011
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[4,5,3,7,6,8,2,1]=>1001011
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[6,5,3,2,4,1,7,8]=>[3,4,6,7,5,8,2,1]=>1000011
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[3,4,7,6,5,8,2,1]=>1000111
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[4,3,7,6,5,8,2,1]=>1010111
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[3,5,6,7,4,8,2,1]=>1000011
[[[.,[[[.,.],[.,.]],[.,.]]],.],.]=>[6,4,2,3,5,1,7,8]=>[3,5,7,6,4,8,2,1]=>1000111
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[3,7,6,5,4,8,2,1]=>1001111
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[4,5,6,7,3,8,2,1]=>1000011
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[5,4,6,7,3,8,2,1]=>1001011
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,5,4,7,3,8,2,1]=>1001111
[[[.,[[[.,.],[[.,.],.]],.]],.],.]=>[4,5,2,3,6,1,7,8]=>[5,4,7,6,3,8,2,1]=>1001111
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[4,7,6,5,3,8,2,1]=>1001111
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[5,6,7,4,3,8,2,1]=>1010011
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[6,5,7,4,3,8,2,1]=>1010111
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[5,7,6,4,3,8,2,1]=>1010111
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[6,7,5,4,3,8,2,1]=>1011011
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[7,6,5,4,3,8,2,1]=>1011111
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[3,4,5,6,8,7,2,1]=>1000011
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[4,3,5,6,8,7,2,1]=>1010011
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[4,5,3,6,8,7,2,1]=>1001011
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[4,5,6,3,1,2,7,8]=>[5,4,3,6,8,7,2,1]=>1011011
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[4,3,6,5,8,7,2,1]=>1010111
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[3,6,5,4,8,7,2,1]=>1001111
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[4,5,6,3,8,7,2,1]=>1000111
[[[[.,.],[[[.,[.,.]],.],.]],.],.]=>[4,3,5,6,1,2,7,8]=>[5,6,4,3,8,7,2,1]=>1010111
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[6,5,4,3,8,7,2,1]=>1011111
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[3,4,5,7,8,6,2,1]=>1000101
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[4,3,5,7,8,6,2,1]=>1010101
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[3,5,4,7,8,6,2,1]=>1001101
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[4,5,3,7,8,6,2,1]=>1001101
[[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[4,5,6,2,1,3,7,8]=>[5,4,3,7,8,6,2,1]=>1011101
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[3,4,5,8,7,6,2,1]=>1000111
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[5,4,3,8,7,6,2,1]=>1011111
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>1001001
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[4,3,6,7,8,5,2,1]=>1011001
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[3,4,8,7,6,5,2,1]=>1001111
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[4,3,8,7,6,5,2,1]=>1011111
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>1010001
[[[[.,[[.,.],[.,.]]],[.,.]],.],.]=>[6,4,2,3,1,5,7,8]=>[3,5,7,6,8,4,2,1]=>1010011
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[3,6,7,5,8,4,2,1]=>1010011
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[3,7,6,5,8,4,2,1]=>1010111
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>1010011
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[3,5,7,8,6,4,2,1]=>1010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[3,5,8,7,6,4,2,1]=>1010111
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[3,7,6,8,5,4,2,1]=>1011011
[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[6,3,1,2,4,5,7,8]=>[3,6,8,7,5,4,2,1]=>1011011
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[3,7,8,6,5,4,2,1]=>1011101
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>1011111
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>1100001
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,6,7,8,3,2,1]=>1101001
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[4,6,5,7,8,3,2,1]=>1100101
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,6,4,7,8,3,2,1]=>1100101
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[6,5,4,7,8,3,2,1]=>1101101
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[4,5,7,6,8,3,2,1]=>1100011
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,4,7,6,8,3,2,1]=>1101011
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[4,6,7,5,8,3,2,1]=>1100011
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[4,7,6,5,8,3,2,1]=>1100111
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,6,7,4,8,3,2,1]=>1100011
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[6,5,7,4,8,3,2,1]=>1100111
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,7,6,4,8,3,2,1]=>1100111
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[6,7,5,4,8,3,2,1]=>1101011
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[7,6,5,4,8,3,2,1]=>1101111
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>1100011
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[4,6,5,8,7,3,2,1]=>1100111
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[5,6,4,8,7,3,2,1]=>1100111
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[6,5,4,8,7,3,2,1]=>1101111
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[4,5,7,8,6,3,2,1]=>1100101
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[4,5,2,1,3,6,7,8]=>[5,4,7,8,6,3,2,1]=>1101101
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>1100111
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[4,6,7,8,5,3,2,1]=>1101001
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[4,7,6,8,5,3,2,1]=>1101011
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>1101011
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[4,7,8,6,5,3,2,1]=>1101101
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>1101111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>1110001
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[6,5,7,8,4,3,2,1]=>1110101
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[5,7,6,8,4,3,2,1]=>1110011
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[6,7,5,8,4,3,2,1]=>1110011
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[7,6,5,8,4,3,2,1]=>1110111
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>1110011
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[6,5,8,7,4,3,2,1]=>1110111
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>1110101
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>1110111
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>1111001
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[7,6,8,5,4,3,2,1]=>1111011
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>1111011
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>1111101
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9]=>10000000
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9]=>11000000
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9]=>11100000
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[5,4,3,2,1,6,7,8,9]=>11110000
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[6,5,4,3,2,1,7,8,9]=>11111000
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[7,6,5,4,3,2,1,8,9]=>11111100
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[8,7,6,5,4,3,2,1,9]=>11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9]=>01000000
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[2,1,4,3,5,6,7,8,9]=>10100000
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[7,8,9,5,6,4,3,2,1]=>[3,2,1,5,4,6,7,8,9]=>11010000
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[6,7,8,9,4,5,3,2,1]=>[4,3,2,1,6,5,7,8,9]=>11101000
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[5,4,3,2,1,7,6,8,9]=>11110100
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[6,5,4,3,2,1,8,7,9]=>11111010
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[7,6,5,4,3,2,1,9,8]=>11111101
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9]=>01000000
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9]=>00100000
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,5,1,6,7,8,9]=>00010000
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[2,3,4,5,6,1,7,8,9]=>00001000
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[2,3,4,5,6,7,1,8,9]=>00000100
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[2,3,4,5,6,7,8,1,9]=>00000010
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>00000001
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9,10]=>010000000
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[2,4,3,1,5,6,7,8,9]=>01100000
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9,10]=>001000000
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[2,3,5,4,1,6,7,8,9]=>00110000
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,1,6,7,8,9,10]=>000100000
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>[2,3,4,6,5,1,7,8,9]=>00011000
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,5,6,1,7,8,9,10]=>000010000
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>[2,3,4,5,7,6,1,8,9]=>00001100
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,4,5,6,7,1,8,9,10]=>000001000
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[2,3,4,5,6,8,7,1,9]=>00000110
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[2,3,4,5,6,7,8,1,9,10]=>000000100
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[2,3,4,5,6,7,9,8,1]=>00000011
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[2,3,4,5,6,7,8,9,1,10]=>000000010
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>000000001
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>101010101
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>[8,9,7,10,5,6,3,4,1,2]=>[3,2,4,1,6,5,8,7,10,9]=>011010101
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>[9,10,6,7,5,8,3,4,1,2]=>[2,1,5,4,6,3,8,7,10,9]=>100110101
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>[8,9,6,7,5,10,3,4,1,2]=>[3,2,5,4,6,1,8,7,10,9]=>010110101
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[9,10,7,8,4,5,3,6,1,2]=>[2,1,4,3,7,6,8,5,10,9]=>101001101
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>[8,9,7,10,4,5,3,6,1,2]=>[3,2,4,1,7,6,8,5,10,9]=>011001101
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>[9,10,6,7,4,5,3,8,1,2]=>[2,1,5,4,7,6,8,3,10,9]=>100101101
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[8,9,6,7,4,5,3,10,1,2]=>[3,2,5,4,7,6,8,1,10,9]=>010101101
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>[6,7,5,8,4,9,3,10,1,2]=>[5,4,6,3,7,2,8,1,10,9]=>000111101
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]=>[9,10,7,8,5,6,2,3,1,4]=>[2,1,4,3,6,5,9,8,10,7]=>101010011
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]=>[8,9,7,10,5,6,2,3,1,4]=>[3,2,4,1,6,5,9,8,10,7]=>011010011
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]=>[9,10,6,7,5,8,2,3,1,4]=>[2,1,5,4,6,3,9,8,10,7]=>100110011
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]=>[8,9,6,7,5,10,2,3,1,4]=>[3,2,5,4,6,1,9,8,10,7]=>010110011
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]=>[9,10,7,8,4,5,2,3,1,6]=>[2,1,4,3,7,6,9,8,10,5]=>101001011
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]=>[8,9,7,10,4,5,2,3,1,6]=>[3,2,4,1,7,6,9,8,10,5]=>011001011
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]=>[8,9,7,10,3,4,2,5,1,6]=>[3,2,4,1,8,7,9,6,10,5]=>011000111
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[9,10,6,7,4,5,2,3,1,8]=>[2,1,5,4,7,6,9,8,10,3]=>100101011
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]=>[8,9,6,7,4,5,2,3,1,10]=>[3,2,5,4,7,6,9,8,10,1]=>010101011
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[6,5,7,4,8,3,9,2,10,1]=>000011111
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]=>[10,11,9,12,7,8,5,6,3,4,1,2]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>01101010101
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]=>[11,12,8,9,7,10,5,6,3,4,1,2]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>10011010101
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]]=>[10,11,8,9,7,12,5,6,3,4,1,2]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>01011010101
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]=>[11,12,9,10,6,7,5,8,3,4,1,2]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>10100110101
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]=>[10,11,9,12,6,7,5,8,3,4,1,2]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>01100110101
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]=>[11,12,8,9,6,7,5,10,3,4,1,2]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>10010110101
[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]=>[10,11,8,9,6,7,5,12,3,4,1,2]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>01010110101
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>[11,12,9,10,7,8,4,5,3,6,1,2]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>10101001101
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]=>[10,11,9,12,7,8,4,5,3,6,1,2]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>01101001101
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>[11,12,8,9,7,10,4,5,3,6,1,2]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>10011001101
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]=>[10,11,8,9,7,12,4,5,3,6,1,2]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>01011001101
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]=>[11,12,9,10,6,7,4,5,3,8,1,2]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>10100101101
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]=>[10,11,9,12,6,7,4,5,3,8,1,2]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>01100101101
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]=>[11,12,8,9,6,7,4,5,3,10,1,2]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>10010101101
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>[10,11,8,9,6,7,4,5,3,12,1,2]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>01010101101
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[11,12,9,10,7,8,5,6,2,3,1,4]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>10101010011
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>[10,11,9,12,7,8,5,6,2,3,1,4]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>01101010011
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>[11,12,8,9,7,10,5,6,2,3,1,4]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>10011010011
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>[10,11,8,9,7,12,5,6,2,3,1,4]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>01011010011
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[11,12,9,10,6,7,5,8,2,3,1,4]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>10100110011
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>[10,11,9,12,6,7,5,8,2,3,1,4]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>01100110011
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>[11,12,8,9,6,7,5,10,2,3,1,4]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>10010110011
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>[10,11,8,9,6,7,5,12,2,3,1,4]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>01010110011
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]=>[11,12,9,10,7,8,4,5,2,3,1,6]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>10101001011
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]]=>[10,11,9,12,7,8,4,5,2,3,1,6]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>01101001011
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]=>[11,12,8,9,7,10,4,5,2,3,1,6]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>10011001011
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>[10,11,8,9,7,12,4,5,2,3,1,6]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>01011001011
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]=>[11,12,9,10,6,7,4,5,2,3,1,8]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>10100101011
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>[10,11,9,12,6,7,4,5,2,3,1,8]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>01100101011
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>[11,12,8,9,6,7,4,5,2,3,1,10]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>10010101011
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]=>[10,11,8,9,6,7,4,5,2,3,1,12]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>01010101011
[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>00000111111
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[1,3,5,7,9,10,8,6,4,2]=>001010101
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[1,8,9,7,6,5,4,3,2]=>01111101
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[7,8,6,5,4,3,2,1,9]=>11111010
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[1,9,10,8,7,6,5,4,3,2]=>011111101
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[1,7,9,8,6,5,4,3,2]=>01111011
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[1,8,7,9,6,5,4,3,2]=>01111011
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[6,8,7,5,4,3,2,1,9]=>11110110
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[7,6,8,5,4,3,2,1,9]=>11110110
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[8,9,7,6,5,4,3,2,1,10]=>111111010
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[2,1,9,8,7,6,5,4,3]=>10111111
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[3,2,1,9,8,7,6,5,4]=>11011111
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[4,3,2,1,9,8,7,6,5]=>11101111
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[5,4,3,2,1,9,8,7,6]=>11110111
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[6,5,4,3,2,1,9,8,7]=>11111011
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[1,2,9,8,7,6,5,4,3]=>00111111
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[2,1,10,9,8,7,6,5,4,3]=>101111111
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[2,3,1,9,8,7,6,5,4]=>01011111
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[3,2,1,10,9,8,7,6,5,4]=>110111111
[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]=>[7,6,8,9,1,2,3,4,5]=>[3,4,2,1,9,8,7,6,5]=>10101111
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[4,3,2,1,10,9,8,7,6,5]=>111011111
[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]=>[6,5,7,8,9,1,2,3,4]=>[4,5,3,2,1,9,8,7,6]=>11010111
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>111101111
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[5,4,6,7,8,9,1,2,3]=>[5,6,4,3,2,1,9,8,7]=>11101011
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[6,5,4,3,2,1,10,9,8,7]=>111110111
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>[6,7,5,4,3,2,1,9,8]=>11110101
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[7,6,5,4,3,2,1,10,9,8]=>111111011
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[8,7,6,5,4,3,2,1,10,9]=>111111101
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,9,8]=>00000001
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[3,2,4,5,6,7,8,9,1]=>01000001
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,9,8]=>10000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>0000000001
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[3,2,4,5,6,7,8,9,10,1]=>010000001
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[3,4,2,5,6,7,8,9,1]=>00100001
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[8,6,7,5,4,3,2,1,9]=>[2,4,3,5,6,7,8,9,1]=>00100001
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[2,3,1,4,5,6,7,9,8]=>01000001
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[1,3,2,4,5,6,7,9,8]=>01000001
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,10,9]=>100000001
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[5,6,4,7,3,8,2,9,1,10]=>000011110
[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[10,5,4,6,3,7,2,8,1,9]=>[1,6,7,5,8,4,9,3,10,2]=>000001111
[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[9,8,10,6,7,4,5,2,3,1]=>[2,3,1,5,4,7,6,9,8,10]=>010101010
[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]=>[10,8,7,9,5,6,3,4,1,2]=>[1,3,4,2,6,5,8,7,10,9]=>001010101
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]]=>[12,10,9,11,7,8,5,6,3,4,1,2]=>[1,3,4,2,6,5,8,7,10,9,12,11]=>00101010101
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]=>[9,7,8,5,6,3,4,1,2,10]=>[2,4,3,6,5,8,7,10,9,1]=>001010111
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[8,9,6,7,4,5,2,3,10,1]=>[3,2,5,4,7,6,9,8,1,10]=>010101110
[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]=>[11,9,10,7,8,5,6,3,4,1,2,12]=>[2,4,3,6,5,8,7,10,9,12,11,1]=>00101010111
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,8,9,7]=>00000001
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,7,8,9,6]=>00000001
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[1,2,3,4,6,7,8,9,5]=>00000001
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[1,2,3,5,6,7,8,9,4]=>00000001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[1,2,4,5,6,7,8,9,3]=>00000001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[1,3,4,5,6,7,8,9,2]=>00000001
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,9,8,7]=>00000011
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,9,10,8]=>000000001
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[1,2,3,4,5,8,7,9,6]=>00000011
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,6,8,9,10,7]=>000000001
[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,3,4,2,1,5]=>[1,2,3,4,7,6,8,9,5]=>00000101
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[1,2,3,4,5,7,8,9,10,6]=>000000001
[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[9,8,7,4,5,3,2,1,6]=>[1,2,3,6,5,7,8,9,4]=>00001001
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[1,2,3,4,6,7,8,9,10,5]=>000000001
[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]=>[9,8,5,6,4,3,2,1,7]=>[1,2,5,4,6,7,8,9,3]=>00010001
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[1,2,3,5,6,7,8,9,10,4]=>000000001
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[1,4,3,5,6,7,8,9,2]=>00100001
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[1,2,4,5,6,7,8,9,10,3]=>000000001
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[1,3,4,5,6,7,8,9,10,2]=>000000001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>10000001
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>11000001
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,6,7,8,9,4,3,2,1]=>11100001
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[6,7,8,9,5,4,3,2,1]=>11110001
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>11111001
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>11111101
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>100000001
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>110000001
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[5,6,7,8,9,10,4,3,2,1]=>111000001
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[6,5,4,3,1,2,7,8,9]=>[4,5,6,7,9,8,3,2,1]=>11000011
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>111100001
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[5,4,3,1,2,6,7,8,9]=>[5,6,7,9,8,4,3,2,1]=>11100011
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[7,8,9,10,6,5,4,3,2,1]=>111110001
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[6,7,9,8,5,4,3,2,1]=>11110011
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[8,9,10,7,6,5,4,3,2,1]=>111111001
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[7,9,8,6,5,4,3,2,1]=>11111011
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>111111101
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]=>[9,8,6,7,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9]=>00100000
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[1,2,3,5,4,6,7,8,9]=>00010000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[1,2,3,4,6,5,7,8,9]=>00001000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,7,6,8,9]=>00000100
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,8,7,9]=>00000010
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]=>[10,9,7,8,6,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9,10]=>001000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[1,2,3,5,4,6,7,8,9,10]=>000100000
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8,9,10]=>000010000
[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,4,5,3,2,1]=>[1,2,3,4,5,7,6,8,9,10]=>000001000
[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,6,8,7,9,10]=>000000100
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,9,8,10]=>000000010
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8,10]=>010101010
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[10,8,9,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,6,9,10,8]=>010101001
[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[12,10,11,8,9,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,6,9,8,11,12,10]=>01010101001
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2,9]=>01111110
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[10,11,9,8,7,6,5,4,3,2,1]=>1111111101
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[2,8,9,7,6,5,4,3,1]=>01111101
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[8,9,2,1,3,4,5,6,7]=>[2,1,8,9,7,6,5,4,3]=>10111101
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[2,8,7,6,5,4,3,1,9]=>01111110
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[2,1,8,7,6,5,4,3,9]=>10111110
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[3,5,6,7,8,9,4,2,1]=>10100001
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[2,4,5,6,7,8,9,3,1]=>01000001
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]=>[7,8,6,9,5,4,3,2,1]=>[3,2,4,1,5,6,7,8,9]=>01100000
[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]=>[6,7,8,5,9,4,3,2,1]=>[4,3,2,5,1,6,7,8,9]=>01110000
[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]=>[5,6,7,8,4,9,3,2,1]=>[5,4,3,2,6,1,7,8,9]=>01111000
[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[4,5,6,7,8,3,9,2,1]=>[6,5,4,3,2,7,1,8,9]=>01111100
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[7,6,5,4,3,2,8,1,9]=>01111110
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,7,6,5,4,3,2,9,1]=>01111111
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[8,7,9,6,5,4,3,2,1]=>11111011
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[8,7,6,5,9,4,3,2,1]=>11101111
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[8,7,6,5,4,3,9,2,1]=>10111111
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[6,8,7,9,5,4,3,2,1]=>11110011
[[[[[.,[[[.,.],.],[.,.]]],.],.],.],.]=>[5,2,3,4,1,6,7,8,9]=>[5,8,7,6,9,4,3,2,1]=>11100111
[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]=>[6,2,3,4,5,1,7,8,9]=>[4,8,7,6,5,9,3,2,1]=>11001111
[[[.,[[[[[.,.],.],.],.],[.,.]]],.],.]=>[7,2,3,4,5,6,1,8,9]=>[3,8,7,6,5,4,9,2,1]=>10011111
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>[2,8,7,6,5,4,3,9,1]=>00111111
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,8,7,6,5,4,3,2,10,1]=>011111111
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[6,9,8,7,5,4,3,2,1]=>11110111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[5,9,8,7,6,4,3,2,1]=>11101111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[4,9,8,7,6,5,3,2,1]=>11011111
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[3,9,8,7,6,5,4,2,1]=>10111111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>01111111
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[8,10,9,7,6,5,4,3,2,1]=>111111011
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[7,10,9,8,6,5,4,3,2,1]=>111110111
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[6,10,9,8,7,5,4,3,2,1]=>111101111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[5,10,9,8,7,6,4,3,2,1]=>111011111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[4,10,9,8,7,6,5,3,2,1]=>110111111
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[3,10,9,8,7,6,5,4,2,1]=>101111111
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>011111111
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[1,7,6,5,4,3,2,9,8]=>01111101
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[1,3,4,5,6,7,8,2,9]=>00000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[1,3,4,5,6,7,9,8,2]=>00000011
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[2,1,4,5,6,7,8,9,3]=>10000001
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>1111111111
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,7,9,8,6]=>00000011
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>[2,3,4,5,6,8,9,7,1]=>00000101
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[2,3,4,5,6,7,8,10,9,1]=>000000011
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[5,3,1,2,4,6,7,8,9]=>[5,7,9,8,6,4,3,2,1]=>11101011
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[6,2,3,4,5,7,8,9,10,1]=>[5,9,8,7,6,4,3,2,1,10]=>111011110
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[1,3,4,5,6,7,8,9,2,10]=>000000010
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[6,5,4,3,2,1,8,9,7]=>11111001
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[7,6,5,4,3,2,9,8,1]=>01111111
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[2,1,3,4,5,6,8,9,7]=>10000001
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>001111111
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[4,3,2,5,6,7,8,9,1]=>01100001
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[4,3,2,5,6,7,8,9,10,1]=>011000001
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[2,3,4,5,6,7,8,9,10,1,11]=>0000000010
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>00011111
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>00001111
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>00000111
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>00111111
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>000111111
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[1,2,4,9,8,7,6,5,3]=>00011111
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>000011111
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,9,8,7,6,4]=>00001111
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,1,2,3,5]=>[1,2,3,4,6,9,8,7,5]=>00000111
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>000000111
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[10,8,1,2,3,4,5,6,7,9]=>[1,3,10,9,8,7,6,5,4,2]=>001111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9,10,11]=>0100000000
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>[2,1,3,4,5,6,8,7,9]=>10000010
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[3,2,4,5,6,7,8,1,9]=>01000010
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[7,6,8,9,5,4,3,2,1]=>11110101
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[5,6,4,3,2,1,7,8,9]=>11101000
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[4,5,3,2,1,6,7,8,9]=>11010000
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[3,4,5,6,7,8,2,9,1]=>00000011
[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]=>[7,6,5,4,3,8,9,2,1]=>[3,4,5,6,7,2,1,8,9]=>10000100
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[6,5,7,8,9,4,3,2,1]=>11101001
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[1,6,7,8,9,5,4,3,2]=>01110001
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[2,3,9,8,7,6,5,4,1]=>00111111
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[7,8,6,5,4,3,2,9,1]=>01111011
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>[2,3,5,6,7,8,9,4,1]=>00100001
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[9,7,6,5,4,3,2,1,8,10]=>[2,4,5,6,7,8,9,10,3,1]=>010000001
[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[9,6,7,8,5,4,3,2,1]=>[1,4,3,2,5,6,7,8,9]=>01100000
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[2,3,4,5,6,7,1,9,8]=>00000101
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>[2,3,4,5,6,8,7,9,1]=>00000011
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[7,6,9,8,5,4,3,2,1]=>11110111
[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,9,2,10,1]=>[8,7,6,5,4,3,2,9,1,10]=>011111110
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[4,5,6,7,8,9,10,2,3,1]=>[7,6,5,4,3,2,1,9,8,10]=>111111010
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,1,11,10,9,8,7,6,5,4,3]=>1011111111
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,1,2,3,9]=>[2,3,4,5,6,9,8,7,1]=>00000111
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[7,6,5,4,3,2,8,9,1]=>01111101
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[1,8,10,9,7,6,5,4,3,2]=>011111011
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[1,3,4,5,6,7,8,10,9,2]=>000000011
[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[8,7,6,5,4,9,1,2,3]=>[2,3,4,5,6,1,9,8,7]=>00001011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[9,10,7,6,5,4,3,2,1,8]=>[2,1,4,5,6,7,8,9,10,3]=>100000001
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[3,4,2,1,5,6,7,8,9]=>10100000
[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]=>[9,7,8,5,6,4,3,2,1]=>[1,3,2,5,4,6,7,8,9]=>01010000
[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[7,6,8,5,9,4,3,2,1]=>[3,4,2,5,1,6,7,8,9]=>00110000
[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]=>[8,9,6,5,7,4,3,2,1]=>[2,1,4,5,3,6,7,8,9]=>10010000
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.
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
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
searching the database
Sorry, this map was not found in the database.