Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Mp00064: Permutations —reverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ 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]=>[1,3,2]=>01
[[.,.],[.,.]]=>[3,1,2]=>[2,1,3]=>10
[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>10
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>11
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>000
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>001
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>010
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>010
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>011
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>100
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>101
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>100
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>110
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>100
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>110
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[4,2,1,3]=>110
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>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]=>[1,2,3,5,4]=>0001
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,4,3,5]=>0010
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>0010
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>0011
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>0100
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>0101
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>0100
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>0110
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>0100
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>0110
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,5,3,2,4]=>0110
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>0101
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>0111
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>1000
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>1010
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>1011
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>1000
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>1001
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>1000
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>1100
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1100
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>1010
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>1110
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>1000
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>1010
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,1,3,2,4]=>1100
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>1100
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>1110
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>1100
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>1110
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>1010
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>1110
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>1001
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>1101
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[5,4,2,1,3]=>1101
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>1011
[[[[[.,.],.],.],.],.]=>[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]=>[1,2,3,4,6,5]=>00001
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>00010
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>00010
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>00011
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>00101
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>00100
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>00110
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>00100
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>00110
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>00110
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>00101
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>00111
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>01000
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>01001
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>01010
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>01011
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>01000
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>01001
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>01000
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>01100
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01100
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>01010
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>01000
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>01010
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>01100
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>01100
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>01110
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>01100
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>01110
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>01010
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>01110
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>01001
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>01101
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>01101
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>01011
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>01111
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10010
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10100
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10100
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10110
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10110
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10101
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>10000
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>10001
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>10010
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>10010
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>10011
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11010
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>10000
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>10001
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>11000
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>11001
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>11000
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>11001
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>10100
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>10101
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>10000
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>10100
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>11000
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>11000
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>11100
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>11000
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>11100
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>10100
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11100
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>10010
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>11010
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>11010
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>10110
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>10000
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>10010
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>10100
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>10100
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>10110
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>11000
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>11010
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>11000
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>11100
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>11000
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>11100
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>11100
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>11010
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>11110
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>11000
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>11010
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>11100
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>11100
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>11110
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>10100
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>10110
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11100
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11110
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>10010
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>11010
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>11010
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>10110
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>11110
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>10001
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>10101
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>11001
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>11001
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>11101
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>11001
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>11101
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>10101
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>11101
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>10011
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>11011
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>11011
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>10111
[[[[[[.,.],.],.],.],.],.]=>[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]=>[1,2,3,4,5,7,6]=>000001
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>000010
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>000010
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>000011
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>000100
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>000101
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>000100
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>000110
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>000100
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>000110
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>000110
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>000101
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>001000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>001001
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>001010
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>001000
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>001001
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>001000
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>001100
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001100
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>001010
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>001110
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>001000
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>001010
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>001100
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>001100
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>001110
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>001100
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>001110
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>001010
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>001110
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>001001
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>001101
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>001101
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>001011
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>001111
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010010
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010100
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010100
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010110
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010110
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010101
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>010000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>010001
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>010010
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>010010
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>010011
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011010
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>010000
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>010001
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>011000
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>011001
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>011000
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>011001
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>010100
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>010101
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>010000
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>010100
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>011000
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>011000
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>011100
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>011000
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>011100
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>010100
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011100
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>010010
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>011010
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>011010
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>010110
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>010000
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>010010
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>010100
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>010100
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>010110
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>011000
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>011010
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>011000
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>011100
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>011000
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>011100
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>011100
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>011010
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>011110
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>011000
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>011010
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>011100
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>011100
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>011110
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>010100
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>010110
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011100
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011110
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>010010
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>011010
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>011010
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>010110
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>011110
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>010001
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>010101
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>011001
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>011001
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>011101
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>011001
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>011101
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>010101
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>011101
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>010011
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>011011
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>011011
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>010111
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>011111
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100010
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100100
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100100
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100110
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100110
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100101
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101010
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>101000
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>101001
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>101000
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>101100
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101100
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>101010
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>101000
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>101010
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>101100
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>101100
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>101110
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101100
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101110
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>101010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101110
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>101001
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>101101
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101101
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>101011
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>100000
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>100001
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>100010
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>100010
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>100011
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>100100
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>100101
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>100100
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>100110
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>100100
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>100110
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>100110
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>100101
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>100111
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110010
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110100
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110100
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110110
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110110
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110101
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>100000
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>100001
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>100010
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>100010
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>100011
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>110000
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>110001
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>110010
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>110010
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>110011
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>110000
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>110001
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>110010
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>110010
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>110011
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>101000
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>101001
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>101010
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>101010
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>101011
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111010
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>100000
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>100001
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>101000
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>101001
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>110000
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>110001
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>110000
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>110001
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>111000
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>111001
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>110000
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>110001
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>111000
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>111001
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>101000
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>101001
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>111000
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>111001
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>100100
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>100101
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>110100
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>110101
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>110100
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>110101
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>101100
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>101101
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>100000
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>100100
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>101000
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>101000
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>101100
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>110000
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>110100
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>110000
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>111000
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>110000
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>111000
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>111000
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>110100
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>111100
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>110000
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>110100
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>111000
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>111000
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>111100
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>101000
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>101100
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>111000
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>111100
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>100100
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>110100
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>110100
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>101100
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111100
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>100010
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>101010
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>110010
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>110010
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>111010
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>110010
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>111010
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>101010
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>111010
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>100110
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>110110
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>110110
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>101110
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>100000
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>100010
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>100100
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>100100
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>100110
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>101000
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>101010
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>101000
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>101100
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>101000
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>101100
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>101100
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>101010
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>101110
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>110000
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>110010
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>110100
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>110100
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>110110
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>110000
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>110010
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>111000
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>111010
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>110000
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>111000
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>111000
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>110100
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>111100
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>110000
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>110100
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>111000
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>111000
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>111100
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>111000
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>111100
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>110100
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>111100
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>110010
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>111010
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>111010
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>110110
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>111110
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>110000
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>110010
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>110100
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>110100
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>110110
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>111000
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>111010
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>111000
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>111100
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>111000
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>111100
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>111100
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>111010
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>111110
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>101000
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>101010
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>101100
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>101100
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>101110
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>111000
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>111010
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>111100
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>111100
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>111110
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>100100
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>100110
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>110100
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>110110
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>110100
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>110110
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>101100
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>101110
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111100
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111110
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>100010
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>101010
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>110010
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>110010
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>111010
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>110010
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>111010
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>101010
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>111010
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>100110
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>110110
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>110110
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>101110
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111110
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>100001
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>100101
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>101001
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>101001
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>101101
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>110001
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>110101
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>110001
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>111001
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>110001
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>111001
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>111001
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>110101
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>111101
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>110001
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>110101
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>111001
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>111001
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>111101
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>101001
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>101101
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>111001
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>111101
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>100101
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>110101
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>110101
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>101101
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>111101
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>100011
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>101011
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>110011
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>110011
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>111011
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>110011
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>111011
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>101011
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>111011
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>100111
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>110111
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>110111
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>101111
[[[[[[[.,.],.],.],.],.],.],.]=>[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]=>[1,2,3,4,5,6,8,7]=>0000001
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>0000010
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>0000010
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>0000011
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>0000100
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>0000101
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>0000100
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>0000110
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>0000100
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>0000110
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>0000110
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>0000101
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>0000111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[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]=>[1,2,3,5,4,6,8,7]=>0001001
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>0001010
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>0001011
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0001000
[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>0001001
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7,8]=>0001100
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>0001101
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>0001000
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>0001100
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>0001100
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>0001010
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>0001110
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>0001000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>0001010
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>0001100
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>0001100
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>0001110
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>0001100
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>0001110
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>0001010
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>0001110
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>0001001
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>0001101
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>0001101
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>0001011
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>0001111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>0010001
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>0010010
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[1,2,4,3,5,8,7,6]=>0010011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[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]=>[1,2,4,3,6,5,8,7]=>0010101
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6,8]=>0010100
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>0010100
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>0010110
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>0010110
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[1,2,4,3,8,7,5,6]=>0010101
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>0010111
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0010000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>0010001
[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0010010
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>0010010
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>0010011
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7,8]=>0011000
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>0011001
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>0011010
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[1,2,5,4,3,8,7,6]=>0011011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0010000
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>0010001
[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7,8]=>0011000
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7,8]=>0011000
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>0010100
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[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]=>[1,2,7,3,4,5,6,8]=>0010000
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5,8]=>0010100
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6,8]=>0011000
[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5,8]=>0011000
[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[8,6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6,8]=>0011000
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6,8]=>0010100
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5,8]=>0010010
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5,8]=>0011010
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3,8]=>0011110
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>0010000
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>0010010
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[1,2,8,3,4,6,5,7]=>0010100
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[1,2,8,3,4,7,6,5]=>0010110
[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>0011000
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>0011010
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>0011000
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[1,2,8,3,6,5,4,7]=>0011100
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>0011000
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[1,2,8,3,7,4,6,5]=>0011100
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[1,2,8,3,7,5,4,6]=>0011100
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>0011010
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>0011110
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>0011000
[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>0011010
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[7,5,6,3,4,8,2,1]=>[1,2,8,4,3,6,5,7]=>0011100
[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>0011100
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>0011110
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>0010100
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>0011100
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[1,2,8,6,3,4,5,7]=>0010010
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,2,8,6,4,3,5,7]=>0011010
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[1,2,8,6,5,4,3,7]=>0011110
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>0010001
[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[1,2,8,7,3,4,6,5]=>0010101
[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[6,4,5,3,7,8,2,1]=>[1,2,8,7,3,5,4,6]=>0011001
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>0011101
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>0011101
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>0011101
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[1,2,8,7,6,3,4,5]=>0010011
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>0011011
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[1,2,8,7,6,4,3,5]=>0011011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,2,8,7,6,5,3,4]=>0010111
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>0011111
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>0100001
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[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]=>[1,3,2,4,5,8,6,7]=>0100010
[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,2,3,1]=>[1,3,2,4,5,8,7,6]=>0100011
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>0100110
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>0100100
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>0100110
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>0100110
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>0100111
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[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]=>[1,3,2,5,4,8,6,7]=>0101010
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>0101011
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0101000
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7,8]=>0101100
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[1,3,2,6,5,4,8,7]=>0101101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0101000
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>0101100
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>0101100
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5,8]=>0101010
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4,8]=>0101110
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>0101000
[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,2,3,1]=>[1,3,2,8,4,5,7,6]=>0101010
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>0101100
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>0101100
[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>0101100
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[1,3,2,8,5,4,7,6]=>0101110
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[1,3,2,8,6,4,5,7]=>0101010
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>0101110
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>0101001
[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,2,3,1]=>[1,3,2,8,7,4,6,5]=>0101101
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[1,3,2,8,7,5,4,6]=>0101101
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[1,3,2,8,7,6,4,5]=>0101011
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>0101111
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0100000
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0100001
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0100010
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>0100010
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>0100011
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0100100
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0100101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0100100
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>0100100
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>0100110
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>0100110
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>0100101
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>0100111
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>0110000
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>0110010
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>0110010
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>0110011
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[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]=>[1,4,3,2,8,5,6,7]=>0110100
[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>0110110
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>0110111
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0100000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0100001
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0100010
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>0100010
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>0100011
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>0110000
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>0110001
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>0110010
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>0110010
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[1,5,2,4,3,8,7,6]=>0110011
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>0110000
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>0110001
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>0110010
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>0110010
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>0110011
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>0101000
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[1,5,4,2,3,6,8,7]=>0101001
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6,8]=>0101010
[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>0101010
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[1,5,4,2,3,8,7,6]=>0101011
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7,8]=>0111000
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6,8]=>0111010
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[1,5,4,3,2,8,7,6]=>0111011
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0100000
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>0100001
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7,8]=>0110000
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[1,6,2,4,3,5,8,7]=>0110001
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7,8]=>0110000
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[1,6,2,5,3,4,8,7]=>0110001
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>0110000
[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7,8]=>0111000
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>0101000
[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>0101001
[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>0111000
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>0100101
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>0110100
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[1,6,5,3,2,4,8,7]=>0110101
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[1,6,5,4,2,3,8,7]=>0101101
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7,8]=>0111100
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[1,6,5,4,3,2,8,7]=>0111101
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0100000
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[8,5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5,8]=>0100100
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6,8]=>0101000
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5,8]=>0101000
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6,8]=>0110000
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>0110100
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>0110000
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6,8]=>0111000
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5,8]=>0110000
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>0111000
[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[8,5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5,8]=>0111000
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3,8]=>0111100
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0110000
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>0110100
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6,8]=>0111000
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6,8]=>0101000
[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>0111000
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6,8]=>0100100
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>0110100
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6,8]=>0111100
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5,8]=>0100010
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>0110010
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5,8]=>0110010
[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4,8]=>0111010
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>0101010
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3,8]=>0110110
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4,8]=>0110110
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3,8]=>0101110
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[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]=>[1,8,2,3,4,5,6,7]=>0100000
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[1,8,2,3,4,5,7,6]=>0100010
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[1,8,2,3,4,6,5,7]=>0100100
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,8,2,3,4,7,5,6]=>0100100
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>0100110
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>0101000
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>0101000
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>0101100
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>0101100
[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]=>[5,4,6,7,3,2,8,1]=>[1,8,2,3,7,6,4,5]=>0101010
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>0101110
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>0110000
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>0110100
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>0110100
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[1,8,2,4,3,7,6,5]=>0110110
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>0110000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[6,7,4,3,5,2,8,1]=>[1,8,2,5,3,4,7,6]=>0110010
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>0110000
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>0111000
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[1,8,2,6,4,3,5,7]=>0111000
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[7,4,3,5,6,2,8,1]=>[1,8,2,6,5,3,4,7]=>0110100
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>0110000
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[1,8,2,7,3,4,6,5]=>0110100
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>0111000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>0111000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>0111100
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>0111000
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[1,8,2,7,4,3,6,5]=>0111100
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[1,8,2,7,5,3,4,6]=>0110100
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>0111100
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>0110010
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>0111010
[.,[[.,[[[[.,.],[.,.]],.],.]],.]]=>[5,3,4,6,7,2,8,1]=>[1,8,2,7,6,4,3,5]=>0111010
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>0111110
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>0110000
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[1,8,3,2,4,5,7,6]=>0110010
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,8,3,2,4,7,5,6]=>0110100
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>0111000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>0111010
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>0111000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[1,8,3,2,7,5,4,6]=>0111100
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,8,3,2,7,6,4,5]=>0111010
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>0111110
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>0101000
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>0101010
[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[7,5,6,3,2,4,8,1]=>[1,8,4,2,3,6,5,7]=>0101100
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>0101100
[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>0101110
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>0111000
[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>0111010
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[6,5,7,2,3,4,8,1]=>[1,8,4,3,2,7,5,6]=>0111100
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>0111110
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[1,8,5,2,3,4,7,6]=>0100110
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0110100
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>0110110
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[1,8,5,4,2,3,6,7]=>0101100
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>0101110
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>0111100
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>0111110
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>0100010
[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[7,5,3,4,2,6,8,1]=>[1,8,6,2,4,3,5,7]=>0110010
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[1,8,6,2,5,3,4,7]=>0110010
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>0110010
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[1,8,6,3,2,5,4,7]=>0111010
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>0101010
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[1,8,6,5,3,2,4,7]=>0110110
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[1,8,6,5,4,2,3,7]=>0101110
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[1,8,6,5,4,3,2,7]=>0111110
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>0100001
[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]=>[5,6,4,3,2,7,8,1]=>[1,8,7,2,3,4,6,5]=>0100101
[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]=>[6,4,5,3,2,7,8,1]=>[1,8,7,2,3,5,4,6]=>0101001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>0101001
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>0101101
[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>0110001
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[1,8,7,2,5,4,3,6]=>0111001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>0110001
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>0111001
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[1,8,7,2,6,5,3,4]=>0110101
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>0111101
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>0110001
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[1,8,7,3,2,4,6,5]=>0110101
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>0111001
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>0111001
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[1,8,7,4,2,3,5,6]=>0101001
[.,[[[[.,[.,.]],[[.,.],.]],.],.]]=>[5,6,3,2,4,7,8,1]=>[1,8,7,4,2,3,6,5]=>0101101
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>0111001
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[1,8,7,4,3,2,6,5]=>0111101
[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]=>[6,4,3,2,5,7,8,1]=>[1,8,7,5,2,3,4,6]=>0100101
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>0110101
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>0111101
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>0100011
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>0110011
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>0111011
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>0110011
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>0111011
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>0101011
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>0111011
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>0100111
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>0110111
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[1,8,7,6,5,3,2,4]=>0110111
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,8,7,6,5,4,2,3]=>0101111
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>0111111
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[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]=>[2,1,3,4,5,7,6,8]=>1000010
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[2,1,3,4,5,8,6,7]=>1000010
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[2,1,3,4,5,8,7,6]=>1000011
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000100
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000100
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>1000110
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>1000101
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>1000111
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>1001011
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1001000
[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1001001
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>1001101
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>1001000
[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>1001010
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[2,1,3,8,4,6,5,7]=>1001100
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[2,1,3,8,4,7,5,6]=>1001100
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>1001110
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[2,1,3,8,5,4,6,7]=>1001100
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001110
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,1,3,8,6,4,5,7]=>1001010
[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[2,1,3,8,6,5,4,7]=>1001110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>1001001
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>1001101
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>1001101
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>1001011
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>1001111
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010010
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[2,1,4,3,5,8,7,6]=>1010011
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010100
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010110
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010110
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>1010101
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1010000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1010001
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>1011011
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1010001
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1011001
[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1011000
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1011001
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>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]=>[2,1,7,3,4,5,6,8]=>1010000
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>1011000
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>1010010
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>1010110
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3,8]=>1011110
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>1010000
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[2,1,8,3,4,7,5,6]=>1010100
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>1010110
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>1011010
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>1011000
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>1011000
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>1011100
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>1011100
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>1011010
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>1011110
[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>1011010
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1011100
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>1011100
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[2,1,8,4,3,7,6,5]=>1011110
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[2,1,8,5,3,4,6,7]=>1010100
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[2,1,8,5,3,4,7,6]=>1010110
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>1011100
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>1011110
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[7,4,5,3,6,8,1,2]=>[2,1,8,6,3,5,4,7]=>1011010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1011010
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,1,8,6,5,4,3,7]=>1011110
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>1010001
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>1010101
[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>1011001
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[2,1,8,7,3,6,4,5]=>1011001
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[2,1,8,7,3,6,5,4]=>1011101
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>1011001
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>1011101
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>1010101
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>1011101
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>1010011
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>1011011
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>1011011
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>1010111
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>1011111
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>1000000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>1000001
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>1000010
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>1000010
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>1000101
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>1000100
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>1000100
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>1000110
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>1000110
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>1000101
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>1000111
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>1001001
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>1001010
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>1001001
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>1001000
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>1001100
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>1001010
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>1001000
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>1001010
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>1001100
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>1001110
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>1001010
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>1001110
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>1001001
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[3,1,2,8,7,4,6,5]=>1001101
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>1001101
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>1001011
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>1001111
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>1100001
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>1100010
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>1100100
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>1100110
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100110
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>1100101
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>1100111
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1101000
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1101000
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1101100
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101100
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1101010
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>1101110
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>1101000
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>1101010
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[3,2,1,8,4,6,5,7]=>1101100
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>1101100
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>1101110
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>1101100
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>1101110
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>1101010
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101110
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>1101001
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>1101101
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[3,2,1,8,7,5,4,6]=>1101101
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>1101011
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>1101111
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>1000000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>1000001
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>1000010
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>1000010
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>1000011
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>1000100
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>1000101
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>1000100
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>1000110
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>1000100
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>1000110
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>1000110
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>1000101
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>1000111
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>1100000
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>1100010
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>1100101
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>1100100
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>1100110
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>1100110
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>1100101
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>1100111
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1100000
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1100001
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1100010
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1100010
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1100011
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1100100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1100101
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1100100
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1100110
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1100100
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>1100110
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1100110
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>1100101
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1100111
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>1010000
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>1010001
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>1010010
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>1010011
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>1010100
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>1010101
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>1010100
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>1010110
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>1010110
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>1010101
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>1010111
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>1110010
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>1110011
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110100
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>1110100
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>1110110
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110110
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>1110101
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[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]=>[5,1,2,3,4,6,7,8]=>1000000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>1000001
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>1000010
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>1000011
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>1010000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>1010001
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>1010010
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>1010011
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>1100000
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>1100001
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>1100010
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>1100010
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>1100011
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>1100000
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>1100010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>1100011
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>1110000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[5,1,4,3,2,6,8,7]=>1110001
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>1110011
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1100000
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1100011
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1110000
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1110001
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1110010
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>1110010
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1110011
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>1010000
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>1010001
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>1010010
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>1010010
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>1010011
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1110000
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1110001
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1110010
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1110010
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1110011
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>1001000
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>1001010
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>1001011
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>1101000
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[5,4,1,3,2,8,6,7]=>1101010
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>1101011
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1101000
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1101011
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>1011000
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>1011010
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[5,4,3,1,2,8,6,7]=>1011010
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>1011011
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>1111001
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>1111010
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>1111011
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>1000000
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>1000001
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8]=>1001000
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>1010000
[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[7,8,5,3,4,2,1,6]=>[6,1,2,4,3,5,8,7]=>1010001
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7,8]=>1010000
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[6,1,2,5,4,3,8,7]=>1011001
[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6]=>[6,1,3,2,4,5,8,7]=>1100001
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>1101001
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7,8]=>1100000
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>1100001
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7,8]=>1100000
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>1100001
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>1110001
[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>1101001
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>1111001
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1100000
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1110000
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1110001
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[6,2,1,5,3,4,8,7]=>1110001
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>1111000
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[6,2,1,5,4,3,8,7]=>1111001
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>1010000
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>1010001
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>1011001
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1110000
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1110001
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1111000
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1111001
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>1001000
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>1101000
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[6,4,1,3,2,5,8,7]=>1101001
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1101000
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1101001
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>1011000
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>1011001
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1111000
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1111001
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>1000101
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>1010101
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,5,1,4,2,3,8,7]=>1100101
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7,8]=>1110100
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,5,1,4,3,2,8,7]=>1110101
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1100101
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1110101
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>1010101
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1110100
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1110101
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>1001100
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>1001101
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>1101101
[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1101100
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1101101
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>1011100
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>1011101
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>1000000
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5,8]=>1000100
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6,8]=>1001000
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5,8]=>1001000
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>1001100
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6,8]=>1010000
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6,8]=>1010000
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>1010000
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>1011000
[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>1011000
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>1010100
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>1011100
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6,8]=>1100000
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>1101000
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6,8]=>1100000
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>1110000
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[8,6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6,8]=>1110000
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>1110000
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6,8]=>1101000
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>1100000
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>1110000
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3,8]=>1111000
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4,8]=>1111000
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>1101000
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3,8]=>1110100
[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4,8]=>1110100
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3,8]=>1101100
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2,8]=>1111100
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1100000
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6,8]=>1101000
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1110000
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1110100
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1111000
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>1111000
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4,8]=>1110100
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3,8]=>1111100
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>1010000
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>1010100
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>1011000
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1110000
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1110100
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1111000
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1111000
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>1001000
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>1101000
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>1101100
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>1011000
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>1011100
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1111000
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1111100
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>1000100
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>1010100
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>1100100
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>1100100
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>1010100
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1110100
[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>1101100
[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>1011100
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111100
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>1000010
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4,8]=>1001010
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>1011010
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>1100010
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>1110010
[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[8,3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3,8]=>1110010
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3,8]=>1111010
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4,8]=>1011010
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1110010
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4,8]=>1111010
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1101010
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>1011010
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1111010
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>1000110
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>1010110
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>1100110
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>1100110
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>1110110
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1100110
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>1110110
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1110110
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>1001110
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>1101110
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1101110
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>1011110
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>1000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6]=>1000010
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[8,1,2,3,4,6,5,7]=>1000100
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[8,1,2,3,4,7,5,6]=>1000100
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>1000110
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>1001000
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>1001010
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[8,1,2,3,6,4,5,7]=>1001000
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>1001100
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>1001000
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>1001100
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>1001110
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>1010000
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>1010010
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>1010100
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>1010110
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>1010000
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[8,1,2,5,3,4,7,6]=>1010010
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>1011000
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[8,1,2,6,3,4,5,7]=>1010000
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[8,1,2,6,5,3,4,7]=>1010100
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>1011100
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>1010000
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[8,1,2,7,3,4,6,5]=>1010100
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[8,1,2,7,3,5,4,6]=>1011000
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>1011000
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>1011100
[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[8,1,2,7,4,3,6,5]=>1011100
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>1011100
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>1010010
[[.,[.,[[[.,[[.,.],.]],.],.]]],.]=>[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>1011010
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>1011110
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>1100000
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>1100010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>1100100
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>1100110
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>1101000
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>1101010
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>1101100
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>1101100
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[8,1,3,2,7,5,4,6]=>1101100
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[8,1,3,2,7,6,4,5]=>1101010
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[8,1,3,2,7,6,5,4]=>1101110
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>1100000
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[6,7,5,3,2,4,1,8]=>[8,1,4,2,3,5,7,6]=>1100010
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[8,1,4,2,3,6,5,7]=>1100100
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[8,1,4,2,3,7,5,6]=>1100100
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>1100110
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>1110000
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>1110010
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>1110100
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>1110100
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>1110110
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[8,1,5,2,3,4,6,7]=>1100000
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[8,1,5,2,4,3,7,6]=>1110010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>1110000
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>1110010
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[8,1,5,4,2,3,6,7]=>1101000
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>1111000
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[8,1,5,4,3,2,7,6]=>1111010
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>1100000
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[8,1,6,2,3,5,4,7]=>1101000
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[8,1,6,2,4,3,5,7]=>1110000
[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[8,1,6,3,2,4,5,7]=>1110000
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>1111000
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>1101000
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[8,1,6,5,2,3,4,7]=>1100100
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[8,1,6,5,4,3,2,7]=>1111100
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,1,7,2,3,4,5,6]=>1100000
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>1101000
[[.,[[.,[.,[[[.,.],.],.]]],.]],.]=>[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>1101100
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[6,5,3,4,2,7,1,8]=>[8,1,7,2,4,3,5,6]=>1110000
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>1110100
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[8,1,7,2,5,3,4,6]=>1110000
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>1111000
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>1110000
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>1111000
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[8,1,7,2,6,4,3,5]=>1111000
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>1111100
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[8,1,7,3,2,4,5,6]=>1110000
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[6,4,5,2,3,7,1,8]=>[8,1,7,3,2,5,4,6]=>1111000
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[8,1,7,3,2,6,4,5]=>1111000
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>1111100
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>1101000
[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>1101100
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>1111100
[[.,[[[.,[[.,.],.]],[.,.]],.]],.]=>[6,3,4,2,5,7,1,8]=>[8,1,7,5,2,4,3,6]=>1110100
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>1110100
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[8,1,7,5,4,2,3,6]=>1101100
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[8,1,7,5,4,3,2,6]=>1111100
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>1100010
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[8,1,7,6,2,4,3,5]=>1110010
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>1111010
[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>1110010
[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[8,1,7,6,4,2,3,5]=>1101010
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>1111010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>1100110
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[8,1,7,6,5,2,4,3]=>1110110
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>1110110
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[8,1,7,6,5,4,2,3]=>1101110
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>1111110
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>1100000
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[8,2,1,3,4,5,7,6]=>1100010
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[8,2,1,3,4,6,5,7]=>1100100
[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[8,2,1,3,4,7,5,6]=>1100100
[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,3,1,2,8]=>[8,2,1,3,6,4,5,7]=>1101000
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>1101100
[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,3,1,2,8]=>[8,2,1,3,7,4,6,5]=>1101100
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[8,2,1,3,7,6,4,5]=>1101010
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[8,2,1,3,7,6,5,4]=>1101110
[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[6,7,5,3,4,1,2,8]=>[8,2,1,4,3,5,7,6]=>1110010
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1110100
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[8,2,1,4,3,7,5,6]=>1110100
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[5,6,7,3,4,1,2,8]=>[8,2,1,4,3,7,6,5]=>1110110
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[8,2,1,5,4,3,7,6]=>1111010
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>1110000
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1111000
[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[7,4,3,5,6,1,2,8]=>[8,2,1,6,5,3,4,7]=>1110100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>1110000
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[8,2,1,7,3,5,4,6]=>1111000
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[8,2,1,7,4,3,5,6]=>1111000
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[8,2,1,7,4,3,6,5]=>1111100
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>1110100
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>1111100
[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>1110010
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[8,2,1,7,6,3,5,4]=>1111010
[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[5,3,4,6,7,1,2,8]=>[8,2,1,7,6,4,3,5]=>1111010
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[4,3,5,6,7,1,2,8]=>[8,2,1,7,6,5,3,4]=>1110110
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>1111110
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>1010000
[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>1010010
[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>1010100
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[8,3,1,2,4,7,5,6]=>1010100
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[8,3,1,2,4,7,6,5]=>1010110
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>1011000
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>1011010
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>1011000
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>1011100
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>1011000
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[8,3,1,2,7,6,4,5]=>1011010
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>1011110
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1110000
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[8,3,2,1,4,5,7,6]=>1110010
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>1110100
[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[8,3,2,1,4,7,5,6]=>1110100
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>1110110
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1111000
[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1111010
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1111000
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>1111100
[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>1111000
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>1111100
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>1111010
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>1111110
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>1001000
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[6,5,7,3,2,1,4,8]=>[8,4,1,2,3,7,5,6]=>1001100
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>1101000
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[8,4,1,3,2,5,7,6]=>1101010
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[8,4,1,3,2,6,5,7]=>1101100
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[8,4,1,3,2,7,6,5]=>1101110
[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1101000
[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>1101010
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1101100
[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[6,5,7,3,1,2,4,8]=>[8,4,2,1,3,7,5,6]=>1101100
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>1101110
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[8,4,3,1,2,5,7,6]=>1011010
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>1011100
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>1011110
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1111000
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>1111010
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1111100
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>1111100
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>1111110
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>1000100
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[8,5,1,2,4,3,6,7]=>1010100
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[8,5,1,2,4,3,7,6]=>1010110
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>1100100
[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>1100110
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>1100100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>1100110
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1100100
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[8,5,2,1,4,3,6,7]=>1110100
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1110110
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>1010100
[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[6,7,4,2,1,3,5,8]=>[8,5,3,1,2,4,7,6]=>1010110
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1110100
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1110110
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>1001100
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>1001110
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[8,5,4,1,3,2,6,7]=>1101100
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[8,5,4,1,3,2,7,6]=>1101110
[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1101100
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[8,5,4,2,1,3,7,6]=>1101110
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111100
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>1111110
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>1000010
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[8,6,1,2,3,5,4,7]=>1001010
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>1010010
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>1010010
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>1011010
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[8,6,1,3,2,4,5,7]=>1100010
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>1100010
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>1110010
[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>1100010
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>1110010
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>1110010
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>1111010
[[[[.,.],[.,[[.,.],.]]],[.,.]],.]=>[7,4,5,3,1,2,6,8]=>[8,6,2,1,3,5,4,7]=>1101010
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1110010
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>1110010
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>1111010
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[8,6,3,1,2,5,4,7]=>1011010
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1110010
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>1111010
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>1101010
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1101010
[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[8,6,4,3,1,2,5,7]=>1011010
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1111010
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>1000110
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[8,6,5,1,2,4,3,7]=>1010110
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[8,6,5,1,3,2,4,7]=>1100110
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>1110110
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1100110
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[8,6,5,2,1,4,3,7]=>1110110
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1110110
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[8,6,5,4,1,2,3,7]=>1001110
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>1101110
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1101110
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>1011110
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111110
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>1000001
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>1000101
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>1001001
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[8,7,1,2,3,6,5,4]=>1001101
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[8,7,1,2,4,3,5,6]=>1010001
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[8,7,1,2,4,3,6,5]=>1010101
[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[6,4,3,5,2,1,7,8]=>[8,7,1,2,5,3,4,6]=>1010001
[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>1011001
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>1010001
[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>1010101
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>1011101
[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[6,5,4,2,3,1,7,8]=>[8,7,1,3,2,4,5,6]=>1100001
[[[.,[[.,.],[.,[[.,.],.]]]],.],.]=>[5,6,4,2,3,1,7,8]=>[8,7,1,3,2,4,6,5]=>1100101
[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>1101001
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>1101001
[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[6,5,3,2,4,1,7,8]=>[8,7,1,4,2,3,5,6]=>1100001
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[8,7,1,4,3,2,5,6]=>1110001
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[8,7,1,4,3,2,6,5]=>1110101
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[8,7,1,5,2,3,4,6]=>1100001
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[8,7,1,5,4,2,3,6]=>1101001
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>1100001
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>1101001
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[8,7,1,6,2,5,3,4]=>1110001
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>1111001
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[8,7,1,6,4,2,3,5]=>1101001
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>1111001
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>1100101
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[8,7,1,6,5,2,4,3]=>1110101
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[8,7,1,6,5,3,2,4]=>1110101
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>1111101
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1100001
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>1100101
[[[[.,.],[.,[[.,.],[.,.]]]],.],.]=>[6,4,5,3,1,2,7,8]=>[8,7,2,1,3,5,4,6]=>1101001
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>1101001
[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[4,5,6,3,1,2,7,8]=>[8,7,2,1,3,6,5,4]=>1101101
[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>1110001
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>1110101
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>[8,7,2,1,5,3,4,6]=>1110001
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[8,7,2,1,5,4,3,6]=>1111001
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>1110001
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>1111101
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>1010101
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[8,7,3,1,2,6,4,5]=>1011001
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1110001
[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>1110101
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[6,4,5,1,2,3,7,8]=>[8,7,3,2,1,5,4,6]=>1111001
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>1111001
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>1111101
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[8,7,4,1,2,3,5,6]=>1001001
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>1001101
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[8,7,4,1,3,2,6,5]=>1101101
[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[6,5,3,1,2,4,7,8]=>[8,7,4,2,1,3,5,6]=>1101001
[[[[[.,.],[.,.]],[[.,.],.]],.],.]=>[5,6,3,1,2,4,7,8]=>[8,7,4,2,1,3,6,5]=>1101101
[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1111001
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>1111101
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>1000101
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[8,7,5,1,2,4,3,6]=>1010101
[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[8,7,5,1,4,2,3,6]=>1100101
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>1110101
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1100101
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>1010101
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1110101
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>1001101
[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>1101101
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>1011101
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111101
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>1000011
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>1001011
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>1010011
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>1010011
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>1011011
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>1100011
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>1101011
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>1100011
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>1110011
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>1100011
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>1110011
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>1110011
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>1101011
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>1111011
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>1100011
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>1110011
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[8,7,6,2,1,5,3,4]=>1110011
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>1010011
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1110011
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[8,7,6,3,2,1,5,4]=>1111011
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>1001011
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>1101011
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>1101011
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>1011011
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>1111011
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>1000111
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>1010111
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>1100111
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>1100111
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>1110111
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>1100111
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>1110111
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>1010111
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>1110111
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>1001111
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>1101111
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>1101111
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>1011111
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[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]=>[1,2,3,4,5,6,7,9,8]=>00000001
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,9,8,7]=>00000011
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[1,2,3,4,5,9,8,7,6]=>00000111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[1,2,3,4,9,8,7,6,5]=>00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[1,2,3,9,8,7,6,5,4]=>00011111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[1,2,9,8,7,6,5,4,3]=>00111111
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2]=>01111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[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]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7,9]=>00000010
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,9,8]=>00000101
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[1,2,3,4,5,6,10,9,8,7]=>000000111
[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[7,8,9,5,6,4,3,2,1]=>[1,2,3,4,6,5,9,8,7]=>00001011
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[6,7,8,9,4,5,3,2,1]=>[1,2,3,5,4,9,8,7,6]=>00010111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[1,2,3,4,10,9,8,7,6,5]=>000011111
[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[5,6,7,8,9,3,4,2,1]=>[1,2,4,3,9,8,7,6,5]=>00101111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[1,2,3,10,9,8,7,6,5,4]=>000111111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[1,3,2,9,8,7,6,5,4]=>01011111
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[1,2,10,9,8,7,6,5,4,3]=>001111111
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[2,1,9,8,7,6,5,4,3]=>10111111
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[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]=>[1,2,3,4,5,6,9,7,8]=>00000010
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[1,2,3,4,5,9,6,7,8]=>00000100
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[1,2,3,4,9,5,6,7,8]=>00001000
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[1,2,3,9,4,5,6,7,8]=>00010000
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[1,2,9,3,4,5,6,7,8]=>00100000
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[1,9,2,3,4,5,6,7,8]=>01000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8]=>10000000
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,10,8,9]=>000000010
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[1,2,3,4,5,9,7,6,8]=>00000110
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[1,2,3,4,5,6,10,7,8,9]=>000000100
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[1,2,3,4,9,6,5,7,8]=>00001100
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[1,2,3,4,5,10,6,7,8,9]=>000001000
[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]=>[8,7,6,4,5,9,3,2,1]=>[1,2,3,9,5,4,6,7,8]=>00011000
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[1,2,3,4,10,5,6,7,8,9]=>000010000
[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]=>[8,7,6,5,3,4,9,2,1]=>[1,2,9,4,3,5,6,7,8]=>00110000
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[1,2,3,10,4,5,6,7,8,9]=>000100000
[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,2,3,9,1]=>[1,9,3,2,4,5,6,7,8]=>01100000
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[1,2,10,3,4,5,6,7,8,9]=>001000000
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[9,2,1,3,4,5,6,7,8]=>11000000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[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]=>[2,1,4,3,6,5,10,7,9,8]=>101010110
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>[9,10,6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6,10,9]=>101011001
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[9,10,7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7,10,9]=>101100101
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>[8,9,7,10,4,5,3,6,1,2]=>[2,1,6,3,5,4,10,7,9,8]=>101100110
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]=>[9,10,7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7,10,9]=>110010101
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]=>[8,9,7,10,5,6,2,3,1,4]=>[4,1,3,2,6,5,10,7,9,8]=>110010110
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]=>[9,10,6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6,10,9]=>110011001
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]=>[8,9,6,7,4,5,2,3,1,10]=>[10,1,3,2,5,4,7,6,9,8]=>110101010
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[10,1,9,2,8,3,7,4,6,5]=>111110000
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[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]=>[2,1,4,3,6,5,8,7,12,9,11,10]=>10101010110
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]=>[11,12,8,9,7,10,5,6,3,4,1,2]=>[2,1,4,3,6,5,10,7,9,8,12,11]=>10101011001
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]=>[11,12,9,10,6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6,10,9,12,11]=>10101100101
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]=>[10,11,9,12,6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6,12,9,11,10]=>10101100110
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>[11,12,9,10,7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7,10,9,12,11]=>10110010101
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]=>[10,11,9,12,7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7,12,9,11,10]=>10110010110
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>[11,12,8,9,7,10,4,5,3,6,1,2]=>[2,1,6,3,5,4,10,7,9,8,12,11]=>10110011001
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[11,12,9,10,7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7,10,9,12,11]=>11001010101
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>[10,11,9,12,7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7,12,9,11,10]=>11001010110
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>[11,12,8,9,7,10,5,6,2,3,1,4]=>[4,1,3,2,6,5,10,7,9,8,12,11]=>11001011001
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>[11,12,9,10,6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6,10,9,12,11]=>11001100101
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>[10,11,9,12,6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6,12,9,11,10]=>11001100110
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]=>[10,11,8,9,6,7,4,5,2,3,1,12]=>[12,1,3,2,5,4,7,6,9,8,11,10]=>11010101010
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[9,7,5,3,1,2,4,6,8,10]=>101010100
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9]=>11111110
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2,9]=>10111110
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,2,3]=>01011111
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2,10]=>101111110
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3,9]=>11011110
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2,9]=>11011110
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[1,9,8,7,6,5,3,2,4]=>01101111
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[1,9,8,7,6,5,2,4,3]=>01101111
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,2,3]=>010111111
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8]=>11111101
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7]=>11111011
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6]=>11110111
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[4,3,2,1,9,8,7,6,5]=>11101111
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[3,2,1,9,8,7,6,5,4]=>11011111
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9]=>11111100
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>111111101
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,9,8]=>111111011
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>111110111
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>111101111
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[4,3,2,1,10,9,8,7,6,5]=>111011111
[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[4,3,5,6,7,8,9,1,2]=>[2,1,9,8,7,6,5,3,4]=>10101111
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[3,2,1,10,9,8,7,6,5,4]=>110111111
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[2,1,10,9,8,7,6,5,4,3]=>101111111
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,8,7]=>10000010
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[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]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,9,8]=>100000010
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[9,1,2,3,4,5,8,6,7]=>10000100
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[8,6,7,5,4,3,2,1,9]=>[9,1,2,3,4,5,7,6,8]=>10000100
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[2,1,3,4,5,6,9,7,8]=>10000010
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7,9]=>10000010
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[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]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]=>[9,7,8,5,6,3,4,1,2,10]=>[10,2,1,4,3,6,5,8,7,9]=>111010100
[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]=>[11,9,10,7,8,5,6,3,4,1,2,12]=>[12,2,1,4,3,6,5,8,7,10,9,11]=>11101010100
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9]=>10000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9]=>10000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9]=>10000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9]=>10000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9]=>10000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>10000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9,10]=>100000000
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8,9]=>11000000
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9,10]=>100000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9,10]=>100000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9,10]=>100000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9,10]=>100000000
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6,9]=>10000100
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9,10]=>100000000
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[9,8,1,2,3,4,5,6,7]=>10000001
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[9,8,7,1,2,3,4,5,6]=>10000011
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[9,8,7,6,1,2,3,4,5]=>10000111
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[9,8,7,6,5,1,2,3,4]=>10001111
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3]=>10011111
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2]=>10111111
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[10,9,1,2,3,4,5,6,7,8]=>100000001
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[10,9,8,1,2,3,4,5,6,7]=>100000011
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[10,9,8,7,1,2,3,4,5,6]=>100000111
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>100001111
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,2,3,4]=>100011111
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,3,4]=>11001111
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,2,3]=>100111111
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3]=>11011111
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2]=>101111111
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]=>[9,8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8,9]=>00000100
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8,9]=>00001000
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8,9]=>00010000
[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8,9]=>00100000
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8,9]=>01000000
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8,10]=>000000010
[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]=>[10,9,7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7,9,10]=>000000100
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8,9,10]=>000001000
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[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]=>[1,2,3,5,4,6,7,8,9,10]=>000100000
[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8,9,10]=>001000000
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8,9,10]=>010000000
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[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]=>[3,1,2,5,4,7,6,9,8,10]=>100101010
[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[10,8,9,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,9,8,10]=>101001010
[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[10,8,9,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,9,8,10]=>101010010
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[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]=>[11,10,9,8,7,6,5,4,3,1,2]=>1011111111
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[9,7,6,5,4,3,1,2,8]=>10111110
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[8,9,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,9,8]=>10111101
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[1,9,7,6,5,4,3,2,8]=>01111110
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,9,8]=>01111101
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[4,2,1,3,5,6,7,8,9]=>[9,8,7,6,5,3,1,2,4]=>10101111
[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[5,3,2,1,4,6,7,8,9]=>[9,8,7,6,4,1,2,3,5]=>10010111
[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]=>[6,4,3,2,1,5,7,8,9]=>[9,8,7,5,1,2,3,4,6]=>10001011
[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[9,8,6,1,2,3,4,5,7]=>10000101
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[9,7,1,2,3,4,5,6,8]=>10000010
[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]=>[7,8,6,9,5,4,3,2,1]=>[1,2,3,4,5,9,6,8,7]=>00000110
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[1,9,2,8,7,6,5,4,3]=>01111110
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[9,1,8,7,6,5,4,3,2]=>11111110
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,3,2]=>11011111
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[9,8,7,6,1,5,4,3,2]=>11110111
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[9,8,1,7,6,5,4,3,2]=>11111101
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[10,1,9,8,7,6,5,4,3,2]=>111111110
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[9,8,7,6,5,3,2,1,4]=>11101111
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[9,8,7,6,4,3,2,1,5]=>11110111
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[9,8,7,5,4,3,2,1,6]=>11111011
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[9,8,6,5,4,3,2,1,7]=>11111101
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8]=>11111110
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,1,3]=>110111111
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,2,1,4]=>111011111
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[10,9,8,7,6,4,3,2,1,5]=>111101111
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[10,9,8,7,5,4,3,2,1,6]=>111110111
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[10,9,8,6,5,4,3,2,1,7]=>111111011
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,2,1,8]=>111111101
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,1,9]=>111111110
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3,9]=>10111110
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7,9]=>01000000
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7,9]=>11000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,9,8]=>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]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>[9,3,1,2,4,5,6,7,8]=>10100000
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[10,2,1,3,4,5,6,7,8,9]=>110000000
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,2,3,1]=>[1,3,2,4,5,6,9,7,8]=>01000010
[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[7,2,3,4,5,6,8,9,1]=>[1,9,8,6,5,4,3,2,7]=>01111101
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[7,8,2,3,4,5,6,9,1]=>[1,9,6,5,4,3,2,8,7]=>01111110
[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[6,2,3,4,5,7,8,9,10,1]=>[1,10,9,8,7,5,4,3,2,6]=>011110111
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[1,9,2,3,4,5,6,7,8,10]=>010000000
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[9,2,1,8,7,6,5,4,3]=>11111110
[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]=>[8,9,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,9,8]=>01000001
[.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]]=>[6,7,8,5,4,3,2,9,1]=>[1,9,2,3,4,5,8,7,6]=>01000110
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,9,8]=>10000001
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[9,1,2,3,4,5,8,7,6]=>10000110
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,9,8,7]=>100000110
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[1,11,2,3,4,5,6,7,8,9,10]=>0100000000
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9]=>11111000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9]=>11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>11100000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7,9]=>11111100
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[10,8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8,10]=>111111100
[[[[[.,[[.,.],.]],.],.],.],[[.,.],.]]=>[8,9,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,9,8]=>11011101
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,11,9,10]=>0000000010
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[9,8,10,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,10,8,9]=>100000010
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,9,8]=>01000001
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[1,9,2,3,4,5,6,8,7]=>01000010
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[1,10,2,3,4,5,6,7,9,8]=>010000010
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[9,1,8,2,3,4,5,6,7]=>11000000
[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[6,5,4,3,2,7,1,8,9]=>[9,8,1,7,2,3,4,5,6]=>11000001
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,7,8]=>11111100
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>[9,6,1,2,3,4,5,7,8]=>10000100
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[2,1,9,3,4,5,6,7,8]=>10100000
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>[9,1,3,2,4,5,6,7,8]=>11000000
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,4,3]=>11101111
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[4,5,6,7,8,9,10,2,3,1]=>[1,3,2,10,9,8,7,6,5,4]=>010111111
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,11,10]=>1111111101
[[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]]=>[9,10,2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2,10,9]=>101111101
[[[[[[.,.],[.,.]],.],.],.],[[.,.],.]]=>[8,9,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,9,8]=>11011101
[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[8,7,6,1,2,3,4,5,9]=>[9,5,4,3,2,1,6,7,8]=>11111000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3,10]=>110111110
[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]=>[9,10,11,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,11,10,9]=>0000000011
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[9,10,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,10,9]=>100000001
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[11,9,10,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,10,9,11]=>0000000010
[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]=>[9,7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7,9]=>00001010
[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]=>[8,9,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,9,8]=>00001001
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
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
searching the database
Sorry, this map was not found in the database.