Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00066: Permutations —inverse⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[2,1]=>[2,1]=>1
[[.,.],.]=>[1,2]=>[1,2]=>[1,2]=>0
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>11
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>01
[[.,.],[.,.]]=>[3,1,2]=>[2,3,1]=>[3,1,2]=>10
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>10
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>00
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>111
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,1,2]=>[1,4,3,2]=>011
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,2,3,1]=>[4,1,3,2]=>101
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,1,3]=>[3,1,4,2]=>101
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>[1,2,4,3]=>001
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,4,2,1]=>[4,3,1,2]=>110
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[3,4,1,2]=>[1,4,2,3]=>010
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,2,4,1]=>[4,2,1,3]=>110
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,3,4,1]=>[4,1,2,3]=>100
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>110
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>[1,3,2,4]=>010
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,3,1,4]=>[3,1,2,4]=>100
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>100
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>000
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>1111
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,5,4,3,2]=>0111
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,4,2,3,1]=>[5,1,4,3,2]=>1011
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[4,1,5,3,2]=>1011
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>0011
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,3,4,2,1]=>[5,4,1,3,2]=>1101
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,3,4,1,2]=>[1,5,2,4,3]=>0101
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[5,3,1,4,2]=>1101
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[5,1,2,4,3]=>1001
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[4,3,1,5,2]=>1101
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,4,2,5,3]=>0101
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,2,3,1,4]=>[4,1,2,5,3]=>1001
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[3,1,2,5,4]=>1001
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,2,3,5,4]=>0001
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[4,5,3,2,1]=>[5,4,3,1,2]=>1110
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[1,5,4,2,3]=>0110
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,5,2,3,1]=>[5,1,4,2,3]=>1010
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[4,5,2,1,3]=>[4,1,5,2,3]=>1010
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[4,5,1,2,3]=>[1,2,5,3,4]=>0010
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[4,3,5,2,1]=>[5,4,2,1,3]=>1110
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[4,3,5,1,2]=>[1,5,3,2,4]=>0110
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,4,5,2,1]=>[5,4,1,2,3]=>1100
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,4,5,1,2]=>[1,5,2,3,4]=>0100
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,3,2,5,1]=>[5,3,2,1,4]=>1110
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,2,3,5,1]=>[5,1,3,2,4]=>1010
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,4,2,5,1]=>[5,3,1,2,4]=>1100
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,2,4,5,1]=>[5,2,1,3,4]=>1100
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[5,1,2,3,4]=>1000
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>1110
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[1,4,3,2,5]=>0110
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,2,3,1,5]=>[4,1,3,2,5]=>1010
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[3,1,4,2,5]=>1010
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[1,2,4,3,5]=>0010
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,4,2,1,5]=>[4,3,1,2,5]=>1100
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,4,1,2,5]=>[1,4,2,3,5]=>0100
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,2,4,1,5]=>[4,2,1,3,5]=>1100
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[4,1,2,3,5]=>1000
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>1100
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[1,3,2,4,5]=>0100
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[3,1,2,4,5]=>1000
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>1000
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>0000
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>11111
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>01111
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>10111
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>10111
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>00111
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>11011
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,5,3,4,1,2]=>[1,6,2,5,4,3]=>01011
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>11011
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>10011
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>11011
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>01011
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>10011
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>10011
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>00011
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>11101
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,4,5,3,1,2]=>[1,6,5,2,4,3]=>01101
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[6,1,5,2,4,3]=>10101
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,4,5,2,1,3]=>[5,1,6,2,4,3]=>10101
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,4,5,1,2,3]=>[1,2,6,3,5,4]=>00101
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>11101
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,3,5,1,2]=>[1,6,4,2,5,3]=>01101
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>11001
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,3,4,5,1,2]=>[1,6,2,3,5,4]=>01001
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>11101
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>10101
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>11001
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>11001
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>10001
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>11101
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>01101
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>10101
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>10101
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>00101
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>11001
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,3,4,1,2,5]=>[1,5,2,3,6,4]=>01001
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>11001
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>10001
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>11001
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>01001
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>10001
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>10001
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>00001
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>11110
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[1,6,5,4,2,3]=>01110
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[5,6,4,2,3,1]=>[6,1,5,4,2,3]=>10110
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[5,6,4,2,1,3]=>[5,1,6,4,2,3]=>10110
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[5,6,4,1,2,3]=>[1,2,6,5,3,4]=>00110
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[5,6,3,4,2,1]=>[6,5,1,4,2,3]=>11010
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[1,6,2,5,3,4]=>01010
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,6,3,2,4,1]=>[6,4,1,5,2,3]=>11010
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,6,2,3,4,1]=>[6,1,2,5,3,4]=>10010
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[5,6,3,2,1,4]=>[5,4,1,6,2,3]=>11010
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[5,6,3,1,2,4]=>[1,5,2,6,3,4]=>01010
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[5,6,2,3,1,4]=>[5,1,2,6,3,4]=>10010
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[5,6,2,1,3,4]=>[4,1,2,6,3,5]=>10010
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[5,6,1,2,3,4]=>[1,2,3,6,4,5]=>00010
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>11110
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[5,4,6,3,1,2]=>[1,6,5,3,2,4]=>01110
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[5,4,6,2,3,1]=>[6,1,5,3,2,4]=>10110
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[5,1,6,3,2,4]=>10110
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[5,4,6,1,2,3]=>[1,2,6,4,3,5]=>00110
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>11100
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,5,6,3,1,2]=>[1,6,5,2,3,4]=>01100
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[4,5,6,2,3,1]=>[6,1,5,2,3,4]=>10100
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[4,5,6,2,1,3]=>[5,1,6,2,3,4]=>10100
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[1,2,6,3,4,5]=>00100
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>11110
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[5,4,3,6,1,2]=>[1,6,4,3,2,5]=>01110
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>11010
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[5,3,4,6,1,2]=>[1,6,2,4,3,5]=>01010
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>11100
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,5,3,6,1,2]=>[1,6,4,2,3,5]=>01100
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>11100
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,5,6,1,2]=>[1,6,3,2,4,5]=>01100
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>11000
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[3,4,5,6,1,2]=>[1,6,2,3,4,5]=>01000
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>11110
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>10110
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>11010
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>11010
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>10010
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>11100
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,5,2,3,6,1]=>[6,1,4,2,3,5]=>10100
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>11100
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>11000
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>11100
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>10100
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>11000
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>11000
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>10000
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>11110
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>01110
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>10110
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>10110
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>00110
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>11010
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,3,4,1,2,6]=>[1,5,2,4,3,6]=>01010
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>11010
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>10010
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>11010
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>01010
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>10010
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>10010
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>00010
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>11100
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[4,5,3,1,2,6]=>[1,5,4,2,3,6]=>01100
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,5,2,3,1,6]=>[5,1,4,2,3,6]=>10100
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[4,5,2,1,3,6]=>[4,1,5,2,3,6]=>10100
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[4,5,1,2,3,6]=>[1,2,5,3,4,6]=>00100
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>11100
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[4,3,5,1,2,6]=>[1,5,3,2,4,6]=>01100
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>11000
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[3,4,5,1,2,6]=>[1,5,2,3,4,6]=>01000
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>11100
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>10100
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>11000
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>11000
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>10000
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>11100
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>01100
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>10100
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>10100
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>00100
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>11000
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]=>[1,4,2,3,5,6]=>01000
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>11000
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>10000
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>11000
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>01000
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>10000
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>10000
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>00000
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>111111
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>011111
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>101111
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>101111
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>001111
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>110111
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,6,5,3,4,1,2]=>[1,7,2,6,5,4,3]=>010111
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>110111
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>100111
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>110111
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>010111
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>100111
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>100111
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>000111
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>111011
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,6,4,5,3,1,2]=>[1,7,6,2,5,4,3]=>011011
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,6,4,5,2,3,1]=>[7,1,6,2,5,4,3]=>101011
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,6,4,5,2,1,3]=>[6,1,7,2,5,4,3]=>101011
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,6,4,5,1,2,3]=>[1,2,7,3,6,5,4]=>001011
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>111011
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,6,4,3,5,1,2]=>[1,7,5,2,6,4,3]=>011011
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>110011
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,6,3,4,5,1,2]=>[1,7,2,3,6,5,4]=>010011
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>111011
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>101011
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>110011
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>110011
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>100011
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>111011
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>011011
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>101011
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>101011
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>001011
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>110011
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,6,3,4,1,2,5]=>[1,6,2,3,7,5,4]=>010011
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>110011
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>100011
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>110011
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>010011
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>100011
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>100011
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>000011
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>111101
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,5,6,4,3,1,2]=>[1,7,6,5,2,4,3]=>011101
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[7,1,6,5,2,4,3]=>101101
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,5,6,4,2,1,3]=>[6,1,7,5,2,4,3]=>101101
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,5,6,4,1,2,3]=>[1,2,7,6,3,5,4]=>001101
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,5,6,3,4,2,1]=>[7,6,1,5,2,4,3]=>110101
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,5,6,3,4,1,2]=>[1,7,2,6,3,5,4]=>010101
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,5,6,3,2,4,1]=>[7,5,1,6,2,4,3]=>110101
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,5,6,2,3,4,1]=>[7,1,2,6,3,5,4]=>100101
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,5,6,3,2,1,4]=>[6,5,1,7,2,4,3]=>110101
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,5,6,3,1,2,4]=>[1,6,2,7,3,5,4]=>010101
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,5,6,2,3,1,4]=>[6,1,2,7,3,5,4]=>100101
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,5,6,2,1,3,4]=>[5,1,2,7,3,6,4]=>100101
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,5,6,1,2,3,4]=>[1,2,3,7,4,6,5]=>000101
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>111101
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,5,4,6,3,1,2]=>[1,7,6,4,2,5,3]=>011101
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,5,4,6,2,3,1]=>[7,1,6,4,2,5,3]=>101101
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,5,4,6,2,1,3]=>[6,1,7,4,2,5,3]=>101101
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,5,4,6,1,2,3]=>[1,2,7,5,3,6,4]=>001101
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>111001
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,4,5,6,3,1,2]=>[1,7,6,2,3,5,4]=>011001
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,4,5,6,2,3,1]=>[7,1,6,2,3,5,4]=>101001
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,4,5,6,2,1,3]=>[6,1,7,2,3,5,4]=>101001
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,4,5,6,1,2,3]=>[1,2,7,3,4,6,5]=>001001
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>111101
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,5,4,3,6,1,2]=>[1,7,5,4,2,6,3]=>011101
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>110101
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,5,3,4,6,1,2]=>[1,7,2,5,3,6,4]=>010101
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>111001
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,4,5,3,6,1,2]=>[1,7,5,2,3,6,4]=>011001
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>111001
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,4,3,5,6,1,2]=>[1,7,4,2,3,6,5]=>011001
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>110001
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,3,4,5,6,1,2]=>[1,7,2,3,4,6,5]=>010001
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>111101
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>101101
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>110101
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>110101
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>100101
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>111001
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,4,5,2,3,6,1]=>[7,1,5,2,3,6,4]=>101001
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>111001
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>110001
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>111001
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>101001
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>110001
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>110001
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>100001
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>111101
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>011101
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>101101
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>101101
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>001101
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>110101
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,5,3,4,1,2,6]=>[1,6,2,5,3,7,4]=>010101
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>110101
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>100101
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>110101
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>010101
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>100101
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>100101
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>000101
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>111001
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,5,3,1,2,6]=>[1,6,5,2,3,7,4]=>011001
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,4,5,2,3,1,6]=>[6,1,5,2,3,7,4]=>101001
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,4,5,2,1,3,6]=>[5,1,6,2,3,7,4]=>101001
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,4,5,1,2,3,6]=>[1,2,6,3,4,7,5]=>001001
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>111001
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,4,3,5,1,2,6]=>[1,6,4,2,3,7,5]=>011001
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>110001
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,3,4,5,1,2,6]=>[1,6,2,3,4,7,5]=>010001
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>111001
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>101001
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>110001
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>110001
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>100001
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>111001
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>011001
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>101001
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>101001
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>001001
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>110001
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,3,4,1,2,5,6]=>[1,5,2,3,4,7,6]=>010001
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>110001
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>100001
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>110001
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>010001
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>100001
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>100001
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>000001
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>111110
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[1,7,6,5,4,2,3]=>011110
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[6,7,5,4,2,3,1]=>[7,1,6,5,4,2,3]=>101110
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[6,7,5,4,2,1,3]=>[6,1,7,5,4,2,3]=>101110
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[6,7,5,4,1,2,3]=>[1,2,7,6,5,3,4]=>001110
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[6,7,5,3,4,2,1]=>[7,6,1,5,4,2,3]=>110110
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[6,7,5,3,4,1,2]=>[1,7,2,6,5,3,4]=>010110
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[6,7,5,3,2,4,1]=>[7,5,1,6,4,2,3]=>110110
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[6,7,5,2,3,4,1]=>[7,1,2,6,5,3,4]=>100110
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[6,7,5,3,2,1,4]=>[6,5,1,7,4,2,3]=>110110
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[6,7,5,3,1,2,4]=>[1,6,2,7,5,3,4]=>010110
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[6,7,5,2,3,1,4]=>[6,1,2,7,5,3,4]=>100110
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[6,7,5,2,1,3,4]=>[5,1,2,7,6,3,4]=>100110
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[6,7,5,1,2,3,4]=>[1,2,3,7,6,4,5]=>000110
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[6,7,4,5,3,2,1]=>[7,6,5,1,4,2,3]=>111010
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[6,7,4,5,3,1,2]=>[1,7,6,2,5,3,4]=>011010
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[6,7,4,5,2,3,1]=>[7,1,6,2,5,3,4]=>101010
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[6,7,4,5,2,1,3]=>[6,1,7,2,5,3,4]=>101010
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[6,7,4,5,1,2,3]=>[1,2,7,3,6,4,5]=>001010
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[6,7,4,3,5,2,1]=>[7,6,4,1,5,2,3]=>111010
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[1,7,5,2,6,3,4]=>011010
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[6,7,3,4,5,2,1]=>[7,6,1,2,5,3,4]=>110010
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[6,7,3,4,5,1,2]=>[1,7,2,3,6,4,5]=>010010
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,7,4,3,2,5,1]=>[7,5,4,1,6,2,3]=>111010
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,7,4,2,3,5,1]=>[7,1,5,2,6,3,4]=>101010
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,7,3,4,2,5,1]=>[7,5,1,2,6,3,4]=>110010
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,7,3,2,4,5,1]=>[7,4,1,2,6,3,5]=>110010
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,7,2,3,4,5,1]=>[7,1,2,3,6,4,5]=>100010
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[6,7,4,3,2,1,5]=>[6,5,4,1,7,2,3]=>111010
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[6,7,4,3,1,2,5]=>[1,6,5,2,7,3,4]=>011010
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[6,7,4,2,3,1,5]=>[6,1,5,2,7,3,4]=>101010
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[6,7,4,2,1,3,5]=>[5,1,6,2,7,3,4]=>101010
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[6,7,4,1,2,3,5]=>[1,2,6,3,7,4,5]=>001010
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[6,7,3,4,2,1,5]=>[6,5,1,2,7,3,4]=>110010
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[6,7,3,4,1,2,5]=>[1,6,2,3,7,4,5]=>010010
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[6,7,3,2,4,1,5]=>[6,4,1,2,7,3,5]=>110010
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[6,7,2,3,4,1,5]=>[6,1,2,3,7,4,5]=>100010
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[6,7,3,2,1,4,5]=>[5,4,1,2,7,3,6]=>110010
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[6,7,3,1,2,4,5]=>[1,5,2,3,7,4,6]=>010010
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[6,7,2,3,1,4,5]=>[5,1,2,3,7,4,6]=>100010
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[6,7,2,1,3,4,5]=>[4,1,2,3,7,5,6]=>100010
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[6,7,1,2,3,4,5]=>[1,2,3,4,7,5,6]=>000010
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>111110
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[6,5,7,4,3,1,2]=>[1,7,6,5,3,2,4]=>011110
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[6,5,7,4,2,3,1]=>[7,1,6,5,3,2,4]=>101110
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[6,1,7,5,3,2,4]=>101110
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[6,5,7,4,1,2,3]=>[1,2,7,6,4,3,5]=>001110
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[6,5,7,3,4,2,1]=>[7,6,1,5,3,2,4]=>110110
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[6,5,7,3,4,1,2]=>[1,7,2,6,4,3,5]=>010110
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[6,5,7,3,2,4,1]=>[7,5,1,6,3,2,4]=>110110
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[6,5,7,2,3,4,1]=>[7,1,2,6,4,3,5]=>100110
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[6,5,7,3,2,1,4]=>[6,5,1,7,3,2,4]=>110110
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[6,5,7,3,1,2,4]=>[1,6,2,7,4,3,5]=>010110
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[6,5,7,2,3,1,4]=>[6,1,2,7,4,3,5]=>100110
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[6,5,7,2,1,3,4]=>[5,1,2,7,4,3,6]=>100110
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[6,5,7,1,2,3,4]=>[1,2,3,7,5,4,6]=>000110
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>111100
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[5,6,7,4,3,1,2]=>[1,7,6,5,2,3,4]=>011100
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[5,6,7,4,2,3,1]=>[7,1,6,5,2,3,4]=>101100
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[5,6,7,4,2,1,3]=>[6,1,7,5,2,3,4]=>101100
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[5,6,7,4,1,2,3]=>[1,2,7,6,3,4,5]=>001100
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,6,7,3,4,2,1]=>[7,6,1,5,2,3,4]=>110100
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,6,7,3,4,1,2]=>[1,7,2,6,3,4,5]=>010100
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[5,6,7,3,2,4,1]=>[7,5,1,6,2,3,4]=>110100
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[5,6,7,2,3,4,1]=>[7,1,2,6,3,4,5]=>100100
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[5,6,7,3,2,1,4]=>[6,5,1,7,2,3,4]=>110100
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[5,6,7,3,1,2,4]=>[1,6,2,7,3,4,5]=>010100
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[5,6,7,2,3,1,4]=>[6,1,2,7,3,4,5]=>100100
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[5,6,7,2,1,3,4]=>[5,1,2,7,3,4,6]=>100100
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[5,6,7,1,2,3,4]=>[1,2,3,7,4,5,6]=>000100
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>111110
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[6,5,4,7,3,1,2]=>[1,7,6,4,3,2,5]=>011110
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[6,5,4,7,2,3,1]=>[7,1,6,4,3,2,5]=>101110
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[6,5,4,7,2,1,3]=>[6,1,7,4,3,2,5]=>101110
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[6,5,4,7,1,2,3]=>[1,2,7,5,4,3,6]=>001110
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>111010
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[6,4,5,7,3,1,2]=>[1,7,6,2,4,3,5]=>011010
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[6,4,5,7,2,3,1]=>[7,1,6,2,4,3,5]=>101010
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[6,4,5,7,2,1,3]=>[6,1,7,2,4,3,5]=>101010
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[6,4,5,7,1,2,3]=>[1,2,7,3,5,4,6]=>001010
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>111100
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[5,6,4,7,3,1,2]=>[1,7,6,4,2,3,5]=>011100
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[5,6,4,7,2,3,1]=>[7,1,6,4,2,3,5]=>101100
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[5,6,4,7,2,1,3]=>[6,1,7,4,2,3,5]=>101100
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[5,6,4,7,1,2,3]=>[1,2,7,5,3,4,6]=>001100
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>111100
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[5,4,6,7,3,1,2]=>[1,7,6,3,2,4,5]=>011100
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[5,4,6,7,2,3,1]=>[7,1,6,3,2,4,5]=>101100
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[5,4,6,7,2,1,3]=>[6,1,7,3,2,4,5]=>101100
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[5,4,6,7,1,2,3]=>[1,2,7,4,3,5,6]=>001100
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>111000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,5,6,7,3,1,2]=>[1,7,6,2,3,4,5]=>011000
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,5,6,7,2,3,1]=>[7,1,6,2,3,4,5]=>101000
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,5,6,7,2,1,3]=>[6,1,7,2,3,4,5]=>101000
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,5,6,7,1,2,3]=>[1,2,7,3,4,5,6]=>001000
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>111110
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[6,5,4,3,7,1,2]=>[1,7,5,4,3,2,6]=>011110
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>110110
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[6,5,3,4,7,1,2]=>[1,7,2,5,4,3,6]=>010110
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>111010
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[6,4,5,3,7,1,2]=>[1,7,5,2,4,3,6]=>011010
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>111010
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[6,4,3,5,7,1,2]=>[1,7,4,2,5,3,6]=>011010
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>110010
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[6,3,4,5,7,1,2]=>[1,7,2,3,5,4,6]=>010010
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>111100
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,6,4,3,7,1,2]=>[1,7,5,4,2,3,6]=>011100
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,6,3,4,7,2,1]=>[7,6,1,4,2,3,5]=>110100
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,6,3,4,7,1,2]=>[1,7,2,5,3,4,6]=>010100
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>111100
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,4,6,3,7,1,2]=>[1,7,5,3,2,4,6]=>011100
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>111000
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,5,6,3,7,1,2]=>[1,7,5,2,3,4,6]=>011000
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>111100
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,3,6,7,1,2]=>[1,7,4,3,2,5,6]=>011100
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>110100
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,3,4,6,7,1,2]=>[1,7,2,4,3,5,6]=>010100
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>111000
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[4,5,3,6,7,1,2]=>[1,7,4,2,3,5,6]=>011000
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>111000
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[4,3,5,6,7,1,2]=>[1,7,3,2,4,5,6]=>011000
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>110000
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[3,4,5,6,7,1,2]=>[1,7,2,3,4,5,6]=>010000
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>111110
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>101110
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>110110
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>110110
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>100110
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>111010
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,4,5,2,3,7,1]=>[7,1,5,2,4,3,6]=>101010
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>111010
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>110010
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>111010
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>101010
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>110010
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>110010
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>100010
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>111100
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[5,6,4,2,3,7,1]=>[7,1,5,4,2,3,6]=>101100
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[5,6,3,4,2,7,1]=>[7,5,1,4,2,3,6]=>110100
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,6,3,2,4,7,1]=>[7,4,1,5,2,3,6]=>110100
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,6,2,3,4,7,1]=>[7,1,2,5,3,4,6]=>100100
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>111100
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[5,4,6,2,3,7,1]=>[7,1,5,3,2,4,6]=>101100
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>111000
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[4,5,6,2,3,7,1]=>[7,1,5,2,3,4,6]=>101000
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>111100
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>110100
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>111000
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>111000
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>110000
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>111100
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>101100
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>110100
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>110100
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>100100
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>111000
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,5,2,3,6,7,1]=>[7,1,4,2,3,5,6]=>101000
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>111000
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>110000
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>111000
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>101000
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>110000
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>110000
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>100000
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>111110
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>011110
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>101110
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>101110
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>001110
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>110110
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,5,3,4,1,2,7]=>[1,6,2,5,4,3,7]=>010110
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>110110
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>100110
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>110110
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>010110
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>100110
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>100110
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>000110
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>111010
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,4,5,3,1,2,7]=>[1,6,5,2,4,3,7]=>011010
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,4,5,2,3,1,7]=>[6,1,5,2,4,3,7]=>101010
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,4,5,2,1,3,7]=>[5,1,6,2,4,3,7]=>101010
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,4,5,1,2,3,7]=>[1,2,6,3,5,4,7]=>001010
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>111010
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,4,3,5,1,2,7]=>[1,6,4,2,5,3,7]=>011010
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>110010
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,3,4,5,1,2,7]=>[1,6,2,3,5,4,7]=>010010
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>111010
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>101010
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>110010
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>110010
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>100010
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>111010
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>011010
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>101010
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>101010
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>001010
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>110010
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,3,4,1,2,5,7]=>[1,5,2,3,6,4,7]=>010010
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>110010
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>100010
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>110010
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>010010
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>100010
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>100010
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>000010
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>111100
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[5,6,4,3,1,2,7]=>[1,6,5,4,2,3,7]=>011100
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[5,6,4,2,3,1,7]=>[6,1,5,4,2,3,7]=>101100
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[5,6,4,2,1,3,7]=>[5,1,6,4,2,3,7]=>101100
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[5,6,4,1,2,3,7]=>[1,2,6,5,3,4,7]=>001100
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[5,6,3,4,2,1,7]=>[6,5,1,4,2,3,7]=>110100
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[5,6,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>010100
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,6,3,2,4,1,7]=>[6,4,1,5,2,3,7]=>110100
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,6,2,3,4,1,7]=>[6,1,2,5,3,4,7]=>100100
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[5,6,3,2,1,4,7]=>[5,4,1,6,2,3,7]=>110100
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[5,6,3,1,2,4,7]=>[1,5,2,6,3,4,7]=>010100
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[5,6,2,3,1,4,7]=>[5,1,2,6,3,4,7]=>100100
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[5,6,2,1,3,4,7]=>[4,1,2,6,3,5,7]=>100100
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[5,6,1,2,3,4,7]=>[1,2,3,6,4,5,7]=>000100
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>111100
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[5,4,6,3,1,2,7]=>[1,6,5,3,2,4,7]=>011100
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[5,4,6,2,3,1,7]=>[6,1,5,3,2,4,7]=>101100
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[5,4,6,2,1,3,7]=>[5,1,6,3,2,4,7]=>101100
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[5,4,6,1,2,3,7]=>[1,2,6,4,3,5,7]=>001100
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>111000
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,5,6,3,1,2,7]=>[1,6,5,2,3,4,7]=>011000
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[4,5,6,2,3,1,7]=>[6,1,5,2,3,4,7]=>101000
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[4,5,6,2,1,3,7]=>[5,1,6,2,3,4,7]=>101000
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,5,6,1,2,3,7]=>[1,2,6,3,4,5,7]=>001000
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>111100
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[5,4,3,6,1,2,7]=>[1,6,4,3,2,5,7]=>011100
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>110100
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[5,3,4,6,1,2,7]=>[1,6,2,4,3,5,7]=>010100
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>111000
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[4,5,3,6,1,2,7]=>[1,6,4,2,3,5,7]=>011000
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>111000
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[4,3,5,6,1,2,7]=>[1,6,3,2,4,5,7]=>011000
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>110000
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[3,4,5,6,1,2,7]=>[1,6,2,3,4,5,7]=>010000
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>111100
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>101100
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>110100
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>110100
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>100100
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>111000
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,5,2,3,6,1,7]=>[6,1,4,2,3,5,7]=>101000
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>111000
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>110000
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>111000
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>101000
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>110000
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>110000
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>100000
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>111100
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>011100
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>101100
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>101100
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>001100
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>110100
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,3,4,1,2,6,7]=>[1,5,2,4,3,6,7]=>010100
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>110100
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>100100
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>110100
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>010100
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>100100
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>100100
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>000100
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>111000
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,5,3,1,2,6,7]=>[1,5,4,2,3,6,7]=>011000
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,5,2,3,1,6,7]=>[5,1,4,2,3,6,7]=>101000
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,5,2,1,3,6,7]=>[4,1,5,2,3,6,7]=>101000
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[4,5,1,2,3,6,7]=>[1,2,5,3,4,6,7]=>001000
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>111000
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,3,5,1,2,6,7]=>[1,5,3,2,4,6,7]=>011000
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>110000
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[3,4,5,1,2,6,7]=>[1,5,2,3,4,6,7]=>010000
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>111000
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>101000
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>110000
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>110000
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>100000
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>111000
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>011000
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>101000
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>101000
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>001000
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>110000
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[3,4,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>010000
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>110000
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>100000
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>110000
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>010000
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>100000
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>100000
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>000000
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>1111111
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>0111111
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[8,1,7,6,5,4,3,2]=>1011111
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[7,1,8,6,5,4,3,2]=>1011111
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>0011111
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[8,7,1,6,5,4,3,2]=>1101111
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,3,4,1,2]=>[1,8,2,7,6,5,4,3]=>0101111
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[8,6,1,7,5,4,3,2]=>1101111
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>[8,1,2,7,6,5,4,3]=>1001111
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[7,6,1,8,5,4,3,2]=>1101111
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>[7,1,2,8,6,5,4,3]=>1001111
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>0001111
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>1110111
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[8,7,6,4,5,3,1,2]=>[1,8,7,2,6,5,4,3]=>0110111
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[8,7,6,4,5,2,3,1]=>[8,1,7,2,6,5,4,3]=>1010111
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[8,7,6,4,5,2,1,3]=>[7,1,8,2,6,5,4,3]=>1010111
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[8,7,6,4,5,1,2,3]=>[1,2,8,3,7,6,5,4]=>0010111
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>1110111
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>[8,7,1,2,6,5,4,3]=>1100111
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[8,7,6,3,4,5,1,2]=>[1,8,2,3,7,6,5,4]=>0100111
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>1110111
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>[8,6,1,2,7,5,4,3]=>1100111
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[8,7,6,3,2,4,5,1]=>[8,5,1,2,7,6,4,3]=>1100111
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>[8,1,2,3,7,6,5,4]=>1000111
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[7,6,5,1,8,4,3,2]=>1110111
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[1,7,6,2,8,5,4,3]=>0110111
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[7,1,6,2,8,5,4,3]=>1010111
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[6,1,7,2,8,5,4,3]=>1010111
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[1,2,7,3,8,6,5,4]=>0010111
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>[7,6,1,2,8,5,4,3]=>1100111
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[8,7,6,3,4,1,2,5]=>[1,7,2,3,8,6,5,4]=>0100111
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>[7,5,1,2,8,6,4,3]=>1100111
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>[7,1,2,3,8,6,5,4]=>1000111
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[6,5,1,2,8,7,4,3]=>1100111
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>[6,1,2,3,8,7,5,4]=>1000111
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[5,1,2,3,8,7,6,4]=>1000111
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>0000111
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>1111011
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[8,7,5,6,4,3,1,2]=>[1,8,7,6,2,5,4,3]=>0111011
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[8,7,5,6,4,2,3,1]=>[8,1,7,6,2,5,4,3]=>1011011
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,7,5,6,4,2,1,3]=>[7,1,8,6,2,5,4,3]=>1011011
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,1,6,2,5,4,3]=>1101011
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,7,5,6,3,4,1,2]=>[1,8,2,7,3,6,5,4]=>0101011
[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[8,7,5,6,3,2,4,1]=>[8,6,1,7,2,5,4,3]=>1101011
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,7,5,6,2,3,4,1]=>[8,1,2,7,3,6,5,4]=>1001011
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,7,5,6,3,2,1,4]=>[7,6,1,8,2,5,4,3]=>1101011
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[8,7,5,6,3,1,2,4]=>[1,7,2,8,3,6,5,4]=>0101011
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[8,7,5,6,2,3,1,4]=>[7,1,2,8,3,6,5,4]=>1001011
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,7,5,6,1,2,3,4]=>[1,2,3,8,4,7,6,5]=>0001011
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>1111011
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,7,5,4,6,1,2,3]=>[1,2,8,6,3,7,5,4]=>0011011
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[8,7,4,5,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>1110011
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[8,7,4,5,6,2,3,1]=>[8,1,7,2,3,6,5,4]=>1010011
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[8,7,4,5,6,2,1,3]=>[7,1,8,2,3,6,5,4]=>1010011
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[8,7,4,5,6,1,2,3]=>[1,2,8,3,4,7,6,5]=>0010011
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>1111011
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[8,7,4,5,3,6,2,1]=>[8,7,5,1,2,6,4,3]=>1110011
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,1,2,6,5,3]=>1110011
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[7,8,4,3,5,6,2,1]=>[8,7,4,3,5,6,1,2]=>[1,8,5,2,3,7,6,4]=>0110011
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[8,7,3,4,5,6,2,1]=>[8,7,1,2,3,6,5,4]=>1100011
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[8,7,3,4,5,6,1,2]=>[1,8,2,3,4,7,6,5]=>0100011
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[8,5,6,4,3,7,2,1]=>[8,7,5,4,2,3,6,1]=>[8,1,6,5,2,7,4,3]=>1011011
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[8,7,5,3,4,2,6,1]=>[8,6,1,5,2,7,4,3]=>1101011
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[8,7,4,3,5,2,6,1]=>[8,6,4,1,2,7,5,3]=>1110011
[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[8,7,4,3,2,5,6,1]=>[8,5,4,1,2,7,6,3]=>1110011
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[8,7,2,3,4,5,6,1]=>[8,1,2,3,4,7,6,5]=>1000011
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,1,8,3,2]=>1111011
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[1,7,6,5,2,8,4,3]=>0111011
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>[1,2,7,6,3,8,5,4]=>0011011
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[8,7,5,3,4,1,2,6]=>[1,7,2,6,3,8,5,4]=>0101011
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[7,5,1,6,2,8,4,3]=>1101011
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[6,5,1,7,2,8,4,3]=>1101011
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[8,7,5,3,1,2,4,6]=>[1,6,2,7,3,8,5,4]=>0101011
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[8,7,5,2,3,1,4,6]=>[6,1,2,7,3,8,5,4]=>1001011
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[5,1,2,7,3,8,6,4]=>1001011
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[1,2,3,7,4,8,6,5]=>0001011
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[8,7,4,5,3,2,1,6]=>[7,6,5,1,2,8,4,3]=>1110011
[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[7,5,6,3,4,8,2,1]=>[8,7,4,5,2,3,1,6]=>[7,1,6,2,3,8,5,4]=>1010011
[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[8,7,4,5,1,2,3,6]=>[1,2,7,3,4,8,6,5]=>0010011
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>[7,6,1,2,3,8,5,4]=>1100011
[.,[.,[[[[.,.],.],[[.,.],.]],.]]]=>[6,7,3,4,5,8,2,1]=>[8,7,3,4,5,1,2,6]=>[1,7,2,3,4,8,6,5]=>0100011
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[8,7,3,4,2,5,1,6]=>[7,5,1,2,3,8,6,4]=>1100011
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[8,7,2,3,4,5,1,6]=>[7,1,2,3,4,8,6,5]=>1000011
[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>[1,2,6,3,4,8,7,5]=>0010011
[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[8,7,3,4,1,2,5,6]=>[1,6,2,3,4,8,7,5]=>0100011
[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]=>[6,4,3,5,7,8,2,1]=>[8,7,3,2,4,1,5,6]=>[6,4,1,2,3,8,7,5]=>1100011
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[8,7,2,3,4,1,5,6]=>[6,1,2,3,4,8,7,5]=>1000011
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[5,4,1,2,3,8,7,6]=>1100011
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[8,7,2,3,1,4,5,6]=>[5,1,2,3,4,8,7,6]=>1000011
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[4,1,2,3,5,8,7,6]=>1000011
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>0000011
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>1111101
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[8,6,7,5,4,3,1,2]=>[1,8,7,6,5,2,4,3]=>0111101
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[8,1,7,6,5,2,4,3]=>1011101
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[8,6,7,5,4,2,1,3]=>[7,1,8,6,5,2,4,3]=>1011101
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[8,6,7,5,3,4,2,1]=>[8,7,1,6,5,2,4,3]=>1101101
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[8,6,7,5,3,2,4,1]=>[8,6,1,7,5,2,4,3]=>1101101
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[8,6,7,5,2,3,4,1]=>[8,1,2,7,6,3,5,4]=>1001101
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[8,6,7,5,3,1,2,4]=>[1,7,2,8,6,3,5,4]=>0101101
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,6,7,5,1,2,3,4]=>[1,2,3,8,7,4,6,5]=>0001101
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,6,7,4,5,3,2,1]=>[8,7,6,1,5,2,4,3]=>1110101
[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,2,3,1]=>[8,6,7,4,5,3,1,2]=>[1,8,7,2,6,3,5,4]=>0110101
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[8,1,7,2,6,3,5,4]=>1010101
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[8,6,7,4,5,2,1,3]=>[7,1,8,2,6,3,5,4]=>1010101
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,6,7,4,5,1,2,3]=>[1,2,8,3,7,4,6,5]=>0010101
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,6,7,4,3,2,5,1]=>[8,6,5,1,7,2,4,3]=>1110101
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[8,6,7,4,2,3,5,1]=>[8,1,6,2,7,3,5,4]=>1010101
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[8,6,7,3,4,2,5,1]=>[8,6,1,2,7,3,5,4]=>1100101
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[8,6,7,4,3,2,1,5]=>[7,6,5,1,8,2,4,3]=>1110101
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[8,6,7,4,2,3,1,5]=>[7,1,6,2,8,3,5,4]=>1010101
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,6,7,4,2,1,3,5]=>[6,1,7,2,8,3,5,4]=>1010101
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[8,6,7,3,2,1,4,5]=>[6,5,1,2,8,3,7,4]=>1100101
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[8,6,7,2,3,1,4,5]=>[6,1,2,3,8,4,7,5]=>1000101
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[8,6,7,2,1,3,4,5]=>[5,1,2,3,8,4,7,6]=>1000101
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[8,6,7,1,2,3,4,5]=>[1,2,3,4,8,5,7,6]=>0000101
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>1111101
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[8,6,5,7,4,3,1,2]=>[1,8,7,6,4,2,5,3]=>0111101
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[8,6,5,7,4,2,3,1]=>[8,1,7,6,4,2,5,3]=>1011101
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[8,6,5,7,4,1,2,3]=>[1,2,8,7,5,3,6,4]=>0011101
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[8,6,5,7,3,4,1,2]=>[1,8,2,7,5,3,6,4]=>0101101
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[8,6,1,7,4,2,5,3]=>1101101
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,6,5,7,3,2,1,4]=>[7,6,1,8,4,2,5,3]=>1101101
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[8,6,5,7,3,1,2,4]=>[1,7,2,8,5,3,6,4]=>0101101
[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[8,6,5,7,2,1,3,4]=>[6,1,2,8,5,3,7,4]=>1001101
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,6,5,7,1,2,3,4]=>[1,2,3,8,6,4,7,5]=>0001101
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>1111001
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,5,6,7,4,1,2,3]=>[1,2,8,7,3,4,6,5]=>0011001
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[8,5,6,7,3,4,2,1]=>[8,7,1,6,2,3,5,4]=>1101001
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[8,5,6,7,3,4,1,2]=>[1,8,2,7,3,4,6,5]=>0101001
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[8,5,6,7,3,2,4,1]=>[8,6,1,7,2,3,5,4]=>1101001
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1]=>[8,1,2,7,3,4,6,5]=>1001001
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,5,6,7,3,2,1,4]=>[7,6,1,8,2,3,5,4]=>1101001
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[8,5,6,7,2,1,3,4]=>[6,1,2,8,3,4,7,5]=>1001001
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,5,6,7,1,2,3,4]=>[1,2,3,8,4,5,7,6]=>0001001
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>1111101
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[8,6,5,4,7,2,3,1]=>[8,1,7,5,4,2,6,3]=>1011101
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,6,4,5,7,3,2,1]=>[8,7,6,1,4,2,5,3]=>1110101
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,6,4,5,7,2,3,1]=>[8,1,7,2,5,3,6,4]=>1010101
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[8,6,4,5,7,2,1,3]=>[7,1,8,2,5,3,6,4]=>1010101
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[8,6,4,5,7,1,2,3]=>[1,2,8,3,6,4,7,5]=>0010101
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,1,2,5,3]=>1111001
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,5,6,4,7,1,2,3]=>[1,2,8,6,3,4,7,5]=>0011001
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[8,5,4,6,7,3,1,2]=>[1,8,7,4,2,3,6,5]=>0111001
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[8,4,5,6,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>1110001
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[8,4,5,6,7,1,2,3]=>[1,2,8,3,4,5,7,6]=>0010001
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>1111101
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[8,6,4,3,5,7,2,1]=>[8,7,4,1,5,2,6,3]=>1110101
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>1111001
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[8,5,4,3,6,7,1,2]=>[1,8,5,4,2,3,7,6]=>0111001
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,5,3,4,6,7,1,2]=>[1,8,2,5,3,4,7,6]=>0101001
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[8,7,3,2,4,5,6,1]=>[8,4,3,5,6,7,2,1]=>[8,7,3,1,2,4,6,5]=>1110001
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,4,3,5,6,7,1,2]=>[1,8,4,2,3,5,7,6]=>0110001
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[8,3,4,5,6,7,2,1]=>[8,7,1,2,3,4,6,5]=>1100001
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[8,3,4,5,6,7,1,2]=>[1,8,2,3,4,5,7,6]=>0100001
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>1111101
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,2,4,7,1]=>[8,5,1,6,4,2,7,3]=>1101101
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[8,6,4,5,2,3,7,1]=>[8,1,6,2,5,3,7,4]=>1010101
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,1,5,2,7,3]=>1110101
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,6,3,4,5,2,7,1]=>[8,6,1,2,5,3,7,4]=>1100101
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[8,6,4,3,2,5,7,1]=>[8,5,4,1,6,2,7,3]=>1110101
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,6,4,2,3,5,7,1]=>[8,1,5,2,6,3,7,4]=>1010101
[.,[[.,[[[[.,.],.],.],.]],[.,.]]]=>[8,3,4,5,6,2,7,1]=>[8,6,2,3,4,5,7,1]=>[8,1,2,3,6,4,7,5]=>1000101
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,1,2,7,3]=>1111001
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,5,6,4,2,3,7,1]=>[8,1,6,5,2,3,7,4]=>1011001
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>1111001
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[8,4,5,3,6,2,7,1]=>[8,6,4,1,2,3,7,5]=>1110001
[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]=>[8,6,3,2,4,5,7,1]=>[8,4,3,5,6,2,7,1]=>[8,6,3,1,2,4,7,5]=>1110001
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[8,3,4,5,6,2,7,1]=>[8,6,1,2,3,4,7,5]=>1100001
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[8,5,3,4,2,6,7,1]=>[8,5,1,4,2,3,7,6]=>1101001
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[8,5,2,3,4,6,7,1]=>[8,1,2,5,3,4,7,6]=>1001001
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[8,4,5,3,2,6,7,1]=>[8,5,4,1,2,3,7,6]=>1110001
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,1,2,5,7,6]=>1110001
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[8,4,2,3,5,6,7,1]=>[8,1,4,2,3,5,7,6]=>1010001
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[8,3,2,4,5,6,7,1]=>[8,3,1,2,4,5,7,6]=>1100001
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[8,2,3,4,5,6,7,1]=>[8,1,2,3,4,5,7,6]=>1000001
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,1,8,2]=>1111101
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[1,7,6,5,4,2,8,3]=>0111101
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[6,1,7,5,4,2,8,3]=>1011101
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>[1,2,7,6,5,3,8,4]=>0011101
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[7,6,1,5,4,2,8,3]=>1101101
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[8,6,5,2,3,4,1,7]=>[7,1,2,6,5,3,8,4]=>1001101
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[6,5,1,7,4,2,8,3]=>1101101
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>[6,1,2,7,5,3,8,4]=>1001101
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[1,2,3,7,6,4,8,5]=>0001101
[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[8,6,4,5,3,2,1,7]=>[7,6,5,1,4,2,8,3]=>1110101
[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]=>[6,7,5,3,4,2,8,1]=>[8,6,4,5,3,1,2,7]=>[1,7,6,2,5,3,8,4]=>0110101
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,6,4,5,2,3,1,7]=>[7,1,6,2,5,3,8,4]=>1010101
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,6,4,5,2,1,3,7]=>[6,1,7,2,5,3,8,4]=>1010101
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[8,6,4,5,1,2,3,7]=>[1,2,7,3,6,4,8,5]=>0010101
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[8,6,4,3,5,2,1,7]=>[7,6,4,1,5,2,8,3]=>1110101
[.,[[.,[[[.,.],.],[[.,.],.]]],.]]=>[6,7,3,4,5,2,8,1]=>[8,6,3,4,5,1,2,7]=>[1,7,2,3,6,4,8,5]=>0100101
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,6,4,3,2,5,1,7]=>[7,5,4,1,6,2,8,3]=>1110101
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[7,1,5,2,6,3,8,4]=>1010101
[.,[[.,[[[.,[.,.]],.],[.,.]]],.]]=>[7,4,3,5,6,2,8,1]=>[8,6,3,2,4,5,1,7]=>[7,4,1,2,6,3,8,5]=>1100101
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[6,5,4,1,7,2,8,3]=>1110101
[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[8,6,4,3,1,2,5,7]=>[1,6,5,2,7,3,8,4]=>0110101
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[6,1,5,2,7,3,8,4]=>1010101
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>1010101
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[1,2,6,3,7,4,8,5]=>0010101
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>[6,5,1,2,7,3,8,4]=>1100101
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,6,3,4,1,2,5,7]=>[1,6,2,3,7,4,8,5]=>0100101
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>[6,4,1,2,7,3,8,5]=>1100101
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[8,6,2,3,4,1,5,7]=>[6,1,2,3,7,4,8,5]=>1000101
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[5,4,1,2,7,3,8,6]=>1100101
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,7,5,8,6]=>0000101
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,1,2,8,3]=>1111001
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,5,6,4,2,3,1,7]=>[7,1,6,5,2,3,8,4]=>1011001
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[8,5,6,4,1,2,3,7]=>[1,2,7,6,3,4,8,5]=>0011001
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[8,5,6,3,4,2,1,7]=>[7,6,1,5,2,3,8,4]=>1101001
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,6,3,4,1,2,7]=>[1,7,2,6,3,4,8,5]=>0101001
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,5,6,2,3,4,1,7]=>[7,1,2,6,3,4,8,5]=>1001001
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[8,5,6,3,2,1,4,7]=>[6,5,1,7,2,3,8,4]=>1101001
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[8,5,6,3,1,2,4,7]=>[1,6,2,7,3,4,8,5]=>0101001
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,5,6,2,3,1,4,7]=>[6,1,2,7,3,4,8,5]=>1001001
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[8,5,6,2,1,3,4,7]=>[5,1,2,7,3,4,8,6]=>1001001
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,5,6,1,2,3,4,7]=>[1,2,3,7,4,5,8,6]=>0001001
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,1,2,8,4]=>1111001
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,4,5,6,3,2,1,7]=>[7,6,5,1,2,3,8,4]=>1110001
[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[6,5,7,2,3,4,8,1]=>[8,4,5,6,2,1,3,7]=>[6,1,7,2,3,4,8,5]=>1010001
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[8,4,5,6,1,2,3,7]=>[1,2,7,3,4,5,8,6]=>0010001
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[6,7,3,4,2,5,8,1]=>[8,5,3,4,6,1,2,7]=>[1,7,2,5,3,4,8,6]=>0101001
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,4,5,3,6,2,1,7]=>[7,6,4,1,2,3,8,5]=>1110001
[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[8,4,5,3,6,1,2,7]=>[1,7,5,2,3,4,8,6]=>0110001
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[8,4,3,5,6,2,1,7]=>[7,6,3,1,2,4,8,5]=>1110001
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,4,3,5,6,1,2,7]=>[1,7,4,2,3,5,8,6]=>0110001
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[8,3,4,5,6,2,1,7]=>[7,6,1,2,3,4,8,5]=>1100001
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[8,3,4,5,6,1,2,7]=>[1,7,2,3,4,5,8,6]=>0100001
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[8,5,3,2,4,6,1,7]=>[7,4,1,5,2,3,8,6]=>1101001
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,5,2,3,4,6,1,7]=>[7,1,2,5,3,4,8,6]=>1001001
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[8,4,5,2,3,6,1,7]=>[7,1,5,2,3,4,8,6]=>1010001
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,4,3,5,2,6,1,7]=>[7,5,3,1,2,4,8,6]=>1110001
[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[8,3,4,2,5,6,1,7]=>[7,4,1,2,3,5,8,6]=>1100001
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[8,3,2,4,5,6,1,7]=>[7,3,1,2,4,5,8,6]=>1100001
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[8,2,3,4,5,6,1,7]=>[7,1,2,3,4,5,8,6]=>1000001
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,1,2,8,7]=>1111001
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[5,1,6,4,2,3,8,7]=>1011001
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[5,6,3,4,2,7,8,1]=>[8,5,3,4,1,2,6,7]=>[1,6,2,5,3,4,8,7]=>0101001
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[5,4,1,6,2,3,8,7]=>1101001
[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[8,5,3,1,2,4,6,7]=>[1,5,2,6,3,4,8,7]=>0101001
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>[4,1,2,6,3,5,8,7]=>1001001
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[1,2,3,6,4,5,8,7]=>0001001
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[8,4,5,2,3,1,6,7]=>[6,1,5,2,3,4,8,7]=>1010001
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,4,5,1,2,3,6,7]=>[1,2,6,3,4,5,8,7]=>0010001
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>[6,5,1,2,3,4,8,7]=>1100001
[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[8,3,4,5,1,2,6,7]=>[1,6,2,3,4,5,8,7]=>0100001
[.,[[[[.,[[.,.],.]],[.,.]],.],.]]=>[6,3,4,2,5,7,8,1]=>[8,4,2,3,5,1,6,7]=>[6,1,4,2,3,5,8,7]=>1010001
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[8,2,3,4,5,1,6,7]=>[6,1,2,3,4,5,8,7]=>1000001
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>[1,2,5,3,4,6,8,7]=>0010001
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,3,4,1,2,5,6,7]=>[1,5,2,3,4,6,8,7]=>0100001
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>[5,1,2,3,4,6,8,7]=>1000001
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[4,3,1,2,5,6,8,7]=>1100001
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[1,4,2,3,5,6,8,7]=>0100001
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>[4,1,2,3,5,6,8,7]=>1000001
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>[3,1,2,4,5,6,8,7]=>1000001
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>0000001
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>1111110
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[1,8,7,6,5,4,2,3]=>0111110
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[7,8,6,5,4,2,3,1]=>[8,1,7,6,5,4,2,3]=>1011110
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[7,8,6,5,4,2,1,3]=>[7,1,8,6,5,4,2,3]=>1011110
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[7,8,6,5,4,1,2,3]=>[1,2,8,7,6,5,3,4]=>0011110
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[7,8,6,5,3,2,4,1]=>[8,6,1,7,5,4,2,3]=>1101110
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[7,8,6,5,3,2,1,4]=>[7,6,1,8,5,4,2,3]=>1101110
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[7,8,6,5,3,1,2,4]=>[1,7,2,8,6,5,3,4]=>0101110
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[7,8,6,5,2,1,3,4]=>[6,1,2,8,7,5,3,4]=>1001110
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[7,8,6,5,1,2,3,4]=>[1,2,3,8,7,6,4,5]=>0001110
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[7,8,6,4,5,3,2,1]=>[8,7,6,1,5,4,2,3]=>1110110
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[1,8,7,2,6,5,3,4]=>0110110
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[7,8,6,4,3,5,2,1]=>[8,7,5,1,6,4,2,3]=>1110110
[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,3,1,2]=>[7,8,6,3,4,5,2,1]=>[8,7,1,2,6,5,3,4]=>1100110
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[7,8,6,3,4,5,1,2]=>[1,8,2,3,7,6,4,5]=>0100110
[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,3,1,2]=>[7,8,6,4,3,2,5,1]=>[8,6,5,1,7,4,2,3]=>1110110
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[7,8,6,3,4,2,5,1]=>[8,6,1,2,7,5,3,4]=>1100110
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[7,8,6,3,2,4,5,1]=>[8,5,1,2,7,6,3,4]=>1100110
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[7,8,6,4,3,2,1,5]=>[7,6,5,1,8,4,2,3]=>1110110
[[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>[5,6,7,4,8,3,1,2]=>[7,8,6,4,1,2,3,5]=>[1,2,7,3,8,6,4,5]=>0010110
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[7,8,6,3,4,1,2,5]=>[1,7,2,3,8,6,4,5]=>0100110
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[7,8,6,3,2,1,4,5]=>[6,5,1,2,8,7,3,4]=>1100110
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[7,8,6,3,1,2,4,5]=>[1,6,2,3,8,7,4,5]=>0100110
[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[7,8,6,2,3,1,4,5]=>[6,1,2,3,8,7,4,5]=>1000110
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[7,8,6,2,1,3,4,5]=>[5,1,2,3,8,7,4,6]=>1000110
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[7,8,6,1,2,3,4,5]=>[1,2,3,4,8,7,5,6]=>0000110
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,1,4,2,3]=>1111010
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[7,8,5,6,4,2,1,3]=>[7,1,8,6,2,5,3,4]=>1011010
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[7,8,5,6,3,4,2,1]=>[8,7,1,6,2,5,3,4]=>1101010
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[1,8,2,7,3,6,4,5]=>0101010
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[7,8,5,6,2,3,4,1]=>[8,1,2,7,3,6,4,5]=>1001010
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[7,8,5,6,3,2,1,4]=>[7,6,1,8,2,5,3,4]=>1101010
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[7,8,5,6,3,1,2,4]=>[1,7,2,8,3,6,4,5]=>0101010
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[7,8,5,6,2,3,1,4]=>[7,1,2,8,3,6,4,5]=>1001010
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[7,8,5,6,2,1,3,4]=>[6,1,2,8,3,7,4,5]=>1001010
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[7,8,5,6,1,2,3,4]=>[1,2,3,8,4,7,5,6]=>0001010
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[7,8,5,4,6,1,2,3]=>[1,2,8,6,3,7,4,5]=>0011010
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[7,8,4,5,6,3,1,2]=>[1,8,7,2,3,6,4,5]=>0110010
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[7,8,4,5,6,2,3,1]=>[8,1,7,2,3,6,4,5]=>1010010
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[7,8,5,4,3,6,2,1]=>[8,7,5,4,1,6,2,3]=>1111010
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[1,8,6,5,2,7,3,4]=>0111010
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[7,8,5,3,4,6,2,1]=>[8,7,1,5,2,6,3,4]=>1101010
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[7,8,5,3,4,6,1,2]=>[1,8,2,6,3,7,4,5]=>0101010
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[7,8,4,5,3,6,1,2]=>[1,8,6,2,3,7,4,5]=>0110010
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,5,6,1,2]=>[1,8,5,2,3,7,4,6]=>0110010
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[7,8,3,4,5,6,2,1]=>[8,7,1,2,3,6,4,5]=>1100010
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[7,8,3,4,5,6,1,2]=>[1,8,2,3,4,7,5,6]=>0100010
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,1,7,2,3]=>1111010
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[8,6,4,3,5,7,1,2]=>[7,8,4,3,5,2,6,1]=>[8,6,4,1,2,7,3,5]=>1110010
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[7,8,4,3,2,5,6,1]=>[8,5,4,1,2,7,3,6]=>1110010
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[8,4,5,3,6,7,1,2]=>[7,8,4,2,3,5,6,1]=>[8,1,5,2,3,7,4,6]=>1010010
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[7,8,3,4,2,5,6,1]=>[8,5,1,2,3,7,4,6]=>1100010
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[7,8,3,2,4,5,6,1]=>[8,4,1,2,3,7,5,6]=>1100010
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[7,8,2,3,4,5,6,1]=>[8,1,2,3,4,7,5,6]=>1000010
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,1,8,2,3]=>1111010
[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,3,8,1,2]=>[7,8,5,4,3,1,2,6]=>[1,7,6,5,2,8,3,4]=>0111010
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[7,8,5,4,2,1,3,6]=>[6,1,7,5,2,8,3,4]=>1011010
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[7,8,5,4,1,2,3,6]=>[1,2,7,6,3,8,4,5]=>0011010
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[7,8,5,3,4,1,2,6]=>[1,7,2,6,3,8,4,5]=>0101010
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[7,8,5,2,3,4,1,6]=>[7,1,2,6,3,8,4,5]=>1001010
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[7,8,5,3,2,1,4,6]=>[6,5,1,7,2,8,3,4]=>1101010
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[7,8,5,3,1,2,4,6]=>[1,6,2,7,3,8,4,5]=>0101010
[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[7,8,5,2,1,3,4,6]=>[5,1,2,7,3,8,4,6]=>1001010
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[7,8,5,1,2,3,4,6]=>[1,2,3,7,4,8,5,6]=>0001010
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[7,8,4,5,3,2,1,6]=>[7,6,5,1,2,8,3,4]=>1110010
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[7,8,4,5,2,3,1,6]=>[7,1,6,2,3,8,4,5]=>1010010
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[7,8,4,5,1,2,3,6]=>[1,2,7,3,4,8,5,6]=>0010010
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[7,8,3,4,5,2,1,6]=>[7,6,1,2,3,8,4,5]=>1100010
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[7,8,3,4,5,1,2,6]=>[1,7,2,3,4,8,5,6]=>0100010
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[7,8,4,3,2,5,1,6]=>[7,5,4,1,2,8,3,6]=>1110010
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[7,8,3,4,2,5,1,6]=>[7,5,1,2,3,8,4,6]=>1100010
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[7,8,2,3,4,5,1,6]=>[7,1,2,3,4,8,5,6]=>1000010
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[7,8,4,3,2,1,5,6]=>[6,5,4,1,2,8,3,7]=>1110010
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[7,8,4,3,1,2,5,6]=>[1,6,5,2,3,8,4,7]=>0110010
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[7,8,4,2,1,3,5,6]=>[5,1,6,2,3,8,4,7]=>1010010
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[7,8,4,1,2,3,5,6]=>[1,2,6,3,4,8,5,7]=>0010010
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>1100010
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[7,8,3,4,1,2,5,6]=>[1,6,2,3,4,8,5,7]=>0100010
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[7,8,3,2,4,1,5,6]=>[6,4,1,2,3,8,5,7]=>1100010
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[7,8,2,3,4,1,5,6]=>[6,1,2,3,4,8,5,7]=>1000010
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[7,8,3,2,1,4,5,6]=>[5,4,1,2,3,8,6,7]=>1100010
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[7,8,3,1,2,4,5,6]=>[1,5,2,3,4,8,6,7]=>0100010
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[7,8,2,3,1,4,5,6]=>[5,1,2,3,4,8,6,7]=>1000010
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[7,8,2,1,3,4,5,6]=>[4,1,2,3,5,8,6,7]=>1000010
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,8,6,7]=>0000010
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>1111110
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[7,6,8,5,4,3,1,2]=>[1,8,7,6,5,3,2,4]=>0111110
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[7,6,8,5,4,2,3,1]=>[8,1,7,6,5,3,2,4]=>1011110
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[7,1,8,6,5,3,2,4]=>1011110
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[7,6,8,5,4,1,2,3]=>[1,2,8,7,6,4,3,5]=>0011110
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[7,6,8,5,3,4,2,1]=>[8,7,1,6,5,3,2,4]=>1101110
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[7,6,8,5,3,4,1,2]=>[1,8,2,7,6,4,3,5]=>0101110
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[7,6,8,5,3,2,1,4]=>[7,6,1,8,5,3,2,4]=>1101110
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[7,6,8,5,2,3,1,4]=>[7,1,2,8,6,4,3,5]=>1001110
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[7,6,8,5,2,1,3,4]=>[6,1,2,8,7,4,3,5]=>1001110
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[7,6,8,5,1,2,3,4]=>[1,2,3,8,7,5,4,6]=>0001110
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[7,6,8,4,5,3,2,1]=>[8,7,6,1,5,3,2,4]=>1110110
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[7,6,8,4,5,2,3,1]=>[8,1,7,2,6,4,3,5]=>1010110
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[7,1,8,2,6,4,3,5]=>1010110
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[7,6,8,4,3,5,2,1]=>[8,7,5,1,6,3,2,4]=>1110110
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[7,6,8,4,3,2,5,1]=>[8,6,5,1,7,3,2,4]=>1110110
[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,2,1,3]=>[7,6,8,4,2,3,5,1]=>[8,1,6,2,7,4,3,5]=>1010110
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[7,6,8,3,4,2,5,1]=>[8,6,1,2,7,4,3,5]=>1100110
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[7,6,8,2,3,4,5,1]=>[8,1,2,3,7,5,4,6]=>1000110
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[7,6,8,4,3,2,1,5]=>[7,6,5,1,8,3,2,4]=>1110110
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[7,6,8,4,2,3,1,5]=>[7,1,6,2,8,4,3,5]=>1010110
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[7,6,8,4,1,2,3,5]=>[1,2,7,3,8,5,4,6]=>0010110
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[7,6,8,2,3,4,1,5]=>[7,1,2,3,8,5,4,6]=>1000110
[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[7,6,8,3,2,1,4,5]=>[6,5,1,2,8,4,3,7]=>1100110
[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[7,6,8,3,1,2,4,5]=>[1,6,2,3,8,5,4,7]=>0100110
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[7,6,8,2,3,1,4,5]=>[6,1,2,3,8,5,4,7]=>1000110
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[7,6,8,1,2,3,4,5]=>[1,2,3,4,8,6,5,7]=>0000110
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>1111100
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[6,7,8,5,4,3,1,2]=>[1,8,7,6,5,2,3,4]=>0111100
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[6,7,8,5,4,2,1,3]=>[7,1,8,6,5,2,3,4]=>1011100
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[6,7,8,5,4,1,2,3]=>[1,2,8,7,6,3,4,5]=>0011100
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[6,7,8,5,3,4,1,2]=>[1,8,2,7,6,3,4,5]=>0101100
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[6,7,8,5,3,2,4,1]=>[8,6,1,7,5,2,3,4]=>1101100
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[6,7,8,5,2,3,4,1]=>[8,1,2,7,6,3,4,5]=>1001100
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[6,7,8,5,3,2,1,4]=>[7,6,1,8,5,2,3,4]=>1101100
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[6,7,8,5,2,1,3,4]=>[6,1,2,8,7,3,4,5]=>1001100
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[6,7,8,5,1,2,3,4]=>[1,2,3,8,7,4,5,6]=>0001100
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[6,7,8,4,5,3,2,1]=>[8,7,6,1,5,2,3,4]=>1110100
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[6,7,8,4,5,3,1,2]=>[1,8,7,2,6,3,4,5]=>0110100
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[6,7,8,4,5,2,3,1]=>[8,1,7,2,6,3,4,5]=>1010100
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[6,7,8,4,5,1,2,3]=>[1,2,8,3,7,4,5,6]=>0010100
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[6,7,8,4,3,5,2,1]=>[8,7,5,1,6,2,3,4]=>1110100
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,7,8,4,3,5,1,2]=>[1,8,6,2,7,3,4,5]=>0110100
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,7,8,3,4,5,2,1]=>[8,7,1,2,6,3,4,5]=>1100100
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[6,7,8,4,2,3,5,1]=>[8,1,6,2,7,3,4,5]=>1010100
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[6,7,8,3,4,2,5,1]=>[8,6,1,2,7,3,4,5]=>1100100
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[6,7,8,3,2,4,5,1]=>[8,5,1,2,7,3,4,6]=>1100100
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[6,7,8,2,3,4,5,1]=>[8,1,2,3,7,4,5,6]=>1000100
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[6,7,8,4,3,2,1,5]=>[7,6,5,1,8,2,3,4]=>1110100
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[6,7,8,4,3,1,2,5]=>[1,7,6,2,8,3,4,5]=>0110100
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[6,7,8,4,2,3,1,5]=>[7,1,6,2,8,3,4,5]=>1010100
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[6,7,8,4,2,1,3,5]=>[6,1,7,2,8,3,4,5]=>1010100
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[6,7,8,4,1,2,3,5]=>[1,2,7,3,8,4,5,6]=>0010100
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[6,7,8,3,4,1,2,5]=>[1,7,2,3,8,4,5,6]=>0100100
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[6,7,8,3,2,4,1,5]=>[7,5,1,2,8,3,4,6]=>1100100
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[6,7,8,2,3,4,1,5]=>[7,1,2,3,8,4,5,6]=>1000100
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[6,7,8,3,2,1,4,5]=>[6,5,1,2,8,3,4,7]=>1100100
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[6,7,8,3,1,2,4,5]=>[1,6,2,3,8,4,5,7]=>0100100
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[6,7,8,2,3,1,4,5]=>[6,1,2,3,8,4,5,7]=>1000100
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[6,7,8,2,1,3,4,5]=>[5,1,2,3,8,4,6,7]=>1000100
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[6,7,8,1,2,3,4,5]=>[1,2,3,4,8,5,6,7]=>0000100
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>1111110
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[7,6,5,8,4,3,1,2]=>[1,8,7,6,4,3,2,5]=>0111110
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[7,6,5,8,4,2,3,1]=>[8,1,7,6,4,3,2,5]=>1011110
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[7,6,5,8,4,2,1,3]=>[7,1,8,6,4,3,2,5]=>1011110
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[7,6,5,8,4,1,2,3]=>[1,2,8,7,5,4,3,6]=>0011110
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[7,6,5,8,3,4,2,1]=>[8,7,1,6,4,3,2,5]=>1101110
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[7,6,5,8,3,4,1,2]=>[1,8,2,7,5,4,3,6]=>0101110
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[7,6,5,8,3,2,4,1]=>[8,6,1,7,4,3,2,5]=>1101110
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[7,6,5,8,2,3,4,1]=>[8,1,2,7,5,4,3,6]=>1001110
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[7,6,1,8,4,3,2,5]=>1101110
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[7,6,5,8,3,1,2,4]=>[1,7,2,8,5,4,3,6]=>0101110
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[7,6,5,8,1,2,3,4]=>[1,2,3,8,6,5,4,7]=>0001110
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>1111010
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[7,5,6,8,4,3,1,2]=>[1,8,7,6,2,4,3,5]=>0111010
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[7,5,6,8,4,2,3,1]=>[8,1,7,6,2,4,3,5]=>1011010
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[7,5,6,8,4,2,1,3]=>[7,1,8,6,2,4,3,5]=>1011010
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[7,5,6,8,4,1,2,3]=>[1,2,8,7,3,5,4,6]=>0011010
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[7,5,6,8,3,4,1,2]=>[1,8,2,7,3,5,4,6]=>0101010
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[7,5,6,8,3,1,2,4]=>[1,7,2,8,3,5,4,6]=>0101010
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[7,5,6,8,2,3,1,4]=>[7,1,2,8,3,5,4,6]=>1001010
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[7,5,6,8,2,1,3,4]=>[6,1,2,8,3,5,4,7]=>1001010
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[7,5,6,8,1,2,3,4]=>[1,2,3,8,4,6,5,7]=>0001010
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>1111100
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[6,7,5,8,4,3,1,2]=>[1,8,7,6,4,2,3,5]=>0111100
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[6,7,5,8,4,2,3,1]=>[8,1,7,6,4,2,3,5]=>1011100
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[6,7,5,8,4,2,1,3]=>[7,1,8,6,4,2,3,5]=>1011100
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[6,7,5,8,3,4,2,1]=>[8,7,1,6,4,2,3,5]=>1101100
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[6,7,5,8,3,4,1,2]=>[1,8,2,7,5,3,4,6]=>0101100
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[6,7,5,8,3,2,4,1]=>[8,6,1,7,4,2,3,5]=>1101100
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[6,7,5,8,2,3,4,1]=>[8,1,2,7,5,3,4,6]=>1001100
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[6,7,5,8,3,2,1,4]=>[7,6,1,8,4,2,3,5]=>1101100
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[6,7,5,8,3,1,2,4]=>[1,7,2,8,5,3,4,6]=>0101100
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[6,7,5,8,2,3,1,4]=>[7,1,2,8,5,3,4,6]=>1001100
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[6,7,5,8,2,1,3,4]=>[6,1,2,8,5,3,4,7]=>1001100
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[6,7,5,8,1,2,3,4]=>[1,2,3,8,6,4,5,7]=>0001100
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>1111100
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[6,5,7,8,4,3,1,2]=>[1,8,7,6,3,2,4,5]=>0111100
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[6,5,7,8,4,2,1,3]=>[7,1,8,6,3,2,4,5]=>1011100
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[6,5,7,8,3,4,1,2]=>[1,8,2,7,4,3,5,6]=>0101100
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[6,5,7,8,3,2,1,4]=>[7,6,1,8,3,2,4,5]=>1101100
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[6,5,7,8,3,1,2,4]=>[1,7,2,8,4,3,5,6]=>0101100
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[6,5,7,8,2,1,3,4]=>[6,1,2,8,4,3,5,7]=>1001100
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[6,5,7,8,1,2,3,4]=>[1,2,3,8,5,4,6,7]=>0001100
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>1111000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,6,7,8,4,3,1,2]=>[1,8,7,6,2,3,4,5]=>0111000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,6,7,8,4,2,3,1]=>[8,1,7,6,2,3,4,5]=>1011000
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,6,7,8,4,2,1,3]=>[7,1,8,6,2,3,4,5]=>1011000
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,6,7,8,4,1,2,3]=>[1,2,8,7,3,4,5,6]=>0011000
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[5,6,7,8,3,4,2,1]=>[8,7,1,6,2,3,4,5]=>1101000
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[5,6,7,8,3,4,1,2]=>[1,8,2,7,3,4,5,6]=>0101000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[5,6,7,8,3,2,4,1]=>[8,6,1,7,2,3,4,5]=>1101000
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[5,6,7,8,2,3,4,1]=>[8,1,2,7,3,4,5,6]=>1001000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[5,6,7,8,3,2,1,4]=>[7,6,1,8,2,3,4,5]=>1101000
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[5,6,7,8,3,1,2,4]=>[1,7,2,8,3,4,5,6]=>0101000
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[5,6,7,8,2,3,1,4]=>[7,1,2,8,3,4,5,6]=>1001000
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[5,6,7,8,2,1,3,4]=>[6,1,2,8,3,4,5,7]=>1001000
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>[1,2,3,8,4,5,6,7]=>0001000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>1111110
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[7,6,5,4,8,3,1,2]=>[1,8,7,5,4,3,2,6]=>0111110
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[7,6,5,4,8,2,3,1]=>[8,1,7,5,4,3,2,6]=>1011110
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[7,6,5,4,8,2,1,3]=>[7,1,8,5,4,3,2,6]=>1011110
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[7,6,5,4,8,1,2,3]=>[1,2,8,6,5,4,3,7]=>0011110
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[7,6,4,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>1110110
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[7,6,4,5,8,3,1,2]=>[1,8,7,2,5,4,3,6]=>0110110
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[7,6,4,5,8,2,3,1]=>[8,1,7,2,5,4,3,6]=>1010110
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[7,6,8,3,4,2,1,5]=>[7,6,4,5,8,2,1,3]=>[7,1,8,2,5,4,3,6]=>1010110
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[7,6,4,5,8,1,2,3]=>[1,2,8,3,6,5,4,7]=>0010110
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>1111010
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[7,5,6,4,8,2,3,1]=>[8,1,7,5,2,4,3,6]=>1011010
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,1,4,2,5]=>1111010
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[7,5,4,6,8,2,1,3]=>[7,1,8,4,2,5,3,6]=>1011010
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[7,5,4,6,8,1,2,3]=>[1,2,8,5,3,6,4,7]=>0011010
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[7,4,5,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>1110010
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[7,4,5,6,8,1,2,3]=>[1,2,8,3,4,6,5,7]=>0010010
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>1111100
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,3,1,2,5]=>[6,7,5,4,8,2,1,3]=>[7,1,8,5,4,2,3,6]=>1011100
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[6,7,4,5,8,3,2,1]=>[8,7,6,1,4,2,3,5]=>1110100
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[6,7,4,5,8,3,1,2]=>[1,8,7,2,5,3,4,6]=>0110100
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[6,7,4,5,8,2,3,1]=>[8,1,7,2,5,3,4,6]=>1010100
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[6,7,4,5,8,1,2,3]=>[1,2,8,3,6,4,5,7]=>0010100
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>1111100
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[6,5,7,4,8,3,1,2]=>[1,8,7,5,3,2,4,6]=>0111100
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[6,5,7,4,8,2,3,1]=>[8,1,7,5,3,2,4,6]=>1011100
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[6,5,7,4,8,2,1,3]=>[7,1,8,5,3,2,4,6]=>1011100
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[6,5,7,4,8,1,2,3]=>[1,2,8,6,4,3,5,7]=>0011100
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>1111000
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,6,7,4,8,2,1,3]=>[7,1,8,5,2,3,4,6]=>1011000
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,6,7,4,8,1,2,3]=>[1,2,8,6,3,4,5,7]=>0011000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>1111100
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[6,5,4,7,8,3,1,2]=>[1,8,7,4,3,2,5,6]=>0111100
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[6,5,4,7,8,1,2,3]=>[1,2,8,5,4,3,6,7]=>0011100
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[6,4,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>1110100
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[6,4,5,7,8,1,2,3]=>[1,2,8,3,5,4,6,7]=>0010100
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>1111000
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[5,6,4,7,8,3,1,2]=>[1,8,7,4,2,3,5,6]=>0111000
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,6,4,7,8,1,2,3]=>[1,2,8,5,3,4,6,7]=>0011000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>1111000
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[5,4,6,7,8,3,1,2]=>[1,8,7,3,2,4,5,6]=>0111000
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,6,7,8,1,2,3]=>[1,2,8,4,3,5,6,7]=>0011000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>1110000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[4,5,6,7,8,3,1,2]=>[1,8,7,2,3,4,5,6]=>0110000
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[4,5,6,7,8,2,3,1]=>[8,1,7,2,3,4,5,6]=>1010000
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[4,5,6,7,8,2,1,3]=>[7,1,8,2,3,4,5,6]=>1010000
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[4,5,6,7,8,1,2,3]=>[1,2,8,3,4,5,6,7]=>0010000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>1111110
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,3,8,1,2]=>[1,8,6,5,4,3,2,7]=>0111110
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[7,6,4,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>1110110
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[7,6,3,4,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>1100110
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[7,6,3,4,5,8,1,2]=>[1,8,2,3,6,5,4,7]=>0100110
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[7,5,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>1111010
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[7,5,6,3,4,8,1,2]=>[1,8,2,6,3,5,4,7]=>0101010
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>1111010
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[7,4,5,6,3,8,2,1]=>[8,7,5,1,2,4,3,6]=>1110010
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,1,5,2,6]=>1111010
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[7,5,4,3,6,8,1,2]=>[1,8,5,4,2,6,3,7]=>0111010
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[7,5,3,4,6,8,2,1]=>[8,7,1,4,2,5,3,6]=>1101010
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[7,5,3,4,6,8,1,2]=>[1,8,2,5,3,6,4,7]=>0101010
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[7,3,4,5,6,8,1,2]=>[1,8,2,3,4,6,5,7]=>0100010
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>1111100
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,7,4,5,3,8,2,1]=>[8,7,5,1,4,2,3,6]=>1110100
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,7,4,5,3,8,1,2]=>[1,8,6,2,5,3,4,7]=>0110100
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,5,7,4,3,8,1,2]=>[1,8,6,5,3,2,4,7]=>0111100
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>1111000
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[5,6,7,3,4,8,1,2]=>[1,8,2,6,3,4,5,7]=>0101000
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>1111100
[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[6,4,5,7,3,8,1,2]=>[1,8,6,2,4,3,5,7]=>0110100
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[5,6,4,7,3,8,1,2]=>[1,8,6,4,2,3,5,7]=>0111000
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>1111000
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[5,4,6,7,3,8,1,2]=>[1,8,6,3,2,4,5,7]=>0111000
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>1110000
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[4,5,6,7,3,8,1,2]=>[1,8,6,2,3,4,5,7]=>0110000
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>1111100
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,4,3,7,8,1,2]=>[1,8,5,4,3,2,6,7]=>0111100
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[6,5,3,4,7,8,2,1]=>[8,7,1,4,3,2,5,6]=>1101100
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,4,3,5,7,8,1,2]=>[1,8,4,2,5,3,6,7]=>0110100
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[6,3,4,5,7,8,2,1]=>[8,7,1,2,4,3,5,6]=>1100100
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,3,4,5,7,8,1,2]=>[1,8,2,3,5,4,6,7]=>0100100
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[5,6,4,3,7,8,1,2]=>[1,8,5,4,2,3,6,7]=>0111000
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[5,6,3,4,7,8,1,2]=>[1,8,2,5,3,4,6,7]=>0101000
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[5,4,6,3,7,8,1,2]=>[1,8,5,3,2,4,6,7]=>0111000
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>1110000
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>1111000
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[5,4,3,6,7,8,1,2]=>[1,8,4,3,2,5,6,7]=>0111000
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[5,3,4,6,7,8,2,1]=>[8,7,1,3,2,4,5,6]=>1101000
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[5,3,4,6,7,8,1,2]=>[1,8,2,4,3,5,6,7]=>0101000
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[4,5,3,6,7,8,1,2]=>[1,8,4,2,3,5,6,7]=>0110000
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>1110000
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[4,3,5,6,7,8,1,2]=>[1,8,3,2,4,5,6,7]=>0110000
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>1100000
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,8,1,2]=>[1,8,2,3,4,5,6,7]=>0100000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>1111110
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,2,3,8,1]=>[8,1,6,5,4,3,2,7]=>1011110
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,6,5,3,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>1101110
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,2,4,8,1]=>[8,5,1,6,4,3,2,7]=>1101110
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,6,5,2,3,4,8,1]=>[8,1,2,6,5,4,3,7]=>1001110
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,6,4,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>1110110
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,6,4,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>1110110
[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]=>[8,6,3,4,5,2,1,7]=>[7,6,3,4,5,2,8,1]=>[8,6,1,2,5,4,3,7]=>1100110
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,6,4,2,3,5,8,1]=>[8,1,5,2,6,4,3,7]=>1010110
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,6,3,2,4,5,8,1]=>[8,4,1,2,6,5,3,7]=>1100110
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,6,2,3,4,5,8,1]=>[8,1,2,3,6,5,4,7]=>1000110
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>1111010
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,5,6,3,4,2,8,1]=>[8,6,1,5,2,4,3,7]=>1101010
[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]=>[8,5,6,3,2,4,1,7]=>[7,5,4,6,2,3,8,1]=>[8,1,6,4,2,5,3,7]=>1011010
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,4,5,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>1110010
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[7,4,5,6,2,3,8,1]=>[8,1,6,2,3,5,4,7]=>1010010
[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]=>[8,6,3,4,2,5,1,7]=>[7,5,3,4,6,2,8,1]=>[8,6,1,4,2,5,3,7]=>1101010
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,4,5,3,6,2,8,1]=>[8,6,4,1,2,5,3,7]=>1110010
[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[8,6,2,3,4,5,1,7]=>[7,3,4,5,6,2,8,1]=>[8,6,1,2,3,5,4,7]=>1100010
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[7,5,4,2,3,6,8,1]=>[8,1,5,4,2,6,3,7]=>1011010
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,5,3,2,4,6,8,1]=>[8,4,1,5,2,6,3,7]=>1101010
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[8,4,3,2,5,6,1,7]=>[7,4,3,2,5,6,8,1]=>[8,4,3,1,2,6,5,7]=>1110010
[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,4,2,3,5,6,8,1]=>[8,1,4,2,3,6,5,7]=>1010010
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,3,2,4,5,6,8,1]=>[8,3,1,2,4,6,5,7]=>1100010
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,2,3,4,5,6,8,1]=>[8,1,2,3,4,6,5,7]=>1000010
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>1111100
[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]=>[8,5,4,6,3,1,2,7]=>[6,7,5,3,2,4,8,1]=>[8,5,1,6,4,2,3,7]=>1101100
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[6,7,4,5,2,3,8,1]=>[8,1,6,2,5,3,4,7]=>1010100
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[6,7,4,3,2,5,8,1]=>[8,5,4,1,6,2,3,7]=>1110100
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[6,7,3,2,4,5,8,1]=>[8,4,1,2,6,3,5,7]=>1100100
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[6,7,2,3,4,5,8,1]=>[8,1,2,3,6,4,5,7]=>1000100
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>1111100
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[6,5,7,3,4,2,8,1]=>[8,6,1,5,3,2,4,7]=>1101100
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[6,5,7,3,2,4,8,1]=>[8,5,1,6,3,2,4,7]=>1101100
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>1111000
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[5,6,7,4,2,3,8,1]=>[8,1,6,5,2,3,4,7]=>1011000
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[5,6,7,3,4,2,8,1]=>[8,6,1,5,2,3,4,7]=>1101000
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[5,6,7,2,3,4,8,1]=>[8,1,2,6,3,4,5,7]=>1001000
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>1111100
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[6,4,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>1110100
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[6,4,5,7,2,3,8,1]=>[8,1,6,2,4,3,5,7]=>1010100
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[5,6,4,7,2,3,8,1]=>[8,1,6,4,2,3,5,7]=>1011000
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[5,4,6,7,2,3,8,1]=>[8,1,6,3,2,4,5,7]=>1011000
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>1110000
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[4,5,6,7,2,3,8,1]=>[8,1,6,2,3,4,5,7]=>1010000
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>1111100
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[6,5,3,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>1101100
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[6,4,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>1110100
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[6,4,3,5,7,2,8,1]=>[8,6,3,1,4,2,5,7]=>1110100
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[6,3,4,5,7,2,8,1]=>[8,6,1,2,4,3,5,7]=>1100100
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[5,6,3,4,7,2,8,1]=>[8,6,1,4,2,3,5,7]=>1101000
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>1111000
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>1110000
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>1100000
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>1111100
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[6,5,4,2,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>1011100
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[6,5,3,2,4,7,8,1]=>[8,4,1,5,3,2,6,7]=>1101100
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[6,5,2,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>1001100
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[6,3,4,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>1100100
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[6,2,3,4,5,7,8,1]=>[8,1,2,3,5,4,6,7]=>1000100
[[[[.,.],[.,[[.,.],.]]],.],[.,.]]=>[8,4,5,3,1,2,6,7]=>[5,6,4,2,3,7,8,1]=>[8,1,5,4,2,3,6,7]=>1011000
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[5,6,2,3,4,7,8,1]=>[8,1,2,5,3,4,6,7]=>1001000
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>1111000
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[5,4,6,2,3,7,8,1]=>[8,1,5,3,2,4,6,7]=>1011000
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>1110000
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[4,5,6,2,3,7,8,1]=>[8,1,5,2,3,4,6,7]=>1010000
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>1111000
[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>1110000
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>1100000
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>1111000
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[5,4,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>1011000
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[5,3,4,2,6,7,8,1]=>[8,4,1,3,2,5,6,7]=>1101000
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[5,2,3,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>1001000
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,5,2,3,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>1010000
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>1110000
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>1100000
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>1110000
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[4,2,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>1010000
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>1100000
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>1100000
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>1000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>1111110
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8]=>0111110
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,2,3,1,8]=>[7,1,6,5,4,3,2,8]=>1011110
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[1,2,7,6,5,4,3,8]=>0011110
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[7,6,5,3,4,1,2,8]=>[1,7,2,6,5,4,3,8]=>0101110
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,2,4,1,8]=>[7,5,1,6,4,3,2,8]=>1101110
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>[7,1,2,6,5,4,3,8]=>1001110
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[6,5,1,7,4,3,2,8]=>1101110
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[7,6,5,2,3,1,4,8]=>[6,1,2,7,5,4,3,8]=>1001110
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,6,5,4,8]=>0001110
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[7,6,4,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>1110110
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,6,4,5,2,3,1,8]=>[7,1,6,2,5,4,3,8]=>1010110
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>1100110
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,2,5,1,8]=>[7,5,4,1,6,3,2,8]=>1110110
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>[7,1,5,2,6,4,3,8]=>1010110
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[7,4,3,5,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>[7,4,1,2,6,5,3,8]=>1100110
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[7,6,2,3,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>1000110
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>[1,6,5,2,7,4,3,8]=>0110110
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[5,1,6,2,7,4,3,8]=>1010110
[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[7,6,2,3,4,1,5,8]=>[6,1,2,3,7,5,4,8]=>1000110
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[5,4,1,2,7,6,3,8]=>1100110
[[.,[.,[[[[.,.],[.,.]],.],.]]],.]=>[5,3,4,6,7,2,1,8]=>[7,6,2,3,1,4,5,8]=>[5,1,2,3,7,6,4,8]=>1000110
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,6,5,8]=>0000110
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,1,3,2,8]=>1111010
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[7,5,6,4,3,1,2,8]=>[1,7,6,5,2,4,3,8]=>0111010
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,5,6,4,2,3,1,8]=>[7,1,6,5,2,4,3,8]=>1011010
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,5,6,3,4,2,1,8]=>[7,6,1,5,2,4,3,8]=>1101010
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,5,6,3,4,1,2,8]=>[1,7,2,6,3,5,4,8]=>0101010
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,5,6,2,3,4,1,8]=>[7,1,2,6,3,5,4,8]=>1001010
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,5,6,3,1,2,4,8]=>[1,6,2,7,3,5,4,8]=>0101010
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[7,5,6,2,1,3,4,8]=>[5,1,2,7,3,6,4,8]=>1001010
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[7,5,6,1,2,3,4,8]=>[1,2,3,7,4,6,5,8]=>0001010
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,1,4,2,8]=>1111010
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[7,5,4,6,2,3,1,8]=>[7,1,6,4,2,5,3,8]=>1011010
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[7,5,4,6,2,1,3,8]=>[6,1,7,4,2,5,3,8]=>1011010
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[7,5,4,6,1,2,3,8]=>[1,2,7,5,3,6,4,8]=>0011010
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,4,5,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>1110010
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,4,5,6,1,2,3,8]=>[1,2,7,3,4,6,5,8]=>0010010
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,1,5,2,8]=>1111010
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[7,5,3,4,6,1,2,8]=>[1,7,2,5,3,6,4,8]=>0101010
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,4,5,3,6,2,1,8]=>[7,6,4,1,2,5,3,8]=>1110010
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[7,3,4,5,6,2,1,8]=>[7,6,1,2,3,5,4,8]=>1100010
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[7,5,4,2,3,6,1,8]=>[7,1,5,4,2,6,3,8]=>1011010
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,1,4,2,6,3,8]=>1101010
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[7,5,3,2,4,6,1,8]=>[7,4,1,5,2,6,3,8]=>1101010
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,4,5,2,3,6,1,8]=>[7,1,5,2,3,6,4,8]=>1010010
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[7,4,3,5,2,6,1,8]=>[7,5,3,1,2,6,4,8]=>1110010
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[7,2,3,4,5,6,1,8]=>[7,1,2,3,4,6,5,8]=>1000010
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[6,4,5,3,2,7,1,8]=>[7,5,4,2,3,1,6,8]=>[6,1,5,4,2,7,3,8]=>1011010
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,5,3,4,1,2,6,8]=>[1,6,2,5,3,7,4,8]=>0101010
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[7,5,3,2,4,1,6,8]=>[6,4,1,5,2,7,3,8]=>1101010
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[5,4,1,6,2,7,3,8]=>1101010
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[1,5,2,6,3,7,4,8]=>0101010
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[7,5,2,3,1,4,6,8]=>[5,1,2,6,3,7,4,8]=>1001010
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[1,2,3,6,4,7,5,8]=>0001010
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,4,5,2,1,3,6,8]=>[5,1,6,2,3,7,4,8]=>1010010
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[7,4,5,1,2,3,6,8]=>[1,2,6,3,4,7,5,8]=>0010010
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,4,3,5,2,1,6,8]=>[6,5,3,1,2,7,4,8]=>1110010
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,2,3,4,5,1,6,8]=>[6,1,2,3,4,7,5,8]=>1000010
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[5,4,3,1,2,7,6,8]=>1110010
[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[4,5,3,2,6,7,1,8]=>[7,4,3,1,2,5,6,8]=>[1,5,4,2,3,7,6,8]=>0110010
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>[1,2,5,3,4,7,6,8]=>0010010
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[7,3,4,1,2,5,6,8]=>[1,5,2,3,4,7,6,8]=>0100010
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>[4,3,1,2,5,7,6,8]=>1100010
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[1,4,2,3,5,7,6,8]=>0100010
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,2,3,1,4,5,6,8]=>[4,1,2,3,5,7,6,8]=>1000010
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>[3,1,2,4,5,7,6,8]=>1000010
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,6,8]=>0000010
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>1111100
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[6,7,5,4,3,1,2,8]=>[1,7,6,5,4,2,3,8]=>0111100
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[6,7,5,4,2,3,1,8]=>[7,1,6,5,4,2,3,8]=>1011100
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[6,7,5,2,3,4,1,8]=>[7,1,2,6,5,3,4,8]=>1001100
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[6,7,5,2,1,3,4,8]=>[5,1,2,7,6,3,4,8]=>1001100
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[6,7,5,1,2,3,4,8]=>[1,2,3,7,6,4,5,8]=>0001100
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[6,7,4,5,3,2,1,8]=>[7,6,5,1,4,2,3,8]=>1110100
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[6,7,4,5,2,3,1,8]=>[7,1,6,2,5,3,4,8]=>1010100
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[7,6,4,3,5,1,2,8]=>[6,7,4,3,5,2,1,8]=>[7,6,4,1,5,2,3,8]=>1110100
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[6,7,3,4,5,1,2,8]=>[1,7,2,3,6,4,5,8]=>0100100
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[6,7,4,3,2,5,1,8]=>[7,5,4,1,6,2,3,8]=>1110100
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[6,7,4,2,3,5,1,8]=>[7,1,5,2,6,3,4,8]=>1010100
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[7,3,4,5,6,1,2,8]=>[6,7,2,3,4,5,1,8]=>[7,1,2,3,6,4,5,8]=>1000100
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[6,7,4,3,2,1,5,8]=>[6,5,4,1,7,2,3,8]=>1110100
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[6,7,4,2,3,1,5,8]=>[6,1,5,2,7,3,4,8]=>1010100
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[6,7,3,4,1,2,5,8]=>[1,6,2,3,7,4,5,8]=>0100100
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[6,7,3,2,4,1,5,8]=>[6,4,1,2,7,3,5,8]=>1100100
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[6,7,2,3,4,1,5,8]=>[6,1,2,3,7,4,5,8]=>1000100
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[6,7,3,1,2,4,5,8]=>[1,5,2,3,7,4,6,8]=>0100100
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[6,7,1,2,3,4,5,8]=>[1,2,3,4,7,5,6,8]=>0000100
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>1111100
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[6,5,7,4,2,1,3,8]=>[6,1,7,5,3,2,4,8]=>1011100
[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[6,5,7,3,4,1,2,8]=>[1,7,2,6,4,3,5,8]=>0101100
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[6,5,7,3,2,4,1,8]=>[7,5,1,6,3,2,4,8]=>1101100
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[6,5,7,2,3,4,1,8]=>[7,1,2,6,4,3,5,8]=>1001100
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[6,5,7,1,2,3,4,8]=>[1,2,3,7,5,4,6,8]=>0001100
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>1111000
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3,8]=>[1,2,7,6,3,4,5,8]=>0011000
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[5,6,7,2,3,4,1,8]=>[7,1,2,6,3,4,5,8]=>1001000
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[5,6,7,3,1,2,4,8]=>[1,6,2,7,3,4,5,8]=>0101000
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[5,6,7,2,3,1,4,8]=>[6,1,2,7,3,4,5,8]=>1001000
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[5,6,7,2,1,3,4,8]=>[5,1,2,7,3,4,6,8]=>1001000
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[5,6,7,1,2,3,4,8]=>[1,2,3,7,4,5,6,8]=>0001000
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>1111100
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[5,6,4,7,2,3,1,8]=>[7,1,6,4,2,3,5,8]=>1011000
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[5,6,4,7,1,2,3,8]=>[1,2,7,5,3,4,6,8]=>0011000
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>1111000
[[[[.,[.,.]],.],[.,[[.,.],.]]],.]=>[6,7,5,2,1,3,4,8]=>[5,4,6,7,3,1,2,8]=>[1,7,6,3,2,4,5,8]=>0111000
[[[[.,[.,.]],.],[[.,[.,.]],.]],.]=>[6,5,7,2,1,3,4,8]=>[5,4,6,7,2,1,3,8]=>[6,1,7,3,2,4,5,8]=>1011000
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[5,4,6,7,1,2,3,8]=>[1,2,7,4,3,5,6,8]=>0011000
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>1110000
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[4,5,6,7,3,1,2,8]=>[1,7,6,2,3,4,5,8]=>0110000
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[4,5,6,7,2,3,1,8]=>[7,1,6,2,3,4,5,8]=>1010000
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[4,5,6,7,2,1,3,8]=>[6,1,7,2,3,4,5,8]=>1010000
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[4,5,6,7,1,2,3,8]=>[1,2,7,3,4,5,6,8]=>0010000
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>1111100
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[6,5,4,3,7,1,2,8]=>[1,7,5,4,3,2,6,8]=>0111100
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[6,4,3,5,7,1,2,8]=>[1,7,4,2,5,3,6,8]=>0110100
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[6,3,4,5,7,1,2,8]=>[1,7,2,3,5,4,6,8]=>0100100
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>1111000
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[5,6,3,4,7,1,2,8]=>[1,7,2,5,3,4,6,8]=>0101000
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>1111000
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>1111000
[[[[[.,[.,.]],.],.],[[.,.],.]],.]=>[6,7,2,1,3,4,5,8]=>[4,3,5,6,7,1,2,8]=>[1,7,3,2,4,5,6,8]=>0110000
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>1100000
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[3,4,5,6,7,1,2,8]=>[1,7,2,3,4,5,6,8]=>0100000
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>1111100
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[6,5,3,2,4,7,1,8]=>[7,4,1,5,3,2,6,8]=>1101100
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[6,3,4,5,2,7,1,8]=>[7,5,1,2,4,3,6,8]=>1100100
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[6,4,2,3,5,7,1,8]=>[7,1,4,2,5,3,6,8]=>1010100
[[[.,[[[.,[.,.]],.],.]],[.,.]],.]=>[7,3,2,4,5,1,6,8]=>[6,3,2,4,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>1100100
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[6,2,3,4,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>1000100
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[5,6,3,4,2,7,1,8]=>[7,5,1,4,2,3,6,8]=>1101000
[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[5,4,6,2,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>1011000
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>1111000
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[5,3,4,6,2,7,1,8]=>[7,5,1,3,2,4,6,8]=>1101000
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>1110000
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>1100000
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>1111000
[[[[.,[.,[[.,.],.]]],.],[.,.]],.]=>[7,3,4,2,1,5,6,8]=>[5,4,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>1011000
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[5,2,3,4,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>1001000
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[4,5,2,3,6,7,1,8]=>[7,1,4,2,3,5,6,8]=>1010000
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>1100000
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>1110000
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[4,2,3,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>1010000
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>1100000
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>1100000
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>1000000
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>1111100
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[1,6,5,4,3,2,7,8]=>0111100
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>[5,1,6,4,3,2,7,8]=>1011100
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>[1,2,6,5,4,3,7,8]=>0011100
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>1101100
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>[5,4,1,6,3,2,7,8]=>1101100
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,5,4,7,8]=>0001100
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[6,4,5,2,1,3,7,8]=>[5,1,6,2,4,3,7,8]=>1010100
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[6,4,3,5,1,2,7,8]=>[1,6,4,2,5,3,7,8]=>0110100
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,1,5,2,7,8]=>1110100
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>1000100
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[5,4,3,1,6,2,7,8]=>1110100
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[1,5,4,2,6,3,7,8]=>0110100
[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>1010100
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>[1,2,5,3,6,4,7,8]=>0010100
[[[.,[[[.,[.,[.,.]]],.],.]],.],.]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>[4,3,1,2,6,5,7,8]=>1100100
[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[6,3,1,2,4,5,7,8]=>[1,4,2,3,6,5,7,8]=>0100100
[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[6,2,3,1,4,5,7,8]=>[4,1,2,3,6,5,7,8]=>1000100
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>0000100
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>1111000
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[5,6,4,2,1,3,7,8]=>[5,1,6,4,2,3,7,8]=>1011000
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]=>[1,6,2,5,3,4,7,8]=>0101000
[[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[6,4,3,5,1,2,7,8]=>[5,6,3,2,4,1,7,8]=>[6,4,1,5,2,3,7,8]=>1101000
[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[5,6,2,3,4,1,7,8]=>[6,1,2,5,3,4,7,8]=>1001000
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[5,6,3,2,1,4,7,8]=>[5,4,1,6,2,3,7,8]=>1101000
[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[5,6,1,2,3,4,7,8]=>[1,2,3,6,4,5,7,8]=>0001000
[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[6,5,4,2,1,3,7,8]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>1111000
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[5,4,6,3,1,2,7,8]=>[1,6,5,3,2,4,7,8]=>0111000
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7,8]=>[5,1,6,3,2,4,7,8]=>1011000
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>1110000
[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[4,5,6,2,1,3,7,8]=>[5,1,6,2,3,4,7,8]=>1010000
[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[4,5,6,1,2,3,7,8]=>[1,2,6,3,4,5,7,8]=>0010000
[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>[6,5,3,2,1,4,7,8]=>1111000
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[5,4,3,6,1,2,7,8]=>[1,6,4,3,2,5,7,8]=>0111000
[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[3,4,5,6,1,2,7,8]=>[1,6,2,3,4,5,7,8]=>0100000
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>1111000
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[6,2,3,4,1,5,7,8]=>[5,2,3,4,6,1,7,8]=>[6,1,2,4,3,5,7,8]=>1001000
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>1110000
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>1110000
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>1100000
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[4,3,2,5,6,1,7,8]=>[6,3,2,1,4,5,7,8]=>1110000
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[6,2,1,3,4,5,7,8]=>1100000
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>1000000
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>1111000
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>0111000
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>1011000
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>0011000
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>1101000
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,3,4,1,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>0101000
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>1101000
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>1001000
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[1,4,2,5,3,6,7,8]=>0101000
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>1001000
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>0001000
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>1110000
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>1010000
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[4,5,1,2,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>0010000
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>1110000
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>1100000
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[3,4,5,1,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>0100000
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>1110000
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[5,1,3,2,4,6,7,8]=>1010000
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>1100000
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>1100000
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>1000000
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>1110000
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>0110000
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>1010000
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>1010000
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>0010000
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>1100000
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>0100000
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>1100000
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>1000000
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>1100000
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>0100000
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>1000000
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>1000000
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>0000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>11111111
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>01111111
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>00111111
[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>00011111
[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>00001111
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>00000111
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>00000011
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>00000001
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>00000000
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>111111111
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,3,2]=>011111111
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,3,1]=>[9,1,8,7,6,5,4,3,2]=>10111111
[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>001111111
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,1,2]=>[1,9,2,8,7,6,5,4,3]=>01011111
[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>000111111
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>000011111
[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>000001111
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>000000111
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,8,7]=>00000101
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>000000011
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,7,8]=>00000010
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>000000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>000000000
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[8,1,9,7,6,5,4,3,2]=>10111111
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[8,7,1,9,6,5,4,3,2]=>11011111
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,1,9,5,4,3,2]=>11101111
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,1,9,4,3,2]=>11110111
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,1,9,3,2]=>11111011
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,1,9,2]=>11111101
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>11111110
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1,10,8,7,6,5,4,3,2]=>101111111
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[9,8,7,6,5,2,3,1,4]=>[8,1,2,9,7,6,5,4,3]=>10011111
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,1,10,7,6,5,4,3,2]=>110111111
[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]=>[8,7,5,6,9,4,3,2,1]=>[9,8,7,6,3,4,2,1,5]=>[8,7,1,2,9,6,5,4,3]=>11001111
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,1,10,3,2]=>111111011
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>11111100
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>111111101
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>111111110
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[10,8,6,4,2,1,3,5,7,9]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>111110000
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>11111100000
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>10000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>100000000
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>11000000
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>[3,1,2,4,5,6,7,9,8]=>10000001
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>1000000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>110000000
[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>11000000
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>10100000
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>0000000001
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,1,2]=>[1,9,2,3,4,5,6,7,8]=>01000000
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,1,2,3]=>[1,2,9,3,4,5,6,7,8]=>00100000
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[5,6,7,8,9,1,2,3,4]=>[1,2,3,9,4,5,6,7,8]=>00010000
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,9,5,6,7,8]=>00001000
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,7,8]=>00000100
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>11000000
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,1,2]=>[1,10,2,3,4,5,6,7,8,9]=>010000000
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[4,5,6,7,8,9,2,1,3]=>[8,1,9,2,3,4,5,6,7]=>10100000
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,1,2,3]=>[1,2,10,3,4,5,6,7,8,9]=>001000000
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[5,6,7,8,9,10,1,2,3,4]=>[1,2,3,10,4,5,6,7,8,9]=>000100000
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,8,9]=>000010000
[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]=>[5,4,6,7,8,9,1,2,3]=>[7,8,9,2,1,3,4,5,6]=>[5,1,2,3,4,9,6,7,8]=>10000100
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,8,9]=>000001000
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,7,8,9]=>000000100
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,8,9]=>000000010
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>11111110
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9]=>01111110
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,2,3]=>01111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>111111110
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>1111111110
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>011111110
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,2,3]=>011111110
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[11,10,9,8,7,6,5,4,3,1,2]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>1111111110
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>101010101
[.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>10101010101
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>11111110
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>11111110
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>11111110
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>11111110
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>11111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>11111110
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>11111100
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>111111110
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>111111110
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>111111110
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>111111110
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>111111110
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>111111110
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>111111110
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>11111100
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>11111000
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>11110000
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>11100000
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>11000000
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>10000000
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>111111100
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>111111000
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>111110000
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[6,5,4,3,1,2,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>11110000
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>111100000
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[5,4,3,1,2,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>11100000
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>111000000
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>11000000
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>110000000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>10000000
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>100000000
[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]=>[9,8,6,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,2,1]=>[9,8,1,7,6,5,4,3,2]=>11011111
[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>11101111
[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,4,5,3,2,1]=>[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>11110111
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>11111101
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>101111111
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>111101111
[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,4,5,3,2,1]=>[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>111110111
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,3,2]=>111111101
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[10,8,9,6,7,4,5,2,3,1]=>[10,1,9,2,8,3,7,4,6,5]=>101010101
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[9,2,3,4,5,6,7,8,1]=>[9,1,2,3,4,5,6,8,7]=>10000001
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>1000000000
[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[8,2,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>11000000
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[8,9,2,1,3,4,5,6,7]=>[4,3,5,6,7,8,9,1,2]=>[1,9,3,2,4,5,6,7,8]=>01100000
[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[8,2,3,4,5,6,7,9,1]=>[9,2,3,4,5,6,7,1,8]=>[8,1,2,3,4,5,6,9,7]=>10000001
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[9,3,4,5,6,7,8,1,2]=>[1,9,2,3,4,5,6,8,7]=>01000001
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,3,4,5,6,7,8,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>100000001
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>11111100
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,8,6,9,7]=>00000101
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>00000010
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>01000000
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>00010000
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>00000100
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>10100000
[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[8,2,3,4,5,6,7,1,9]=>[8,2,3,4,5,6,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>10000010
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>000000010
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>10000000
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>10000000
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>10000000
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>10000000
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>10000000
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>100000000
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>100000000
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>100000000
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>100000000
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>100000000
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>100000000
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>100000000
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[8,9,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,6,7]=>10000010
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,1,8,2]=>11111101
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>11111100
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,9,1,2]=>[1,9,7,6,5,4,3,2,8]=>01111110
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>0000000000
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>111111100
[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,2,1,3,9]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>11111100
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>111111100
[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[7,2,3,4,5,6,8,9,1]=>[9,2,3,4,5,6,1,7,8]=>[7,1,2,3,4,5,6,9,8]=>10000001
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[5,3,1,2,4,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>11000000
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[8,7,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,7,6,8]=>00000110
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,1,2]=>[1,9,8,7,6,5,3,2,4]=>01111110
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>110000000
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,1,11,2]=>1111111101
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>11100000
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>11110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>11111000
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>11000000
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>111000000
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>111100000
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>111110000
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>111111000
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>[9,7,8,6,5,4,3,1,2]=>[1,9,8,7,6,5,2,4,3]=>01111101
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>0111111111
[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[8,7,5,4,3,2,1,6,9]=>[7,6,5,4,3,8,2,1,9]=>[8,7,5,4,3,2,1,6,9]=>11111100
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[9,7,6,5,4,3,2,1,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>111111100
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[8,2,3,4,5,6,7,9,1]=>[9,1,2,3,4,5,7,6,8]=>10000010
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>01000000
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,10,11,1,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>0100000000
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,1,2,3,9]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>11111000
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[3,4,2,5,6,7,8,9,10,1]=>[10,3,1,2,4,5,6,7,8,9]=>110000000
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,1,2,9]=>111111100
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[9,3,4,5,6,7,8,2,1]=>[9,8,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,7,6]=>10000011
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
inverse
Description
Sends a permutation to its inverse.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
searching the database
Sorry, this map was not found in the database.