Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]=>
[.,[.,.]]=>[2,1]=>[2,1]=>[2,1]=>0
[[.,.],.]=>[1,2]=>[1,2]=>[1,2]=>1
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>00
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[3,2,1]=>00
[[.,.],[.,.]]=>[3,1,2]=>[3,2,1]=>[3,2,1]=>00
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1,3]=>01
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,2,3]=>11
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>000
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,3,2,1]=>[4,3,2,1]=>000
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,3,2,1]=>[4,3,2,1]=>000
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,2,3,1]=>[2,4,3,1]=>000
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[2,4,3,1]=>000
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[4,3,2,1]=>[4,3,2,1]=>000
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,3,2,1]=>[4,3,2,1]=>000
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[4,3,2,1]=>[4,3,2,1]=>000
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,2,3,1]=>[2,4,3,1]=>000
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>001
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[3,2,1,4]=>001
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,2,1,4]=>[3,2,1,4]=>001
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>011
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>111
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,2,4,1]=>[3,2,5,4,1]=>0000
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,3,2,4,1]=>[3,2,5,4,1]=>0000
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,3,2,4,1]=>[3,2,5,4,1]=>0000
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,2,3,4,1]=>[2,3,5,4,1]=>0000
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[2,3,5,4,1]=>0000
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[5,3,2,4,1]=>[3,2,5,4,1]=>0000
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,2,3,4,1]=>[2,3,5,4,1]=>0000
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,2,3,1,5]=>[2,4,3,1,5]=>0001
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[2,4,3,1,5]=>0001
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,2,3,1,5]=>[2,4,3,1,5]=>0001
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>0011
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>0011
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>0011
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>0111
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>1111
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>00000
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>00000
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>00000
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,2,3,4,5,1]=>[2,3,4,6,5,1]=>00000
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,3,4,6,5,1]=>00000
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>00000
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[6,2,3,4,5,1]=>[2,3,4,6,5,1]=>00000
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>00001
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>00001
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>00001
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,2,3,4,1,6]=>[2,3,5,4,1,6]=>00001
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,3,5,4,1,6]=>00001
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>00001
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,2,3,4,1,6]=>[2,3,5,4,1,6]=>00001
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>00011
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>00011
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>00011
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,2,3,1,5,6]=>[2,4,3,1,5,6]=>00011
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,4,3,1,5,6]=>00011
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>00011
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>00011
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>00011
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,2,3,1,5,6]=>[2,4,3,1,5,6]=>00011
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>00111
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>00111
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>00111
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>01111
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>11111
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>000000
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>000000
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>000000
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,3,4,5,7,6,1]=>000000
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,3,4,5,7,6,1]=>000000
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>000000
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[7,2,3,4,5,6,1]=>[2,3,4,5,7,6,1]=>000000
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>000001
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>000001
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>000001
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,3,4,6,5,1,7]=>000001
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,3,4,6,5,1,7]=>000001
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>000001
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,2,3,4,5,1,7]=>[2,3,4,6,5,1,7]=>000001
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>000011
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>000011
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>000011
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,3,5,4,1,6,7]=>000011
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,3,5,4,1,6,7]=>000011
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>000011
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,2,3,4,1,6,7]=>[2,3,5,4,1,6,7]=>000011
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>000111
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>000111
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>000111
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,4,3,1,5,6,7]=>000111
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,4,3,1,5,6,7]=>000111
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>000111
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>000111
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>000111
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,2,3,1,5,6,7]=>[2,4,3,1,5,6,7]=>000111
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>001111
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>001111
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>001111
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>011111
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>111111
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]=>[7,8,4,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[7,4,5,3,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>0000001
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>0000001
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>0000001
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>0000001
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>0000001
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>0000001
[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>0000001
[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[6,5,7,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>0000001
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>0000001
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>0000001
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[4,3,2,6,5,1,7,8]=>0000011
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[4,3,2,6,5,1,7,8]=>0000011
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[4,3,2,6,5,1,7,8]=>0000011
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>0000111
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>0000111
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>0000111
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>0000111
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>0000111
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>0000111
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>0000111
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>0001111
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>0001111
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>0001111
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>0001111
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>0001111
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>0001111
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>0001111
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>0001111
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>0001111
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>0011111
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>0011111
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>0011111
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>0111111
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>1111111
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
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
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