Identifier
Mp00017:
Binary trees
—to 312-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
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>[3,1,2]=>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
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[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
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,4,3,2]=>[4,3,1,2]=>000
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>[4,3,1,2]=>000
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[2,4,1,3]=>000
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[4,1,2,3]=>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
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>[3,1,2,4]=>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
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[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
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,2,4,3,1]=>[5,2,4,3,1]=>0000
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,4,3,1]=>[5,2,4,3,1]=>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
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[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
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[5,4,3,1,2]=>0000
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,5,4,3,2]=>[5,4,3,1,2]=>0000
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,5,4,3,2]=>[5,4,3,1,2]=>0000
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,3,4,2]=>[3,5,4,1,2]=>0000
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[3,5,4,1,2]=>0000
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[5,2,4,1,3]=>0000
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[5,2,4,1,3]=>0000
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[5,4,1,2,3]=>0000
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[5,4,1,2,3]=>0000
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[3,2,5,1,4]=>0000
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[3,2,5,1,4]=>0000
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[3,5,1,2,4]=>0000
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[2,5,1,3,4]=>0000
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[5,1,2,3,4]=>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
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[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
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[4,3,1,2,5]=>0001
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[4,3,1,2,5]=>0001
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,4,1,3,5]=>0001
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[4,1,2,3,5]=>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
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[3,1,2,4,5]=>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
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[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
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[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
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[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
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,2,5,4,3,1]=>[6,5,2,4,3,1]=>00000
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,2,5,4,3,1]=>[6,5,2,4,3,1]=>00000
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,2,5,4,3,1]=>[6,5,2,4,3,1]=>00000
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,5,4,3,1]=>[6,5,2,4,3,1]=>00000
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,3,2,5,4,1]=>[3,6,2,5,4,1]=>00000
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,3,2,5,4,1]=>[3,6,2,5,4,1]=>00000
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,3,2,5,4,1]=>[3,6,2,5,4,1]=>00000
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,2,3,5,4,1]=>[6,2,3,5,4,1]=>00000
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,5,4,1]=>[6,2,3,5,4,1]=>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
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[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
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>00000
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,2,4,3,5,1]=>[4,2,3,6,5,1]=>00000
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,4,3,5,1]=>[4,2,3,6,5,1]=>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
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[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
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,6,3,5,4,2]=>[6,3,5,4,1,2]=>00000
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,6,3,5,4,2]=>[6,3,5,4,1,2]=>00000
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,4,3,5,2]=>[4,3,6,5,1,2]=>00000
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,4,3,5,2]=>[4,3,6,5,1,2]=>00000
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,4,3,5,2]=>[4,3,6,5,1,2]=>00000
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,3,4,5,2]=>[3,4,6,5,1,2]=>00000
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[3,4,6,5,1,2]=>00000
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[6,5,2,4,1,3]=>00000
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,6,5,4,3]=>[6,5,2,4,1,3]=>00000
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,6,5,4,3]=>[6,5,2,4,1,3]=>00000
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,4,5,3]=>[2,6,4,5,1,3]=>00000
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,6,4,5,1,3]=>00000
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>00000
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>00000
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>00000
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,4,5,3]=>[4,6,5,1,2,3]=>00000
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[4,6,5,1,2,3]=>00000
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[3,6,2,5,1,4]=>00000
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,1,6,5,4]=>[3,6,2,5,1,4]=>00000
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,6,5,4]=>[3,6,2,5,1,4]=>00000
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[3,6,2,5,1,4]=>00000
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[6,3,5,1,2,4]=>00000
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[6,3,5,1,2,4]=>00000
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[6,2,5,1,3,4]=>00000
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[6,2,5,1,3,4]=>00000
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>00000
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>00000
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,6,1,5]=>00000
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,6,1,5]=>00000
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,6,1,5]=>00000
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,2,3,1,6,5]=>[2,4,3,6,1,5]=>00000
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[2,4,3,6,1,5]=>00000
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[4,3,6,1,2,5]=>00000
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[4,3,6,1,2,5]=>00000
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,4,6,1,3,5]=>00000
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[4,6,1,2,3,5]=>00000
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[3,2,6,1,4,5]=>00000
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[3,2,6,1,4,5]=>00000
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[3,6,1,2,4,5]=>00000
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,6,1,3,4,5]=>00000
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>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
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[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
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>00001
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,2,4,3,1,6]=>[5,2,4,3,1,6]=>00001
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,4,3,1,6]=>[5,2,4,3,1,6]=>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
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[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
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>00001
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>00001
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>00001
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,3,4,2,6]=>[3,5,4,1,2,6]=>00001
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[3,5,4,1,2,6]=>00001
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[5,2,4,1,3,6]=>00001
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[5,2,4,1,3,6]=>00001
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>00001
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>00001
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[3,2,5,1,4,6]=>00001
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[3,2,5,1,4,6]=>00001
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[3,5,1,2,4,6]=>00001
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,5,1,3,4,6]=>00001
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>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
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[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
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>00011
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>00011
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,4,1,3,5,6]=>00011
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>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
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>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
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[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
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[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
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[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
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>000000
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>000000
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>000000
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>000000
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>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
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[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
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[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
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[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
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>000000
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>000000
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>000000
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>000000
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>000000
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,2,6,5,4,3,1]=>[7,6,5,2,4,3,1]=>000000
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,2,6,5,4,3,1]=>[7,6,5,2,4,3,1]=>000000
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,2,6,5,4,3,1]=>[7,6,5,2,4,3,1]=>000000
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,2,6,4,5,3,1]=>[2,7,6,4,5,3,1]=>000000
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,2,6,4,5,3,1]=>[2,7,6,4,5,3,1]=>000000
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,2,6,5,4,3,1]=>[7,6,5,2,4,3,1]=>000000
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,2,6,5,4,3,1]=>[7,6,5,2,4,3,1]=>000000
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,2,6,5,4,3,1]=>[7,6,5,2,4,3,1]=>000000
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,2,6,4,5,3,1]=>[2,7,6,4,5,3,1]=>000000
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,2,6,4,5,3,1]=>[2,7,6,4,5,3,1]=>000000
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,3,2,6,5,4,1]=>[7,3,6,2,5,4,1]=>000000
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,3,2,6,5,4,1]=>[7,3,6,2,5,4,1]=>000000
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,3,2,6,5,4,1]=>[7,3,6,2,5,4,1]=>000000
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,3,2,6,5,4,1]=>[7,3,6,2,5,4,1]=>000000
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,3,2,6,5,4,1]=>[7,3,6,2,5,4,1]=>000000
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,3,2,6,5,4,1]=>[7,3,6,2,5,4,1]=>000000
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,2,3,6,5,4,1]=>[7,6,2,3,5,4,1]=>000000
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,2,3,6,5,4,1]=>[7,6,2,3,5,4,1]=>000000
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,2,3,6,5,4,1]=>[7,6,2,3,5,4,1]=>000000
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,2,3,6,5,4,1]=>[7,6,2,3,5,4,1]=>000000
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,4,3,2,6,5,1]=>[4,3,7,2,6,5,1]=>000000
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,4,3,2,6,5,1]=>[4,3,7,2,6,5,1]=>000000
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,4,3,2,6,5,1]=>[4,3,7,2,6,5,1]=>000000
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,4,3,2,6,5,1]=>[4,3,7,2,6,5,1]=>000000
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,4,3,2,6,5,1]=>[4,3,7,2,6,5,1]=>000000
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,4,3,2,6,5,1]=>[4,3,7,2,6,5,1]=>000000
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,4,3,2,6,5,1]=>[4,3,7,2,6,5,1]=>000000
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,2,4,3,6,5,1]=>[4,7,2,3,6,5,1]=>000000
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,2,4,3,6,5,1]=>[4,7,2,3,6,5,1]=>000000
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,3,2,4,6,5,1]=>[3,7,2,4,6,5,1]=>000000
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,3,2,4,6,5,1]=>[3,7,2,4,6,5,1]=>000000
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,3,2,4,6,5,1]=>[3,7,2,4,6,5,1]=>000000
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,2,3,4,6,5,1]=>[7,2,3,4,6,5,1]=>000000
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,2,3,4,6,5,1]=>[7,2,3,4,6,5,1]=>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
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[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
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[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
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[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
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>000000
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>000000
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,2,5,4,3,6,1]=>[5,4,2,3,7,6,1]=>000000
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,2,5,4,3,6,1]=>[5,4,2,3,7,6,1]=>000000
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,2,5,4,3,6,1]=>[5,4,2,3,7,6,1]=>000000
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,2,5,4,3,6,1]=>[5,4,2,3,7,6,1]=>000000
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,3,2,5,4,6,1]=>[3,5,2,4,7,6,1]=>000000
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,3,2,5,4,6,1]=>[3,5,2,4,7,6,1]=>000000
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,3,2,5,4,6,1]=>[3,5,2,4,7,6,1]=>000000
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,2,3,5,4,6,1]=>[5,2,3,4,7,6,1]=>000000
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,2,3,5,4,6,1]=>[5,2,3,4,7,6,1]=>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
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[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
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>000000
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,2,4,3,5,6,1]=>[4,2,3,5,7,6,1]=>000000
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,2,4,3,5,6,1]=>[4,2,3,5,7,6,1]=>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
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[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
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>000000
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>000000
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>000000
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>000000
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>000000
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>000000
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>000000
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>000000
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,7,3,6,5,4,2]=>[7,6,3,5,4,1,2]=>000000
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,7,3,6,5,4,2]=>[7,6,3,5,4,1,2]=>000000
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,7,3,6,5,4,2]=>[7,6,3,5,4,1,2]=>000000
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,7,3,6,5,4,2]=>[7,6,3,5,4,1,2]=>000000
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,7,4,3,6,5,2]=>[4,7,3,6,5,1,2]=>000000
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,7,4,3,6,5,2]=>[4,7,3,6,5,1,2]=>000000
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,7,4,3,6,5,2]=>[4,7,3,6,5,1,2]=>000000
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,7,3,4,6,5,2]=>[7,3,4,6,5,1,2]=>000000
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,7,3,4,6,5,2]=>[7,3,4,6,5,1,2]=>000000
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>000000
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>000000
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>000000
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>000000
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>000000
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>000000
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>000000
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,3,5,4,6,2]=>[5,3,4,7,6,1,2]=>000000
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,3,5,4,6,2]=>[5,3,4,7,6,1,2]=>000000
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,4,3,5,6,2]=>[4,3,5,7,6,1,2]=>000000
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,4,3,5,6,2]=>[4,3,5,7,6,1,2]=>000000
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,4,3,5,6,2]=>[4,3,5,7,6,1,2]=>000000
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,3,4,5,6,2]=>[3,4,5,7,6,1,2]=>000000
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[3,4,5,7,6,1,2]=>000000
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>000000
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,7,4,6,5,3]=>[7,2,6,4,5,1,3]=>000000
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,7,4,6,5,3]=>[7,2,6,4,5,1,3]=>000000
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,5,4,6,3]=>[7,2,5,4,6,1,3]=>000000
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,5,4,6,3]=>[7,2,5,4,6,1,3]=>000000
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,5,4,6,3]=>[7,2,5,4,6,1,3]=>000000
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,4,5,6,3]=>[2,4,7,5,6,1,3]=>000000
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,4,7,5,6,1,3]=>000000
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>000000
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,7,4,6,5,3]=>[7,4,6,5,1,2,3]=>000000
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,7,4,6,5,3]=>[7,4,6,5,1,2,3]=>000000
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,5,4,6,3]=>[5,4,7,6,1,2,3]=>000000
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,5,4,6,3]=>[5,4,7,6,1,2,3]=>000000
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,5,4,6,3]=>[5,4,7,6,1,2,3]=>000000
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,4,5,6,3]=>[4,5,7,6,1,2,3]=>000000
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[4,5,7,6,1,2,3]=>000000
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[7,3,6,2,5,1,4]=>000000
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,2,1,7,6,5,4]=>[7,3,6,2,5,1,4]=>000000
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,2,1,7,6,5,4]=>[7,3,6,2,5,1,4]=>000000
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,2,1,7,5,6,4]=>[7,3,2,5,6,1,4]=>000000
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[7,3,2,5,6,1,4]=>000000
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[7,3,6,2,5,1,4]=>000000
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,2,1,7,6,5,4]=>[7,3,6,2,5,1,4]=>000000
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,2,1,7,6,5,4]=>[7,3,6,2,5,1,4]=>000000
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,2,1,7,5,6,4]=>[7,3,2,5,6,1,4]=>000000
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[7,3,2,5,6,1,4]=>000000
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[7,6,3,5,1,2,4]=>000000
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,7,6,5,4]=>[7,6,3,5,1,2,4]=>000000
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,7,6,5,4]=>[7,6,3,5,1,2,4]=>000000
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,5,6,4]=>[3,7,5,6,1,2,4]=>000000
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[3,7,5,6,1,2,4]=>000000
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[7,6,2,5,1,3,4]=>000000
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,7,6,5,4]=>[7,6,2,5,1,3,4]=>000000
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,7,6,5,4]=>[7,6,2,5,1,3,4]=>000000
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,5,6,4]=>[2,7,5,6,1,3,4]=>000000
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,7,5,6,1,3,4]=>000000
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>000000
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>000000
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>000000
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,5,6,4]=>[5,7,6,1,2,3,4]=>000000
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[5,7,6,1,2,3,4]=>000000
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,7,2,6,1,5]=>000000
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,7,2,6,1,5]=>000000
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,7,2,6,1,5]=>000000
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,7,2,6,1,5]=>000000
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,7,2,6,1,5]=>000000
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,7,2,6,1,5]=>000000
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,2,3,1,7,6,5]=>[2,4,7,3,6,1,5]=>000000
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[2,4,7,3,6,1,5]=>000000
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,3,1,7,6,5]=>[2,4,7,3,6,1,5]=>000000
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[2,4,7,3,6,1,5]=>000000
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[4,7,3,6,1,2,5]=>000000
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,4,3,2,7,6,5]=>[4,7,3,6,1,2,5]=>000000
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,3,2,7,6,5]=>[4,7,3,6,1,2,5]=>000000
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[4,7,3,6,1,2,5]=>000000
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[7,2,4,6,1,3,5]=>000000
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[7,2,4,6,1,3,5]=>000000
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[7,4,6,1,2,3,5]=>000000
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[7,4,6,1,2,3,5]=>000000
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[3,7,2,6,1,4,5]=>000000
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[3,7,2,6,1,4,5]=>000000
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[3,7,2,6,1,4,5]=>000000
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[3,7,2,6,1,4,5]=>000000
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[7,3,6,1,2,4,5]=>000000
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[7,3,6,1,2,4,5]=>000000
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[7,2,6,1,3,4,5]=>000000
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[7,2,6,1,3,4,5]=>000000
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>000000
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>000000
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>000000
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>000000
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>000000
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>000000
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>000000
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>000000
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>000000
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[5,2,4,3,1,7,6]=>[5,2,4,3,7,1,6]=>000000
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[5,2,4,3,1,7,6]=>[5,2,4,3,7,1,6]=>000000
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,3,2,4,1,7,6]=>[3,2,5,4,7,1,6]=>000000
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,3,2,4,1,7,6]=>[3,2,5,4,7,1,6]=>000000
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,3,2,4,1,7,6]=>[3,2,5,4,7,1,6]=>000000
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[2,3,5,4,7,1,6]=>000000
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[2,3,5,4,7,1,6]=>000000
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[5,4,3,7,1,2,6]=>000000
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,5,4,3,2,7,6]=>[5,4,3,7,1,2,6]=>000000
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,5,4,3,2,7,6]=>[5,4,3,7,1,2,6]=>000000
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,3,4,2,7,6]=>[3,5,4,7,1,2,6]=>000000
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[3,5,4,7,1,2,6]=>000000
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[5,2,4,7,1,3,6]=>000000
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[5,2,4,7,1,3,6]=>000000
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[5,4,7,1,2,3,6]=>000000
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[5,4,7,1,2,3,6]=>000000
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[3,2,5,7,1,4,6]=>000000
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[3,2,5,7,1,4,6]=>000000
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[3,5,7,1,2,4,6]=>000000
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,5,7,1,3,4,6]=>000000
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[5,7,1,2,3,4,6]=>000000
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,7,1,5,6]=>000000
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,7,1,5,6]=>000000
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,7,1,5,6]=>000000
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[2,4,3,7,1,5,6]=>000000
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[2,4,3,7,1,5,6]=>000000
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[4,3,7,1,2,5,6]=>000000
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[4,3,7,1,2,5,6]=>000000
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,4,7,1,3,5,6]=>000000
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[4,7,1,2,3,5,6]=>000000
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[3,2,7,1,4,5,6]=>000000
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[3,2,7,1,4,5,6]=>000000
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[3,7,1,2,4,5,6]=>000000
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,7,1,3,4,5,6]=>000000
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>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
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[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
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[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
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[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
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>000001
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>000001
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,2,5,4,3,1,7]=>[6,5,2,4,3,1,7]=>000001
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,2,5,4,3,1,7]=>[6,5,2,4,3,1,7]=>000001
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,2,5,4,3,1,7]=>[6,5,2,4,3,1,7]=>000001
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,2,5,4,3,1,7]=>[6,5,2,4,3,1,7]=>000001
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,3,2,5,4,1,7]=>[3,6,2,5,4,1,7]=>000001
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,3,2,5,4,1,7]=>[3,6,2,5,4,1,7]=>000001
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,3,2,5,4,1,7]=>[3,6,2,5,4,1,7]=>000001
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,2,3,5,4,1,7]=>[6,2,3,5,4,1,7]=>000001
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,5,4,1,7]=>[6,2,3,5,4,1,7]=>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
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[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
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>000001
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,2,4,3,5,1,7]=>[4,2,3,6,5,1,7]=>000001
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,2,4,3,5,1,7]=>[4,2,3,6,5,1,7]=>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
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[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
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>000001
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>000001
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>000001
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>000001
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>000001
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>000001
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>000001
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,6,3,5,4,2,7]=>[6,3,5,4,1,2,7]=>000001
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,6,3,5,4,2,7]=>[6,3,5,4,1,2,7]=>000001
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,4,3,5,2,7]=>[4,3,6,5,1,2,7]=>000001
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,4,3,5,2,7]=>[4,3,6,5,1,2,7]=>000001
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,4,3,5,2,7]=>[4,3,6,5,1,2,7]=>000001
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,3,4,5,2,7]=>[3,4,6,5,1,2,7]=>000001
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[3,4,6,5,1,2,7]=>000001
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[6,5,2,4,1,3,7]=>000001
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,6,5,4,3,7]=>[6,5,2,4,1,3,7]=>000001
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,6,5,4,3,7]=>[6,5,2,4,1,3,7]=>000001
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,4,5,3,7]=>[2,6,4,5,1,3,7]=>000001
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,6,4,5,1,3,7]=>000001
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>000001
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>000001
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>000001
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,4,5,3,7]=>[4,6,5,1,2,3,7]=>000001
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[4,6,5,1,2,3,7]=>000001
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[3,6,2,5,1,4,7]=>000001
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[3,6,2,5,1,4,7]=>000001
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[3,6,2,5,1,4,7]=>000001
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[3,6,2,5,1,4,7]=>000001
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[6,3,5,1,2,4,7]=>000001
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[6,3,5,1,2,4,7]=>000001
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[6,2,5,1,3,4,7]=>000001
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[6,2,5,1,3,4,7]=>000001
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>000001
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>000001
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,6,1,5,7]=>000001
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,6,1,5,7]=>000001
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,6,1,5,7]=>000001
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[2,4,3,6,1,5,7]=>000001
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[2,4,3,6,1,5,7]=>000001
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[4,3,6,1,2,5,7]=>000001
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[4,3,6,1,2,5,7]=>000001
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,4,6,1,3,5,7]=>000001
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[4,6,1,2,3,5,7]=>000001
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[3,2,6,1,4,5,7]=>000001
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[3,2,6,1,4,5,7]=>000001
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[3,6,1,2,4,5,7]=>000001
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,6,1,3,4,5,7]=>000001
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>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
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[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
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,2,4,3,1,6,7]=>[5,2,4,3,1,6,7]=>000011
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,4,3,1,6,7]=>[5,2,4,3,1,6,7]=>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
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[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
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>000011
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>000011
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>000011
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,3,4,2,6,7]=>[3,5,4,1,2,6,7]=>000011
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[3,5,4,1,2,6,7]=>000011
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[5,2,4,1,3,6,7]=>000011
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[5,2,4,1,3,6,7]=>000011
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>000011
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>000011
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[3,2,5,1,4,6,7]=>000011
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[3,2,5,1,4,6,7]=>000011
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[3,5,1,2,4,6,7]=>000011
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,5,1,3,4,6,7]=>000011
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>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
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[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
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>000111
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>000111
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,4,1,3,5,6,7]=>000111
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>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
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>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
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[6,8,7,5,4,3,2,1]=>[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
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[5,7,8,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[5,6,8,7,4,3,2,1]=>[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
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[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
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[4,7,8,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[4,6,8,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[4,7,6,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[4,6,7,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[4,5,7,8,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[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
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[5,7,6,4,8,3,2,1]=>[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
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[4,6,7,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[5,4,7,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[4,5,7,6,8,3,2,1]=>[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
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[4,6,5,7,8,3,2,1]=>[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
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[3,8,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[3,6,7,5,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[4,3,6,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[3,4,6,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]=>[4,5,3,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]=>[4,3,5,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[3,4,5,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]=>[4,5,6,3,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[4,8,3,7,6,5,2,1]=>0000000
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[4,8,3,7,6,5,2,1]=>0000000
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,8,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[2,7,6,8,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[2,4,6,7,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[2,5,4,8,7,6,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[2,4,5,7,8,6,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[2,5,6,4,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[4,8,3,7,6,5,2,1]=>0000000
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[4,8,3,7,6,5,2,1]=>0000000
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,2,5,4,1]=>0000000
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[4,3,2,7,8,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,2,5,4,1]=>0000000
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[4,3,2,6,8,7,5,1]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,2,5,4,1]=>0000000
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,2,5,4,1]=>0000000
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[3,4,2,7,8,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,2,5,4,1]=>0000000
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,2,5,4,1]=>0000000
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,1]=>[8,3,2,7,6,5,4,1]=>[8,7,3,6,2,5,4,1]=>0000000
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[4,6,5,3,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[5,4,6,3,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[4,5,6,3,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[3,6,5,4,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[3,5,6,4,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[5,4,3,6,2,8,7,1]=>[8,5,3,4,2,7,6,1]=>[3,5,4,8,2,7,6,1]=>0000000
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[2,4,6,5,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,8,2,7,6,1]=>0000000
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[4,3,2,6,5,8,7,1]=>[8,3,2,5,4,7,6,1]=>[3,5,8,2,4,7,6,1]=>0000000
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[3,4,2,6,5,8,7,1]=>[8,3,2,5,4,7,6,1]=>[3,5,8,2,4,7,6,1]=>0000000
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,3,2,5,4,7,6,1]=>[3,5,8,2,4,7,6,1]=>0000000
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[2,3,4,6,5,8,7,1]=>[8,2,3,5,4,7,6,1]=>[5,8,2,3,4,7,6,1]=>0000000
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[8,4,3,2,5,7,6,1]=>[4,3,8,2,5,7,6,1]=>0000000
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[8,4,3,2,5,7,6,1]=>[4,3,8,2,5,7,6,1]=>0000000
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[4,3,2,5,6,8,7,1]=>[8,3,2,4,5,7,6,1]=>[3,8,2,4,5,7,6,1]=>0000000
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[3,4,2,5,6,8,7,1]=>[8,3,2,4,5,7,6,1]=>[3,8,2,4,5,7,6,1]=>0000000
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[8,3,2,4,5,7,6,1]=>[3,8,2,4,5,7,6,1]=>0000000
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[4,7,6,5,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[4,6,5,7,3,2,8,1]=>[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
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[3,5,7,6,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[3,5,6,7,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[4,3,7,6,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]=>[4,3,6,7,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>0000000
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[3,4,7,6,5,2,8,1]=>[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
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[4,6,5,3,7,2,8,1]=>[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
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[3,6,5,4,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>0000000
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[2,4,6,5,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>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
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[3,6,5,4,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[.,[[.,.],[[.,.],.]]],.],.]]=>[3,5,6,4,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>0000000
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[2,6,5,4,3,7,8,1]=>[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
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[3,5,4,2,6,7,8,1]=>[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
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[2,4,5,3,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>0000000
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[1,4,6,5,8,7,3,2]=>[1,8,7,4,6,5,3,2]=>[8,4,7,6,5,3,1,2]=>0000000
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[1,5,4,6,8,7,3,2]=>[1,8,7,4,6,5,3,2]=>[8,4,7,6,5,3,1,2]=>0000000
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[1,4,7,6,5,8,3,2]=>[1,8,7,5,4,6,3,2]=>[5,4,8,7,6,3,1,2]=>0000000
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[1,3,5,7,6,8,4,2]=>[1,8,7,5,4,6,3,2]=>[5,4,8,7,6,3,1,2]=>0000000
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,8,3,7,6,5,4,2]=>[8,7,6,3,5,4,1,2]=>0000000
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[1,8,3,7,6,5,4,2]=>[8,7,6,3,5,4,1,2]=>0000000
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[1,4,3,6,8,7,5,2]=>[1,8,3,7,6,5,4,2]=>[8,7,6,3,5,4,1,2]=>0000000
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[1,8,3,7,5,6,4,2]=>[3,8,7,5,6,4,1,2]=>0000000
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[1,8,3,7,6,5,4,2]=>[8,7,6,3,5,4,1,2]=>0000000
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[1,8,3,7,5,6,4,2]=>[3,8,7,5,6,4,1,2]=>0000000
[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[1,3,4,6,7,8,5,2]=>[1,8,3,7,5,6,4,2]=>[3,8,7,5,6,4,1,2]=>0000000
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[1,5,4,3,8,7,6,2]=>[1,8,4,3,7,6,5,2]=>[8,4,7,3,6,5,1,2]=>0000000
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[1,3,5,4,7,8,6,2]=>[1,8,4,3,7,6,5,2]=>[8,4,7,3,6,5,1,2]=>0000000
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[1,3,4,7,6,5,8,2]=>[1,8,3,6,5,4,7,2]=>[6,5,3,4,8,7,1,2]=>0000000
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[1,3,5,4,7,6,8,2]=>[1,8,4,3,6,5,7,2]=>[4,6,3,5,8,7,1,2]=>0000000
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>[4,3,5,6,8,7,1,2]=>0000000
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[2,1,6,8,7,5,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[2,1,7,6,8,5,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[2,1,5,8,7,6,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[2,1,5,7,8,6,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[2,1,8,7,5,6,4,3]=>[5,8,7,6,2,4,1,3]=>0000000
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,8,7,5,6,4,3]=>[5,8,7,6,2,4,1,3]=>0000000
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[2,1,8,7,5,6,4,3]=>[5,8,7,6,2,4,1,3]=>0000000
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[2,1,8,7,5,6,4,3]=>[5,8,7,6,2,4,1,3]=>0000000
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,6,8,7,5,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,2,4,1,3]=>0000000
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[2,1,8,7,5,6,4,3]=>[5,8,7,6,2,4,1,3]=>0000000
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[2,1,8,5,4,7,6,3]=>[2,8,5,7,4,6,1,3]=>0000000
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[1,2,7,6,5,8,4,3]=>[1,2,8,7,5,6,4,3]=>[5,8,7,6,4,1,2,3]=>0000000
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[1,2,5,7,6,8,4,3]=>[1,2,8,7,5,6,4,3]=>[5,8,7,6,4,1,2,3]=>0000000
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[1,2,6,5,7,8,4,3]=>[1,2,8,7,5,6,4,3]=>[5,8,7,6,4,1,2,3]=>0000000
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,8,7,5,6,4,3]=>[5,8,7,6,4,1,2,3]=>0000000
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[1,2,8,7,5,6,4,3]=>[5,8,7,6,4,1,2,3]=>0000000
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[1,2,5,7,6,4,8,3]=>[1,2,8,6,5,4,7,3]=>[6,5,4,8,7,1,2,3]=>0000000
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[1,2,5,6,7,4,8,3]=>[1,2,8,6,5,4,7,3]=>[6,5,4,8,7,1,2,3]=>0000000
[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[1,2,4,7,6,5,8,3]=>[1,2,8,6,5,4,7,3]=>[6,5,4,8,7,1,2,3]=>0000000
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[1,3,2,6,5,8,7,4]=>[1,3,2,8,5,7,6,4]=>[8,3,7,5,6,1,2,4]=>0000000
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,5,7,6,4]=>[8,5,7,6,1,2,3,4]=>0000000
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,5,7,6,4]=>[8,5,7,6,1,2,3,4]=>0000000
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,5,7,4]=>[6,5,8,7,1,2,3,4]=>0000000
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,6,5,7,4]=>[6,5,8,7,1,2,3,4]=>0000000
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,6,5,7,4]=>[6,5,8,7,1,2,3,4]=>0000000
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,5,6,7,4]=>[5,6,8,7,1,2,3,4]=>0000000
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[5,6,8,7,1,2,3,4]=>0000000
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,8,3,2,6,7,1,5]=>0000000
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,8,3,2,6,7,1,5]=>0000000
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,8,3,2,6,7,1,5]=>0000000
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,8,3,2,6,7,1,5]=>0000000
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,8,3,7,2,6,1,5]=>0000000
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,8,3,2,6,7,1,5]=>0000000
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,8,3,2,6,7,1,5]=>0000000
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[8,2,4,7,3,6,1,5]=>0000000
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,2,3,1,8,7,6,5]=>[8,2,4,7,3,6,1,5]=>0000000
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,2,3,1,8,7,6,5]=>[8,2,4,7,3,6,1,5]=>0000000
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,3,6,7,1,5]=>0000000
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,3,6,7,1,5]=>0000000
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[8,2,4,7,3,6,1,5]=>0000000
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,8,7,6,5]=>[8,2,4,7,3,6,1,5]=>0000000
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,8,7,6,5]=>[8,2,4,7,3,6,1,5]=>0000000
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,3,6,7,1,5]=>0000000
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,3,6,7,1,5]=>0000000
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[8,4,7,3,6,1,2,5]=>0000000
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[8,4,7,3,6,1,2,5]=>0000000
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[1,3,4,2,7,8,6,5]=>[1,4,3,2,8,7,6,5]=>[8,4,7,3,6,1,2,5]=>0000000
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,8,7,6,5]=>[8,4,7,3,6,1,2,5]=>0000000
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[8,7,2,4,6,1,3,5]=>0000000
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,7,6,5]=>[8,7,2,4,6,1,3,5]=>0000000
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,7,6,5]=>[8,7,2,4,6,1,3,5]=>0000000
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,6,7,5]=>[2,8,4,6,7,1,3,5]=>0000000
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,8,4,6,7,1,3,5]=>0000000
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[8,7,4,6,1,2,3,5]=>0000000
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,8,7,6,5]=>[8,7,4,6,1,2,3,5]=>0000000
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,8,7,6,5]=>[8,7,4,6,1,2,3,5]=>0000000
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,6,7,5]=>[4,8,6,7,1,2,3,5]=>0000000
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[4,8,6,7,1,2,3,5]=>0000000
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[8,3,7,2,6,1,4,5]=>0000000
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[3,2,1,4,8,7,6,5]=>[8,3,7,2,6,1,4,5]=>0000000
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[3,2,1,4,6,8,7,5]=>[3,2,1,4,8,7,6,5]=>[8,3,7,2,6,1,4,5]=>0000000
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[8,3,7,2,6,1,4,5]=>0000000
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,8,7,6,5]=>[8,3,7,2,6,1,4,5]=>0000000
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[8,7,3,6,1,2,4,5]=>0000000
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,8,7,6,5]=>[8,7,3,6,1,2,4,5]=>0000000
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[8,7,2,6,1,3,4,5]=>0000000
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>0000000
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>0000000
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>0000000
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,6,7,5]=>[6,8,7,1,2,3,4,5]=>0000000
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[6,8,7,1,2,3,4,5]=>0000000
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,3,2,4,1,8,7,6]=>[3,2,5,8,4,7,1,6]=>0000000
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,3,2,4,1,8,7,6]=>[3,2,5,8,4,7,1,6]=>0000000
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[3,2,5,8,4,7,1,6]=>0000000
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[5,3,2,4,1,8,7,6]=>[3,2,5,8,4,7,1,6]=>0000000
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[2,4,3,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[3,2,5,8,4,7,1,6]=>0000000
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,8,7,6]=>[8,5,7,1,2,3,4,6]=>0000000
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[8,5,7,1,2,3,4,6]=>0000000
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,8,2,7,1,5,6]=>0000000
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[4,3,8,2,7,1,5,6]=>0000000
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[3,4,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,8,2,7,1,5,6]=>0000000
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,2,3,1,5,8,7,6]=>[2,4,8,3,7,1,5,6]=>0000000
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[2,4,8,3,7,1,5,6]=>0000000
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,8,7,6]=>[2,4,8,3,7,1,5,6]=>0000000
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[2,4,8,3,7,1,5,6]=>0000000
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]=>[1,4,3,2,5,8,7,6]=>[4,8,3,7,1,2,5,6]=>0000000
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[4,8,3,7,1,2,5,6]=>0000000
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,8,7,6]=>[4,8,3,7,1,2,5,6]=>0000000
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[4,8,3,7,1,2,5,6]=>0000000
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>[3,8,2,7,1,4,5,6]=>0000000
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[3,2,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[3,8,2,7,1,4,5,6]=>0000000
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[3,8,2,7,1,4,5,6]=>0000000
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[4,6,5,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[3,6,5,4,2,8,1,7]=>0000000
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[3,6,5,4,2,8,1,7]=>0000000
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[3,4,5,6,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[3,6,5,4,2,8,1,7]=>0000000
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[2,6,5,4,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[2,5,6,4,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,4,6,5,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,8,1,7]=>0000000
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[6,3,2,5,4,1,8,7]=>[3,6,2,5,4,8,1,7]=>0000000
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[6,5,2,4,8,1,3,7]=>0000000
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[6,5,2,4,8,1,3,7]=>0000000
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,6,5,4,3,8,7]=>[6,5,2,4,8,1,3,7]=>0000000
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,6,4,5,8,1,3,7]=>0000000
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,6,4,5,8,1,3,7]=>0000000
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]=>[2,1,3,6,5,4,8,7]=>[6,2,5,8,1,3,4,7]=>0000000
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]=>[1,2,3,6,5,4,8,7]=>[6,5,8,1,2,3,4,7]=>0000000
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[6,5,8,1,2,3,4,7]=>0000000
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,6,8,1,5,7]=>0000000
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,6,8,1,5,7]=>0000000
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,6,8,1,5,7]=>0000000
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,4,3,6,8,1,5,7]=>0000000
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,4,3,6,8,1,5,7]=>0000000
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,4,6,8,1,3,5,7]=>0000000
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,8,1,6,7]=>0000000
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[4,5,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,8,1,6,7]=>0000000
[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]=>[3,5,4,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,8,1,6,7]=>0000000
[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]=>[2,5,4,3,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,8,1,6,7]=>0000000
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[2,4,5,3,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,8,1,6,7]=>0000000
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[3,2,5,4,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>[5,2,4,3,8,1,6,7]=>0000000
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[1,3,5,4,2,6,8,7]=>[1,5,4,3,2,6,8,7]=>[5,4,3,8,1,2,6,7]=>0000000
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[5,2,4,8,1,3,6,7]=>0000000
[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[5,2,4,8,1,3,6,7]=>0000000
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[5,4,8,1,2,3,6,7]=>0000000
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,8,1,5,6,7]=>0000000
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[4,8,1,2,3,5,6,7]=>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
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[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
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[4,6,7,5,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[4,5,7,6,3,2,1,8]=>[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
[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[4,6,5,7,3,2,1,8]=>[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
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[3,5,7,6,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[3,5,6,7,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]=>[4,5,3,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,3,6,5,4,2,1,8]=>0000001
[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]=>[3,5,4,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,3,6,5,4,2,1,8]=>0000001
[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]=>[4,3,5,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,3,6,5,4,2,1,8]=>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
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[2,5,6,7,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[3,2,4,6,7,5,1,8]=>[7,2,3,6,5,4,1,8]=>[7,6,2,3,5,4,1,8]=>0000001
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[2,3,4,7,6,5,1,8]=>[7,2,3,6,5,4,1,8]=>[7,6,2,3,5,4,1,8]=>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
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[3,6,5,4,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>0000001
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[3,4,6,5,2,7,1,8]=>[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
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[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
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[2,5,4,6,3,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>0000001
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[3,2,6,5,4,7,1,8]=>[7,2,5,4,3,6,1,8]=>[5,4,2,3,7,6,1,8]=>0000001
[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[3,2,1,5,7,6,4,8]=>[3,2,1,7,6,5,4,8]=>[7,3,6,2,5,1,4,8]=>0000001
[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[3,2,1,6,5,7,4,8]=>[3,2,1,7,5,6,4,8]=>[7,3,2,5,6,1,4,8]=>0000001
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[3,2,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[7,3,2,5,6,1,4,8]=>0000001
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[2,3,1,6,7,5,4,8]=>[3,2,1,7,6,5,4,8]=>[7,3,6,2,5,1,4,8]=>0000001
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,5,6,4,8]=>[7,3,2,5,6,1,4,8]=>0000001
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[7,3,2,5,6,1,4,8]=>0000001
[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[1,3,2,7,6,5,4,8]=>[7,6,3,5,1,2,4,8]=>0000001
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>0000001
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[1,2,3,6,7,5,4,8]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>0000001
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[1,2,3,5,7,6,4,8]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>0000001
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,5,6,4,8]=>[5,7,6,1,2,3,4,8]=>0000001
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[5,7,6,1,2,3,4,8]=>0000001
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,7,2,6,1,5,8]=>0000001
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,7,2,6,1,5,8]=>0000001
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,2,3,1,7,6,5,8]=>[2,4,7,3,6,1,5,8]=>0000001
[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[2,4,7,3,6,1,5,8]=>0000001
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[4,2,3,1,7,6,5,8]=>[2,4,7,3,6,1,5,8]=>0000001
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[2,4,7,3,6,1,5,8]=>0000001
[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[1,2,4,3,6,7,5,8]=>[1,2,4,3,7,6,5,8]=>[7,4,6,1,2,3,5,8]=>0000001
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[3,7,2,6,1,4,5,8]=>0000001
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[3,7,2,6,1,4,5,8]=>0000001
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,7,1,6,8]=>0000001
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,7,1,6,8]=>0000001
[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[3,5,4,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,7,1,6,8]=>0000001
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[2,5,4,3,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,7,1,6,8]=>0000001
[[[.,[[.,.],[[.,.],.]]],[.,.]],.]=>[2,4,5,3,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,7,1,6,8]=>0000001
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[3,2,5,4,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[5,2,4,3,7,1,6,8]=>0000001
[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[3,4,2,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>[3,2,5,4,7,1,6,8]=>0000001
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>[3,2,5,4,7,1,6,8]=>0000001
[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[1,3,5,4,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>[5,4,3,7,1,2,6,8]=>0000001
[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[1,4,3,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]=>[3,5,4,7,1,2,6,8]=>0000001
[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[1,3,4,5,2,7,6,8]=>[1,5,3,4,2,7,6,8]=>[3,5,4,7,1,2,6,8]=>0000001
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[3,2,5,7,1,4,6,8]=>0000001
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[3,2,5,7,1,4,6,8]=>0000001
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[3,5,7,1,2,4,6,8]=>0000001
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[5,7,1,2,3,4,6,8]=>0000001
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,7,1,5,6,8]=>0000001
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[3,7,1,2,4,5,6,8]=>0000001
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[7,1,2,3,4,5,6,8]=>0000001
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[4,3,2,6,5,1,7,8]=>[6,3,2,5,4,1,7,8]=>[3,6,2,5,4,1,7,8]=>0000011
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[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
[[[.,[[.,[[.,.],[.,.]]],.]],.],.]=>[3,5,4,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[4,3,2,6,5,1,7,8]=>0000011
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[1,5,4,3,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[4,3,6,5,1,2,7,8]=>0000011
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,6,1,5,7,8]=>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
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[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
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>0000111
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>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
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[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
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[1,3,5,4,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>0000111
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[3,5,4,1,2,6,7,8]=>0000111
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[3,5,1,2,4,6,7,8]=>0000111
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>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
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[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
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>0001111
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>0001111
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>0001111
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>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
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>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 312-avoiding permutation
Description
Return a 312-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 minimal element of this 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 minimal element of this 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.
searching the database
Sorry, this map was not found in the database.