Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00067: Permutations —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]=>[2,3,1]=>[2,3,1]=>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]=>[2,3,4,1]=>[2,3,4,1]=>000 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>[4,2,3,1]=>000 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[3,2,4,1]=>[3,2,4,1]=>000 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[4,3,2,1]=>000 [.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[2,4,3,1]=>000 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,3,4,2]=>[3,1,4,2]=>000 [[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>[4,3,1,2]=>000 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[4,2,1,3]=>000 [[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[4,1,2,3]=>000 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>[2,3,1,4]=>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]=>[2,3,4,5,1]=>[2,3,4,5,1]=>0000 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[5,2,3,4,1]=>0000 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[2,4,3,5,1]=>[4,2,3,5,1]=>0000 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[5,4,2,3,1]=>0000 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[2,5,3,4,1]=>0000 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[3,2,4,5,1]=>[3,2,4,5,1]=>0000 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[3,2,5,4,1]=>[5,3,2,4,1]=>0000 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[4,3,2,5,1]=>[4,3,2,5,1]=>0000 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[4,2,3,5,1]=>[2,4,3,5,1]=>0000 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[3,5,4,2,1]=>0000 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>0000 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[5,2,4,3,1]=>0000 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[3,5,2,4,1]=>0000 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[2,3,5,4,1]=>0000 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,3,4,5,2]=>[3,1,4,5,2]=>0000 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,3,5,4,2]=>[5,3,1,4,2]=>0000 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,4,3,5,2]=>[4,3,1,5,2]=>0000 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[5,4,3,1,2]=>0000 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[5,1,3,4,2]=>0000 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[4,2,1,5,3]=>0000 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[5,4,2,1,3]=>0000 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[4,1,2,5,3]=>0000 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[5,4,1,2,3]=>0000 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[5,2,3,1,4]=>0000 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[5,3,2,1,4]=>0000 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[5,3,1,2,4]=>0000 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[5,2,1,3,4]=>0000 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[5,1,2,3,4]=>0000 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[2,3,4,1,5]=>0001 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[4,2,3,1,5]=>0001 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[3,2,4,1,5]=>[3,2,4,1,5]=>0001 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>0001 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[2,4,3,1,5]=>0001 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[3,1,4,2,5]=>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]=>[4,2,1,3,5]=>0001 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[4,1,2,3,5]=>0001 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[2,3,1,4,5]=>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]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>00000 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>00000 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>00000 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>00000 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[2,6,3,4,5,1]=>00000 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>00000 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>00000 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>00000 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[2,5,3,4,6,1]=>00000 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[6,2,4,5,3,1]=>00000 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>00000 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[6,2,5,3,4,1]=>00000 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[4,6,2,3,5,1]=>00000 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[2,3,6,4,5,1]=>00000 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>00000 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>00000 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>00000 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>00000 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[3,6,2,4,5,1]=>00000 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>00000 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>00000 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[2,4,3,5,6,1]=>00000 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[6,2,4,3,5,1]=>00000 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[3,5,4,2,6,1]=>00000 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>00000 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[5,2,4,3,6,1]=>00000 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[3,5,2,4,6,1]=>00000 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[2,3,5,4,6,1]=>00000 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[3,4,6,5,2,1]=>00000 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[6,3,5,4,2,1]=>00000 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[4,6,3,5,2,1]=>00000 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>00000 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>00000 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[4,2,6,5,3,1]=>00000 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[6,5,2,4,3,1]=>00000 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[6,3,5,2,4,1]=>00000 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[6,2,3,5,4,1]=>00000 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[3,4,6,2,5,1]=>00000 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[4,6,3,2,5,1]=>00000 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[2,6,4,3,5,1]=>00000 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[3,2,6,4,5,1]=>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]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>00000 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>00000 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>00000 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>00000 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[6,1,3,4,5,2]=>00000 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>00000 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>00000 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>00000 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[5,1,3,4,6,2]=>00000 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[6,4,1,5,3,2]=>00000 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>00000 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[6,5,1,3,4,2]=>00000 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[4,6,3,1,5,2]=>00000 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[3,1,6,4,5,2]=>00000 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>00000 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>00000 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>00000 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>00000 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[6,2,4,1,5,3]=>00000 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>00000 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>00000 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>00000 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>00000 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[6,1,4,2,5,3]=>00000 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>00000 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>00000 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>00000 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>00000 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>00000 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>00000 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>00000 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>00000 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>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]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>00000 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>00000 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>00000 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>00000 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[6,2,4,3,1,5]=>00000 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>00000 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>00000 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[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[4,6,3,1,5,2,7]=>000001 [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[3,1,6,4,5,2,7]=>000001 [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>000001 [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>000001 [[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>000001 [[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>000001 [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[6,2,4,1,5,3,7]=>000001 [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>000001 [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>000001 [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>000001 [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>000001 [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[6,1,4,2,5,3,7]=>000001 [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>000001 [[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>000001 [[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>000001 [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>000001 [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>000001 [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>000001 [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>000001 [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>000001 [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>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]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>000001 [[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>000001 [[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>000001 [[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>000001 [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[6,2,4,3,1,5,7]=>000001 [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>000001 [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>000001 [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>000001 [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>000001 [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>000001 [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>000001 [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>000001 [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>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]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>000011 [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>000011 [[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>000011 [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>000011 [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[2,5,3,4,1,6,7]=>000011 [[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>000011 [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>000011 [[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>000011 [[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>[2,4,3,5,1,6,7]=>000011 [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[3,5,4,2,1,6,7]=>000011 [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>000011 [[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[5,2,4,3,1,6,7]=>000011 [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,5,2,4,1,6,7]=>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]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>000011 [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>000011 [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>000011 [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>000011 [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[5,1,3,4,2,6,7]=>000011 [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>000011 [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>000011 [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>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]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>000011 [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>000011 [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>000011 [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>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]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>000111 [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>000111 [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>000111 [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>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]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>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]=>[4,2,1,3,5,6,7]=>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]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>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]=>[2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,1]=>0000000 [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[8,7,6,2,3,4,5,1]=>0000000 [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]=>[8,2,7,3,4,5,6,1]=>0000000 [.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[2,3,8,4,5,6,7,1]=>0000000 [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[5,4,8,7,6,3,2,1]=>[2,3,6,5,4,7,8,1]=>[6,5,2,3,4,7,8,1]=>0000000 [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[4,5,8,7,6,3,2,1]=>[2,3,6,4,5,7,8,1]=>[2,6,3,4,5,7,8,1]=>0000000 [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[5,6,4,8,7,3,2,1]=>[2,3,7,6,5,4,8,1]=>[7,6,5,2,3,4,8,1]=>0000000 [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[4,6,5,8,7,3,2,1]=>[2,3,7,4,6,5,8,1]=>[7,2,6,3,4,5,8,1]=>0000000 [.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>[2,3,7,4,5,6,8,1]=>0000000 [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[8,7,6,5,2,3,4,1]=>0000000 [.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[2,3,8,7,5,6,4,1]=>[8,2,7,5,3,6,4,1]=>0000000 [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>[2,8,5,3,6,4,7,1]=>0000000 [.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>[6,8,5,2,3,4,7,1]=>0000000 [.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>[8,6,4,2,3,5,7,1]=>0000000 [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[3,6,5,8,7,4,2,1]=>[2,4,3,7,6,5,8,1]=>[7,6,4,2,3,5,8,1]=>0000000 [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[3,7,6,5,8,4,2,1]=>[2,4,3,8,6,7,5,1]=>[8,4,6,2,3,7,5,1]=>0000000 [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[5,4,3,7,8,6,2,1]=>[2,6,4,5,3,8,7,1]=>[8,6,2,4,5,3,7,1]=>0000000 [.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[2,6,3,4,5,7,8,1]=>[2,3,6,4,5,7,8,1]=>0000000 [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[6,5,4,3,8,7,2,1]=>[2,7,4,5,6,3,8,1]=>[4,2,7,5,6,3,8,1]=>0000000 [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[4,6,5,3,8,7,2,1]=>[2,7,5,4,6,3,8,1]=>[5,7,4,2,6,3,8,1]=>0000000 [.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[5,8,7,4,2,6,3,1]=>0000000 [.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>[4,2,3,8,5,6,7,1]=>0000000 [.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[3,2,5,6,8,7,4,1]=>[4,3,2,7,5,6,8,1]=>[4,7,3,2,5,6,8,1]=>0000000 [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[2,3,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,1]=>[2,4,3,5,6,7,8,1]=>0000000 [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>[5,4,3,2,6,7,8,1]=>0000000 [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[4,3,5,2,8,7,6,1]=>[6,5,4,3,2,7,8,1]=>[6,5,4,3,2,7,8,1]=>0000000 [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[7,5,4,3,6,2,8,1]=>[5,7,4,3,6,2,8,1]=>0000000 [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[2,6,5,4,3,8,7,1]=>[7,2,4,5,6,3,8,1]=>[4,2,5,7,6,3,8,1]=>0000000 [.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[7,2,4,5,3,6,8,1]=>[4,2,5,7,3,6,8,1]=>0000000 [.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[4,5,7,6,3,2,8,1]=>[8,3,6,4,5,7,2,1]=>[3,4,8,6,5,7,2,1]=>0000000 [.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>0000000 [.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>0000000 [.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>0000000 [.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[8,4,7,6,3,5,2,1]=>0000000 [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[2,7,6,5,4,3,8,1]=>[8,2,4,5,6,7,3,1]=>[4,2,5,6,8,7,3,1]=>0000000 [.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[2,4,5,7,6,3,8,1]=>[8,2,6,4,5,7,3,1]=>[4,2,8,6,5,7,3,1]=>0000000 [.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[3,2,6,7,5,4,8,1]=>[8,3,2,5,7,6,4,1]=>[8,7,3,2,5,6,4,1]=>0000000 [.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[8,7,6,3,5,2,4,1]=>0000000 [.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[8,5,7,4,3,2,6,1]=>0000000 [.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[8,3,7,5,2,4,6,1]=>0000000 [.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[3,4,6,8,5,2,7,1]=>0000000 [.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>[6,8,5,2,4,3,7,1]=>0000000 [.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>[3,4,2,5,8,6,7,1]=>0000000 [.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[4,3,2,8,5,6,7,1]=>0000000 [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,2]=>[8,3,1,4,5,6,7,2]=>0000000 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[1,3,4,8,5,6,7,2]=>[3,1,8,4,5,6,7,2]=>0000000 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[1,3,5,4,6,7,8,2]=>[5,3,1,4,6,7,8,2]=>0000000 [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[1,4,5,7,8,6,3,2]=>[1,3,6,4,5,8,7,2]=>[8,6,1,3,4,5,7,2]=>0000000 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[1,3,5,8,7,6,4,2]=>[1,4,3,6,5,7,8,2]=>[6,4,3,1,5,7,8,2]=>0000000 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>[8,6,4,3,1,5,7,2]=>0000000 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[1,4,3,8,6,5,7,2]=>[6,8,4,3,1,5,7,2]=>0000000 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>[5,4,3,1,6,7,8,2]=>0000000 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]=>[8,7,5,4,3,1,6,2]=>0000000 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[1,5,3,4,6,7,8,2]=>[5,1,3,4,6,7,8,2]=>0000000 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[1,7,6,5,4,3,8,2]=>[1,8,4,5,6,7,3,2]=>[4,5,1,8,6,7,3,2]=>0000000 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>[1,6,7,5,4,3,8,2]=>[1,8,4,5,7,6,3,2]=>[8,4,7,1,5,6,3,2]=>0000000 [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>[1,4,7,6,5,3,8,2]=>[1,8,5,4,6,7,3,2]=>[5,8,4,1,6,7,3,2]=>0000000 [[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[1,4,6,7,5,3,8,2]=>[1,8,5,4,7,6,3,2]=>[8,5,7,4,6,1,3,2]=>0000000 [[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[1,5,4,6,7,3,8,2]=>[1,8,7,5,4,6,3,2]=>[5,8,7,4,6,1,3,2]=>0000000 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[1,3,5,6,4,7,8,2]=>[1,8,3,6,5,4,7,2]=>[6,8,5,1,3,4,7,2]=>0000000 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[1,8,4,5,3,6,7,2]=>[4,1,8,5,3,6,7,2]=>0000000 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[2,1,7,8,6,5,4,3]=>[2,1,4,5,6,8,7,3]=>[8,4,2,1,5,6,7,3]=>0000000 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>[8,2,4,1,5,6,7,3]=>0000000 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[2,1,4,7,6,5,8,3]=>[7,6,4,2,1,5,8,3]=>0000000 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[2,1,5,7,6,8,4,3]=>[2,1,4,8,5,7,6,3]=>[8,7,2,4,1,5,6,3]=>0000000 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]=>[6,8,4,2,1,5,7,3]=>0000000 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[2,1,5,4,6,7,8,3]=>[5,4,2,1,6,7,8,3]=>0000000 [[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[2,1,4,6,7,8,5,3]=>[2,1,5,4,8,6,7,3]=>[5,8,4,2,1,6,7,3]=>0000000 [[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[2,1,6,4,5,8,7,3]=>[8,6,2,4,1,5,7,3]=>0000000 [[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[2,1,5,7,6,4,8,3]=>[2,1,8,6,5,7,4,3]=>[6,8,5,7,2,1,4,3]=>0000000 [[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[8,7,6,5,4,2,1,3]=>0000000 [[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[8,7,2,5,6,1,4,3]=>0000000 [[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[8,5,7,4,2,1,6,3]=>0000000 [[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[2,1,5,4,6,7,8,3]=>[2,1,8,5,4,6,7,3]=>[5,8,2,4,1,6,7,3]=>0000000 [[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[4,2,1,8,5,6,7,3]=>0000000 [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,4,5,8,6,7,3]=>[8,1,4,2,5,6,7,3]=>0000000 [[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[1,2,5,7,8,6,4,3]=>[1,2,4,6,5,8,7,3]=>[8,6,4,1,2,5,7,3]=>0000000 [[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[1,2,6,5,8,7,4,3]=>[1,2,4,7,6,5,8,3]=>[7,6,4,1,2,5,8,3]=>0000000 [[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]=>[8,1,2,4,5,6,7,3]=>0000000 [[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[1,2,5,4,6,7,8,3]=>[5,4,1,2,6,7,8,3]=>0000000 [[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[1,2,5,4,8,6,7,3]=>[5,8,4,1,2,6,7,3]=>0000000 [[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[1,2,4,5,7,8,6,3]=>[1,2,6,4,5,8,7,3]=>[8,6,1,4,2,5,7,3]=>0000000 [[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[1,2,4,6,7,5,8,3]=>[1,2,8,4,7,6,5,3]=>[8,7,6,1,4,2,5,3]=>0000000 [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]=>[5,2,3,1,6,7,8,4]=>0000000 [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[2,3,1,6,5,7,8,4]=>[6,5,2,3,1,7,8,4]=>0000000 [[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[2,3,1,6,5,8,7,4]=>[8,6,5,2,3,1,7,4]=>0000000 [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>[8,6,2,7,3,1,5,4]=>0000000 [[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>[8,7,6,5,2,3,1,4]=>0000000 [[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[2,3,1,8,6,5,7,4]=>[6,8,5,2,3,1,7,4]=>0000000 [[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[2,3,1,7,8,6,5,4]=>[3,2,1,5,6,8,7,4]=>[8,5,3,2,1,6,7,4]=>0000000 [[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>[8,7,5,3,2,1,6,4]=>0000000 [[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[2,3,1,5,6,8,7,4]=>[3,2,1,7,5,6,8,4]=>[7,3,5,2,1,6,8,4]=>0000000 [[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,7,5,4]=>[8,6,3,7,2,1,5,4]=>0000000 [[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>[8,7,6,5,3,2,1,4]=>0000000 [[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[1,3,2,5,8,7,6,4]=>[1,3,2,6,5,7,8,4]=>[6,5,3,1,2,7,8,4]=>0000000 [[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]=>[8,7,3,5,1,2,6,4]=>0000000 [[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>[6,8,5,3,1,2,7,4]=>0000000 [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]=>[5,2,1,3,6,7,8,4]=>0000000 [[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[2,1,3,7,6,5,8,4]=>[2,1,3,8,6,7,5,4]=>[8,6,2,7,1,3,5,4]=>0000000 [[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>[8,7,6,5,2,1,3,4]=>0000000 [[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]=>[8,7,2,5,1,3,6,4]=>0000000 [[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[5,1,2,3,6,7,8,4]=>0000000 [[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>[7,6,5,1,2,3,8,4]=>0000000 [[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>[8,6,1,7,2,3,5,4]=>0000000 [[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>0000000 [[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>[8,7,1,5,2,3,6,4]=>0000000 [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>[7,6,2,3,4,1,8,5]=>0000000 [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>[8,7,6,2,3,4,1,5]=>0000000 [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[8,6,4,2,3,1,7,5]=>0000000 [[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[8,7,6,4,2,3,1,5]=>0000000 [[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[2,4,3,1,8,6,7,5]=>[8,4,6,2,3,1,7,5]=>0000000 [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>[8,7,6,3,2,4,1,5]=>0000000 [[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[8,3,6,2,4,1,7,5]=>0000000 [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>[6,4,3,2,1,7,8,5]=>0000000 [[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[8,6,4,3,2,1,7,5]=>0000000 [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>[7,6,4,3,2,1,8,5]=>0000000 [[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[8,7,6,4,3,2,1,5]=>0000000 [[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[8,4,6,3,2,1,7,5]=>0000000 [[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[8,7,6,2,4,3,1,5]=>0000000 [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[8,2,6,4,3,1,7,5]=>0000000 [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>[6,3,1,4,2,7,8,5]=>0000000 [[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>[8,7,6,3,1,4,2,5]=>0000000 [[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[8,3,6,1,4,2,7,5]=>0000000 [[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>[6,4,3,1,2,7,8,5]=>0000000 [[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,7,6,8,5]=>[7,6,4,3,1,2,8,5]=>0000000 [[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[8,7,6,4,3,1,2,5]=>0000000 [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>[6,4,2,1,3,7,8,5]=>0000000 [[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[8,6,4,2,1,3,7,5]=>0000000 [[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>[7,6,4,2,1,3,8,5]=>0000000 [[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[8,7,6,4,2,1,3,5]=>0000000 [[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[8,4,6,2,1,3,7,5]=>0000000 [[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[1,2,4,3,7,8,6,5]=>[1,2,4,3,6,8,7,5]=>[8,6,4,1,2,3,7,5]=>0000000 [[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[8,7,6,4,1,2,3,5]=>0000000 [[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>[8,7,6,2,3,1,4,5]=>0000000 [[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>[6,3,2,1,4,7,8,5]=>0000000 [[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[8,7,6,3,2,1,4,5]=>0000000 [[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[8,7,6,3,1,2,4,5]=>0000000 [[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[8,7,6,2,1,3,4,5]=>0000000 [[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>0000000 [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]=>[7,2,3,4,5,1,8,6]=>0000000 [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[2,5,4,3,1,7,8,6]=>[7,5,4,2,3,1,8,6]=>0000000 [[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[3,2,5,4,1,7,8,6]=>[7,5,3,2,4,1,8,6]=>0000000 [[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[8,7,5,4,3,2,1,6]=>0000000 [[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,7,8,6]=>[7,2,3,5,4,1,8,6]=>0000000 [[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>[8,7,4,1,2,5,3,6]=>0000000 [[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[8,7,5,1,2,3,4,6]=>0000000 [[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[2,4,3,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>[8,7,3,2,4,1,5,6]=>0000000 [[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>[7,4,3,2,1,5,8,6]=>0000000 [[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[8,7,4,3,2,1,5,6]=>0000000 [[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[1,4,3,2,5,7,8,6]=>[1,3,4,2,5,8,7,6]=>[8,7,3,1,4,2,5,6]=>0000000 [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[8,7,3,2,1,4,5,6]=>0000000 [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>[8,6,5,2,3,4,1,7]=>0000000 [[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>[8,2,6,3,4,5,1,7]=>0000000 [[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>[8,6,4,2,3,5,1,7]=>0000000 [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[2,6,4,5,3,1,8,7]=>[8,6,2,4,5,3,1,7]=>0000000 [[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[8,6,5,4,3,2,1,7]=>0000000 [[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>[8,3,6,5,4,2,1,7]=>0000000 [[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[8,6,3,5,2,4,1,7]=>0000000 [[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[8,6,4,2,1,5,3,7]=>0000000 [[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[8,6,5,4,2,1,3,7]=>0000000 [[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[8,6,2,4,1,5,3,7]=>0000000 [[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]=>[1,2,4,5,6,3,8,7]=>[8,4,1,2,5,6,3,7]=>0000000 [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]=>[2,3,1,5,6,4,8,7]=>[8,5,2,3,1,6,4,7]=>0000000 [[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[3,2,1,5,6,4,8,7]=>[2,3,1,6,5,4,8,7]=>[8,6,5,2,3,1,4,7]=>0000000 [[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[2,3,1,6,5,4,8,7]=>[3,2,1,5,6,4,8,7]=>[8,5,3,2,1,6,4,7]=>0000000 [[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[8,6,5,1,2,3,4,7]=>0000000 [[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[8,6,4,2,3,1,5,7]=>0000000 [[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[8,6,3,2,4,1,5,7]=>0000000 [[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[8,6,4,3,2,1,5,7]=>0000000 [[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[8,6,2,4,3,1,5,7]=>0000000 [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[8,6,4,2,1,3,5,7]=>0000000 [[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[8,4,2,1,5,3,6,7]=>0000000 [[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[8,5,4,2,1,3,6,7]=>0000000 [[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[8,2,3,4,1,5,6,7]=>0000000 [[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[8,4,3,2,1,5,6,7]=>0000000 [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[7,6,2,3,4,5,1,8]=>0000001 [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>[7,2,5,3,6,4,1,8]=>0000001 [[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[7,6,5,2,3,4,1,8]=>0000001 [[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[2,5,3,4,6,7,1,8]=>[2,5,3,4,6,7,1,8]=>0000001 [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>[4,2,7,5,6,3,1,8]=>0000001 [[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[3,5,6,4,7,2,1,8]=>[2,7,3,6,5,4,1,8]=>[7,6,2,5,3,4,1,8]=>0000001 [[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>0000001 [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[4,3,2,7,6,5,1,8]=>[5,3,4,2,6,7,1,8]=>[3,5,4,2,6,7,1,8]=>0000001 [[.,[[.,[[.,.],.]],[.,[.,.]]]],.]=>[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]=>[5,4,3,2,6,7,1,8]=>0000001 [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[6,3,4,5,2,7,1,8]=>[3,4,6,5,2,7,1,8]=>0000001 [[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[4,5,3,2,7,6,1,8]=>[6,3,5,4,2,7,1,8]=>[6,3,5,4,2,7,1,8]=>0000001 [[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[3,5,4,2,7,6,1,8]=>[6,4,3,5,2,7,1,8]=>[4,6,3,5,2,7,1,8]=>0000001 [[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>[4,7,6,5,3,2,1,8]=>0000001 [[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>0000001 [[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>[7,3,6,5,4,2,1,8]=>0000001 [[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>0000001 [[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>[7,6,2,3,5,4,1,8]=>0000001 [[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[7,4,3,5,2,6,1,8]=>[4,3,7,5,2,6,1,8]=>0000001 [[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>[3,5,7,4,2,6,1,8]=>0000001 [[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[2,5,4,3,6,7,1,8]=>[7,2,4,5,3,6,1,8]=>[4,2,5,7,3,6,1,8]=>0000001 [[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[1,3,6,7,5,4,2,8]=>[1,4,3,5,7,6,2,8]=>[7,4,3,1,5,6,2,8]=>0000001 [[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[1,3,5,7,6,4,2,8]=>[1,4,3,6,5,7,2,8]=>[6,4,3,1,5,7,2,8]=>0000001 [[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[2,1,4,7,6,5,3,8]=>[2,1,5,4,6,7,3,8]=>[5,4,2,1,6,7,3,8]=>0000001 [[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]=>[4,1,2,5,6,7,3,8]=>0000001 [[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[1,2,4,7,6,5,3,8]=>[1,2,5,4,6,7,3,8]=>[5,4,1,2,6,7,3,8]=>0000001 [[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[7,3,5,2,1,6,4,8]=>0000001 [[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,5,7,4,8]=>[6,5,3,1,2,7,4,8]=>0000001 [[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>0000001 [[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[7,6,2,3,4,1,5,8]=>0000001 [[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>[6,4,3,2,1,7,5,8]=>0000001 [[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[7,6,4,3,2,1,5,8]=>0000001 [[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[4,2,3,1,6,7,5,8]=>[6,2,4,3,1,7,5,8]=>0000001 [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[6,3,1,4,2,7,5,8]=>0000001 [[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[1,3,4,2,7,6,5,8]=>[1,4,3,2,6,7,5,8]=>[6,4,3,1,2,7,5,8]=>0000001 [[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[7,6,3,2,1,4,5,8]=>0000001 [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]=>[7,2,3,4,5,1,6,8]=>0000001 [[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[4,5,3,2,1,7,6,8]=>[2,3,5,4,1,7,6,8]=>[7,5,2,3,4,1,6,8]=>0000001 [[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[3,4,5,2,1,7,6,8]=>[2,5,3,4,1,7,6,8]=>[7,2,5,3,4,1,6,8]=>0000001 [[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[7,5,2,4,3,1,6,8]=>0000001 [[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[2,3,4,5,1,7,6,8]=>[5,2,3,4,1,7,6,8]=>[7,2,3,5,4,1,6,8]=>0000001 [[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>[7,3,1,4,5,2,6,8]=>0000001 [[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[7,5,3,2,1,4,6,8]=>0000001 [[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[7,5,3,1,2,4,6,8]=>0000001 [[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[7,5,1,2,3,4,6,8]=>0000001 [[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[7,4,3,2,1,5,6,8]=>0000001 [[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[7,4,3,1,2,5,6,8]=>0000001 [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[7,3,1,2,4,5,6,8]=>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 [[[.,[[.,[[.,.],.]],[.,.]]],.],.]=>[3,4,2,6,5,1,7,8]=>[5,4,3,2,6,1,7,8]=>[5,4,3,2,6,1,7,8]=>0000011 [[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,3,5,4,1,7,8]=>0000011 [[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[1,5,4,6,3,2,7,8]=>[1,3,6,5,4,2,7,8]=>[6,5,3,1,4,2,7,8]=>0000011 [[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[1,3,5,6,4,2,7,8]=>[1,4,3,6,5,2,7,8]=>[6,4,3,1,5,2,7,8]=>0000011 [[[[.,.],[[.,[.,.]],[.,.]]],.],.]=>[1,4,3,6,5,2,7,8]=>[1,5,4,3,6,2,7,8]=>[5,4,3,1,6,2,7,8]=>0000011 [[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[2,1,5,6,4,3,7,8]=>[2,1,4,6,5,3,7,8]=>[6,4,2,1,5,3,7,8]=>0000011 [[[[.,[.,.]],[[[.,.],.],.]],.],.]=>[2,1,4,5,6,3,7,8]=>[2,1,6,4,5,3,7,8]=>[6,2,4,1,5,3,7,8]=>0000011 [[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]=>[4,1,2,5,6,3,7,8]=>0000011 [[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[1,2,5,6,4,3,7,8]=>[1,2,4,6,5,3,7,8]=>[6,4,1,2,5,3,7,8]=>0000011 [[[[[.,.],.],[[[.,.],.],.]],.],.]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[6,1,4,2,5,3,7,8]=>0000011 [[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[2,3,1,6,5,4,7,8]=>[3,2,1,5,6,4,7,8]=>[5,3,2,1,6,4,7,8]=>0000011 [[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[6,4,3,2,1,5,7,8]=>0000011 [[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[6,2,4,3,1,5,7,8]=>0000011 [[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[6,4,2,1,3,5,7,8]=>0000011 [[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>0000111 [[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>0000111 [[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>0000111 [[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>0000111 [[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>0000111 [[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[2,5,4,3,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>0000111 [[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[2,4,5,3,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>0000111 [[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>0000111 [[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[2,3,5,4,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>0000111 [[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[3,5,4,2,1,6,7,8]=>0000111 [[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>0000111 [[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>0000111 [[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>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 [[[[[.,.],[[[.,.],.],.]],.],.],.]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>0000111 [[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[5,4,2,1,3,6,7,8]=>0000111 [[[[[[.,.],.],[[.,.],.]],.],.],.]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>0000111 [[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>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]=>[2,3,4,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>0001111 [[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>0001111 [[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>0001111 [[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>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]=>[1,3,4,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>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]=>[4,2,1,3,5,6,7,8]=>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]=>[2,3,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>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.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
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.